an experimental study of nanomagnets and their interactions

an experimental study ofnanomagnets and their interactionsPH.D. THESISCATHRINE FRANDSENDEPARTMENT OF PHYSICSTECHNICAL UNIVERSITY OF DENMARK

Table of contentsiTable of contentsPreface.................................................................................................................................ivAcknowledgements.............................................................................................................ivPART 11. Introduction.................................................................................................................... 11.1 Motivation................................................................................................................. 11.1.1 Nanomagnets and their properties.......................................................................11.1.2 Applications .........................................................................................................41.1.3 Interactions between nanomagnets......................................................................51.1.4 Antiferromagnets..................................................................................................71.1.5 Interactions in systems of antiferromagnetic nanoparticles ................................91.1.6 Ring-shaped magnets .........................................................................................101.2 Outline of the thesis................................................................................................ 112. Experimental methods................................................................................................. 132.1 Techniques.............................................................................................................. 132.1.1 Mössbauer spectroscopy ....................................................................................132.1.2 Neutron scattering..............................................................................................172.1.3 X-ray diffraction.................................................................................................192.1.4 Magnetization measurements.............................................................................202.1.5 Electron microscopy ..........................................................................................202.1.6 Magnetic force microscopy................................................................................202.2 Samples................................................................................................................... 212.2.1 Nanoparticles .....................................................................................................212.2.1.1 Samples and sample treatments ..................................................................222.2.2 Rings...................................................................................................................233. Antiferromagnetic nanoparticles................................................................................ 243.1 Results...................................................................................................................... 243.1.1 Thermoinduced magnetism ................................................................................243.1.2 High-frequency excitation in α-Fe 2 O 3 nanoparticles ........................................253.2 Conclusions and outlook........................................................................................ 264. Inter-particle exchange interactions in pure systems................................................ 274.1 Results and discussions.......................................................................................... 274.1.1 Effects on dynamics............................................................................................274.1.2 Direct observation of exchange coupling between α-Fe 2 O 3 nanoparticles.......304.1.3 Effects on magnetic structure of α-Fe 2 O 3 nanoparticles...................................324.1.4 Network of interacting α-Fe 2 O 3 nanoparticles..................................................33

iiNanomagnets and their interactions4.1.5 Influence of sample treatments ..........................................................................344.1.6 Magnetic assembly?...........................................................................................374.2 Conclusions............................................................................................................. 374.3 Outlook.................................................................................................................... 385. Inter-particle interactions in composites.................................................................... 395.1 Results and discussion............................................................................................ 395.1.1 Effects on dynamics and coercivity....................................................................395.1.2 A Morin-like phase transition induced in α-Fe 2 O 3 nanoparticles.....................425.1.3 Assembly of α-Fe 2 O 3 and NiO nanoparticles ....................................................475.1.4 Controlling the assembly? .................................................................................485.2 Conclusions............................................................................................................. 495.3 Outlook.................................................................................................................... 496. Ring-shaped magnets................................................................................................... 506.1 Results and discussions.......................................................................................... 506.1.1 Domain states of magnetic rings........................................................................506.1.2 Characteriztion of the twisted state ...................................................................526.1.3 Remanent hysteresis loops of the ring arrays....................................................556.1.4 Domain wall creation and annihilation: Micromagnetics.................................566.2 Conclusions............................................................................................................. 576.3 Outlook.................................................................................................................... 57References......................................................................................................................... 59Summary........................................................................................................................... 65Resumé (summary in Danish)......................................................................................... 67PART 2 - PapersReview on antiferromagnetic nanoparticles and their interactions:Paper I: S. Mørup, C. Frandsen, F. Bødker, S.N. Klausen, K. Lefmann, P.-A. Lindgårdand M.F. Hansen, Magnetic properties of nanoparticles of antiferromagnetic materials,Hyperfine Interact. 144/145 (2002) 347.Antiferromagnetic nanoparticles:Paper II: S. Mørup and C. Frandsen, Thermoinduced magnetization in nanoparticles ofantiferromagnetic materials, Phys. Rev. Lett. 92 (2004) 217201.Paper III: S.N. Klausen, K. Lefmann, P.-A. Lindgård, L. Theil Kuhn, C.R.H. Bahl, C.Frandsen, S. Mørup, B. Roessli, N. Cavadini, and C. Niedermayer, Magnetic anisotropyand quantized spin waves in hematite nanoparticles, Phys. Rev. B (in press).

Table of contentsiiiInter-particle interactions:Paper IV: C. Frandsen and S. Mørup, Inter-particle interactions in composites ofantiferromagnetic nanoparticles, J. Magn. Magn. Mater. 266 (2003) 36.Paper V: C. Frandsen, C.W. Ostenfeld, M. Xu, C.S. Jacobsen, L. Keller, K. Lefmann, andS. Mørup, Inter-particle interactions in composites of nanoparticles of ferrimagnetic (γ-Fe 2 O 3 ) and antiferromagnetic (CoO, NiO) materials, Phys. Rev. B (in press).Paper VI: C. Frandsen, H. K. Rasmussen, and S. Mørup, A Mössbauer study of themagnetization of γ-Fe 2 O 3 nanoparticles in applied fields: Influence of interaction withCoO, J. Phys.: Condens. Matter 16 (2004) 6977.Paper VII: C. Frandsen, C.R.H. Bahl, B. Lebech, K. Lefmann, L. Theil Kuhn, L. Keller,N. Hessel Andersen, M. v. Zimmermann, E. Johnson, S.N. Klausen, and S. Mørup, Selfassemblyand exchange coupling of antiferromagnetic nanoparticles, submitted (July2004).Paper VIII: C. Frandsen and S. Mørup, Spin rotation in α-Fe 2 O 3 nanoparticles byinterparticle interactions, submitted (July 2004).Paper IX: M. Xu, C.R.H. Bahl, C. Frandsen, and S. Mørup, Inter-particle interactions inagglomerates of α-Fe 2 O 3 nanoparticles: Influence of grinding, J. Colloid Interface Sci.279 (2004) 132.Ring-magnets:Paper X: F.J. Castaño, C.A. Ross, C. Frandsen, A. Eilez, D. Gil, H.I. Smith, M. Redjdal,F.B. Humphrey, Metastable states in magnetic nanorings, Phys. Rev. B 67 (2003) 184425.Paper XI: F.J. Castaño, C.A. Ross, A. Eilez, W. Jung, and C. Frandsen, Magneticconfigurations in 160-520-nm-diameter ferromagnetic rings, Phys. Rev. B 69 (2004)144421.

ivNanomagnets and their interactionsPrefaceThe present thesis is submitted in candidacy for the Ph.D. degree from the Technical University ofDenmark. It is based on experimental work carried out from September 2001 to August 2004 at* Department of Physics, Technical University of Denmark (DTU), Denmark,* Materials Research Department, Risø National Laboratory (Risø), Denmark* Swiss Spallation Neutron Source, Paul Scherrer Institute (PSI), Switzerland, and* Department of Materials Science and Engineering, Massachusetts Institute of Technology (MIT),USA.The work has been supervised by Steen Mørup, DTU, and co-supervised by Kim Lefmann, Risø.The work has been part of the framework-programme on “Nanomagnetism” (2001-2006),sponsored by the Danish Technical Research Council.The thesis consists of two parts. The first part summarizes the scientific work in which I have beenactively involved. The second part, which indeed represents the major part of the thesis work,consists of the papers, which have been written in connection to this work.The study of ‘nanomagnets and their interactions’ has been manifold with respect tocollaborators, as it appears from the author lists of the papers in Part 2, and with respect toexperimental methods. My main office has been at DTU. Sample preparations, treatments, andcharacterization, as well as studies by Mössbauer spectroscopy of nanoparticles have been carriedout at DTU on an almost daily basis. Magnetization measurements were obtained at DTU.Neutron measurements have been performed at PSI during periods of allocated beam time (> 50days in total). Electron microscopy studies have been conducted first at DTU, and later at the newfacility at Risø. Magnetic force microscopy on ring-shaped magnets has been performed at MIT,summer 2002.AcknowledgementsFirst of all, I want to thank Steen Mørup for very qualified and dedicated supervision. It has beenvery educative to work by his guidance and to learn from his profound expertise on Mössbauerspectroscopy and fine particle magnetism. Many ideas have been discussed and the work in the“Mössbauer group” has been much enjoyed. A number of students have contributed greatly to thestimulating environment in the Mössbauer group. Special thanks go to my two office matesThomas A. Anhøj and Bjarke T. Dalslet, and to Christian R.H. Bahl and Britt Rosendahl Hansen,who both have taken up the idea of studying inter-particle interactions in antiferromagneticsystems. Former student, Christopher W. Ostenfeld, is thanked for his studies, which kick-startedthe work on inter-particle interactions in nanoparticle composites. Franz Bødker is thanked for thestore of nanoparticle samples and recipes he left at DTU. Technical assistance with Mössbauermeasurements – also outside normal working hours – from Helge K. Rasmussen has been highlyappreciated. Lis Lilleballe is thanked for help with numerous sample preparations.The NANOS-group at DTU, which also includes the Mössbauer group, has been a fine forum forexperimental solid-state physics. Claus Schelde Jacobsen is thanked for making it possible torealize magnetization measurements on the composite samples. Leif Gerward is thanked forproviding access to x-ray powder diffraction.From Risø, Kim Lefmann, Stine Nyborg Klausen, Luise Theil Kuhn, Christian R.H, Bahl, BenteLebech, and Per-Anker Lindgård are thanked for a very fruitful collaboration on neutronscattering and for many enthusiastic discussions. Especially, I want to thank my co-advisor KimLefmann for helpful conversations and for good ideas emerging during our stays at PSI. Also, Iwant to thank Kim Lefmann and Stine Nyborg Klausen for introducing me to techniques of neutron

Prefacevscattering, and Bente Lebech for providing her help and expertise on the analysis of neutronpowder diffraction data.At PSI, Lukas Keller is thanked for committed help with neutron powder diffraction measurements.The SINQ, Swiss Spallation Neutron Source, Villigen, Switzerland is thanked for allocation ofbeam time to studies of magnetic nanoparticles.Christian R.H. Bahl is thanked for a great collaboration on alignment of nanoparticles. Especiallyhis high-resolution electron microscopy images and analysis have been a major contribution to thestudies of the local ordering of nanoparticles. Erik Johnson is thanked for offering assess to thenewly established high-resolution microscope at Risø. Erik Johnson and Luise Theil Kuhn areboth thanked for help with imaging. Flemming Grumsen is thanked for images taken at themicroscope at DTU.Niels Hessel Andersen and Martin von Zimmermann are thanked for obtaining HES-XRDmeasurements on interacting nanoparticles. Niels Hessel Andersen is thanked for inspiringdiscussions. HASYLAB at DESY, Hamburg, Germany is thanked for access to studying alignmentof nanoparticles.Caroline A. Ross (MIT) is sincerely thanked for giving me the opportunity to work in her group onthe interesting ring magnet project, which she and Fernando J. Castaño had just initiated. It was avery enjoyable and rewarding stay. She and Fernando J. Castaño, who prepared the smallest andmost perfect rings to date, are thanked for a true enthusiasm for the work and fruitfulcollaboration. Yaowu Hao is thanked for help with initiating the MFM measurements. Henry I.Smith and his group are thanked for access to facilities.Since the time of my master-project at Copenhagen University, I have had an interest inunderstanding the properties of magnetic nanoparticles in geological systems, especially inrevealing the origin of the magnetization in certain rocks. It has been an “on-the-side” projectduring the last three years and results of it have not been included in the thesis. Thanks still go toJens Martin Knudsen, Morten Bo Madsen, Susan Stipp, Suzanne A. McEnroe, Peter Robinson, andLasse Seidelin Bendtsen for the inspiring collaboration. Line Groth-Andersen is thanked for helppreparing samples.A number of people have meant a lot to me over the last years, though they have not been involvedin the ”nano-magnetism” project. The CAMP-group is warmly thanked for kindly “adopting” meand providing a pleasant social environment together with excellent secretary- and it-support.Thanks also to Ole Mogensen and Anders Reves Dinesen for pc-assistance. Journalist at DTU,Michael Strangholt, is thanked for helping bringing the results of thermoinduced magnetism to theDanish news media.Stipend and travel support from the Danish Technical Research Council (via the“Nanomagnetism” framework programme) and from the Danish Natural Science ResearchCouncil (via “DANSCATT”) have been highly appreciated.Last but not least, I am indebted to my dear Jesper for his understanding and support, for hismany fine thoughts on contemporary physics over the years and for valuable comments.Cathrine FrandsenAugust 31, 2004.

Part 1

Chapter 1: Introduction 11. Introduction1.1 Motivation1.1.1 Nanomagnets and their propertiesNanomagnets are magnets with dimensions ranging from a few nanometers to somehundred nanometers. They come in various forms, including the types which are studied inthis thesis: nanoparticles and lithographically patterned rings of magnetic materials (Fig.1.1).(a)(b)500 nmFig. 1.1. Images of the types of nanomagnets studied in this thesis. (a) Highresolutionelectron microscopy image of synthetic magnetic nanoparticles of α-Fe 2 O 3 . (b)Scanning electron microscopy image of lithographically patterned ring-shaped nanomagnets of Co.Nanomagnets are interesting objects because their magnetic properties often differsignificantly from those of bulk materials. It is a question of fundamental character in solidstate physics to ask what happens to the properties of materials, when reducing theirdimensions. Understanding the magnetic properties of nanomagnets, involving both thestatic and dynamic properties, is considered a major challenge [Dormann and Fiorani,1992; Dormann et al., 1997; Natali et al., 2002].With decreasing size, the magnets sustain single-domain magnetizations. Moreover, withfurther size reduction and the relative number of surface atoms increasing, basic magneticproperties are subject to changes. For instance, due to the relative increase in missingexchange bonds at the surface, the magnetic ordering temperature (the Curie or Néeltemperature, T C and T N , respectively) may decrease [Ambrose and Chien, 1996, Klausenet al., 2002]. Also, the magnetic structure may change [Coey, 1971; Kodama et al., 1997;Kündig et al., 1966]. For example, at the surface, magnetic ions may be frustrated due tomissing exchange bonds and this may give rise to spin canting at the surface [Coey, 1971](Fig. 1.2). Spin canting may also occur inside magnets due to magnetic defects (e.g. due tomissing magnetic ions) in the interior. Differences in the crystalline environment at thesurface compared to that of bulk, e.g. from dangling chemical bonds or from surfacereconstruction, may affect the crystal field and thus the magnetic anisotropy of the surfaceions. This can give rise to an additional “surface anisotropy”, which may effect the easydirection of (sublattice) magnetizations in nanomagnets.

2 Nanomagnets and their interactions – Part 1Fig. 1.2. Schematic illustration of a magnet with an overall magnetization (shownby the large arrow) and spin canting at the surface (shown by the small arrows).The magnetic anisotropy of a nanomagnet is often assumed uniaxial with the anisotropyenergy given asE = KVsin 2 θ, (Eq. 1.1)where K is the magnetic anisotropy constant, V is the volume of the magnet, and θ is theangle between the easy axis and the (sublattice) magnetization direction (see Fig. 1.3).KVEeasyaxisθ(a)0π2πθ(b)Fig. 1.3. Magnetic anisotropy energy of magnet with uniaxial anisotropy given byEq. 1.1. (a) Energy as a function of θ. (b) θ is the angle between the magnetization (indicated byan arrow) and the easy axis.For nanomagnets the thermal energy, k B T, may be sufficient to excite the (sublattice)magnetization such that it fluctuates coherently in the anisotropy field within the particles.For small excitations (k B T 0, attemperatures well below T C or T N is significant, with the energy being proportional to(q sw ) 2 and q SW =π/d being the lowest possible excitation, where d is the diameter of themagnet.

Chapter 1: Introduction 3The different q sw = 0 precession states have transition energies of ε 0 . From the equations ofmotions for the magnetic sublattices, it can be derived that the value of ε 0 is proportionalto the anisotropy in a ferro- or ferrimagnet, while in an antiferromagnet it is proportionalto the square root of the anisotropy [Morrish, 1966; Hansen et al., 1997; Lefmann et al.,2001]. At low temperatures, the precession states with small precession angles are mostpopulated, but with increasing temperature, states with larger precession angles becomeincreasingly populated.ε 0ε0Fig. 1.4. Illustration of collective magnetic excitations close to an energy minimum.For larger excitations (k B T KV), the (sublattice) magnetization may surmount theenergy barrier between the easy directions; this is known as superparamagnetism [Néel,1949] (Fig. 1.5). Superparamagnetic relaxation between the two easy directions willfollow the Néel-Brown law [Néel, 1949; Brown, 1963], and the relaxation time (i.e.average time between the transition between the minima) is given byτ = τ 0 exp(KV/k B T), (Eq. 1.2)where τ 0 typically is about 10 -12 -10 -9 s in nanoparticles. As an example, we see that formagnets with a volume of (~5 nm) 3 and an anisotropy of ~10 5 J/m 3 (typical for γ-Fe 2 O 3 ),the relaxation time will be about a nanosecond at room temperature. Due to theexponential dependence of τ on V, magnets with same K but volumes of (~ 20 nm) 3 havea relaxation time of more than a billion years.It is possible that the magnetization of nanomagnets may also tunnel macroscopicallybetween the easy directions [Chudnowsky and Günther, 1988]. In this case, the relaxationis independent of temperature. This macroscopic quantum tunnelling may be dominant atvery low temperatures.Fig. 1.5. Illustration of superparamagnetic relaxation between energy minima.

4 Nanomagnets and their interactions – Part 11.1.2 ApplicationsThe study of nanomagnets is of relevance not only for fundamental studies but also forapplied physics, for instance for technological applications. Data storage on today’s harddisks is based on magnetic recording, where areas of particles are magnetized to representbits of either “0” or “1” (Fig. 1.6a). In the future, single magnets may represent one bit(Fig. 1.6b). The ability to fabricate nanomagnets and to control their properties, e.g. tosuppress superparamagnetism, has been a major factor in achieving the continuouslyincreasing densities of data storage [Menon and Gupta, 1999].(a)500 nm(b)Fig. 1.6. Examples of magnetic data storage. (a) Magnetic force microscopy imageof a piece of hard disk, where areas of γ-Fe 2 O 3 particles are magnetized in different directions.From [DI, 2001]. (b) Scanning electron micrograph of Ni-pillars representing single bits. From[Ross et al., 1999].Understanding the properties of nanomagnets is also of importance for understanding e.g.geological systems, see e.g. [O’Reilly, 1984; Dunlop and Özdemir, 1997; Robinson et al.,2002]. Magnetic grains in the crust of the Earth carry information acquired during theirformation on directions and stabilities of ancient planetary magnetic fields. These magnetshave provided us with evidence of plate tectonics and polar reversals [Vine and Matthews,1963] (see Fig. 1.7). Moreover, in many biological systems, nanomagnets are importantconstituents [Dickson and Frankel, 1992; Pankhurst et al., 2003]. Further, magneticnanoparticles are used for medical treatments, e.g. as contrast-makers in magneticresonance imaging. Stable suspensions of magnetic nanoparticles (ferrofluids) are used inplaces where it is convenient to control the position of a liquid by a magnetic force, e.g. inloud speakers, for lubricating oil between moving parts, in vacuum seals, and in devicesfor space technology.Fig. 1.7. Magnetic stripes of the mid-ocean ridge revealing both polar reversals andseafloor spreading (plate tectonics). From [Skinner and Porter, 1987].

Chapter 1: Introduction 51.1.3 Interactions between nanomagnetsIn systems of nanomagnets, one of the parameters, which is of importance for theproperties of the magnets, is the magnetic interaction between magnets in close proximity.Both the magnetic dipole interaction and exchange interaction can severely influence theproperties, with dipole interactions being mediated by the stray fields of the magnets (Fig.1.8a), and exchange interactions being caused by exchange coupling between surfaceatoms of neighbouring magnets (Fig. 1.8b). The exchange interaction betweennanomagnets is very short ranged (as it falls off exponentially) compared to the dipoleinteraction (which falls off as r -3 , where r is the distance between the magnets), but, on alocal scale, the exchange coupling can be significantly stronger.(a)Fig. 1.8. Schematic illustration of magnetic interaction between magnets. (a) Dipoleinteraction. (b) Exchange interaction.The dipole interactions between nanomagnets have been found to lead to a number ofinteresting effects, e.g. in dilute frozen suspension of particles, weak dipole interactionslead to faster superparamagnetic relaxation [Mørup and Tronc, 1994] and with increasinginteraction to slower relaxation [Djurberg et al., 1997; Jonsson et al., 1998], or even toformation of a spin-glass-like state [Luo et al., 1991; Djurberg et al., 1997; Jonsson et al.,1998] or domain-like state [Puntes et al., 2004]. The dipole interaction between adjacentnanomagnets can also lead to a larger distribution in switching fields, which is inexpedientfor applications, such as data storage, where uniformity is desired [Natali et al., 2002].Interestingly, dipole interactions have also been found to lead to ordered arrangement ofparticles [Ghazali and Lévy, 2003; Tripp et al., 2003; Butter et al., 2003], which mightapply to creating nanostructured devices using magnetic nanoparticles as building blocks(see e.g. Fig. 1.13c).Exchange interaction between nanomagnets has also been found to lead to a significantinfluence on their magnetic properties. One of the most known effects of exchangecoupling between different nanomagnets is “exchange bias” where for instance couplingof a ferromagnet to an antiferromagnet can pin the magnetization of the ferromagnet andlead to increased coercivity and shifted hysteresis loop (see Fig. 1.9). This effect was firstreported for core-shell system of surface oxidized Co-particles [Meiklejohn and Bean,1956]. Later, many studies, especially on composite thin film systems, have revealed theexistence of exchange bias, and the coupling between different materials has been studiedin great detail. Reviews are found in [Berkowitz and Takano, 1999; Nogues and Schuller,1999]. The exchange bias effect has been used extensively in magneto-resistance basedspin valves in hard disc read heads. Here the principle is that a pinned and a non-pinnedferromagnet have different switching fields, thus for the intermediate fields, where themagnets have different directions of magnetization, the resistance will be much larger thanfor parallel magnetizations. New memory devices, such as magnetic RAM units(MRAMs), are also being developed as patterned multi-layered magnetic structures basedon magneto-resistance effects [IBM, 2001], where exchange bias may play a role.(b)

6 Nanomagnets and their interactions – Part 1Fig. 1.9. Principle of exchange bias. (i) When cooling a ferromagnet (FM) and anantiferromagnet (AFM) with T C > T N towards T N in an applied field, the FM will be magnetizedparallel to the field. (ii) Cooling below T N , the magnetization of the antiferromagnet (AFM) will beoriented after the FM due to exchange coupling at the interface between the magnets. (iii) If theanisotropy of the AFM is sufficiently large, then the spins of the AFM remains unaffected whenthe applied field is reversed, and they will exert a microscopic torque on the spins of theferromagnet, trying to keep them in their field-cooled position. (iv) Due to this, a larger field isneeded to reverse the magnetization of the FM, (v) but a smaller field is needed to return it to itsfield-cooled position. Thus, the hysteresis loop is shifted towards negative fields. Typically,exchange biased systems also show an increased coercivity. From [Nogues and Schuller, 1999].Another interesting phenomenon due to exchange coupling, which has been observed incomposite thin film systems of CoO/Fe 3 O 4 and NiO/Fe 3 O 4 , is an increase in the Néeltemperature with decreasing layer thickness of CoO and NiO [Borchers et al., 1995; vander Zaag et al., 2001] rather than a decrease in ordering temperature as often found fornon-coupled thin films [Ambrose and Chien, 1996]. The ordering temperature of Fe 3 O 4 ishigher than that of CoO and NiO, and a mean field-theory model explains the increase inNéel temperature as being due to the different ordering temperatures of the two exchangecoupled materials approaching one another [Borchers et al., 1995].In this thesis, most of the work deals with systems of magnets, which are interestingbecause dominating dipole interactions are absent. This applies to particles ofantiferromagnetic materials, which have insignificant dipole fields, allowing for studyingsolely the exchange coupling between the particles, and it is also the case for rings offerromagnetic materials which can sustain flux closed states. These specific systems aredescribed below.

Chapter 1: Introduction 71.1.4 AntiferromagnetsAntiferromagnets can be described by two similar magnetic sublattices, in which themoments of the magnetic ions are coupled parallel within the same sublattice, butantiparallel to the moments in the other sublattice. This “compensation of moments” givesantiferromagnetic materials the property that, internally, they are magnetically ordered but“on the outside” they appear non-magnetic. For the reason of being non-magnetic,antiferromagnets could, at first sight, appear completely useless and non-interesting, butthis is not the case. Research on bulk antiferromagnets is of relevance for e.g.understanding high-temperature superconductors and colossal magneto-resistance. Nanoantiferromagnetsare widely used e.g. in spin valves as mentioned in Section 1.1.3.Numerous studies, including those presented in Chapter 3, also show that when thedimensions of the antiferromagnetic materials are reduced to some nanometers, thematerials have new intriguing properties [Néel, 1961; Kündig, 1966; Barbara andChudnowsky, 1990; Kodama et al., 1997; Harris et al., 1999]; for instance they may evenbecome magnetic due to uncompensated spins [Néel, 1961].Examples of antiferromagnetic materials are NiO, CoO, Co 3 O 4 , MnO, Cu 2 O, FeO, α-FeOOH and α-Fe 2 O 3 . In this thesis, a number of experiments have been performed onnanoparticles of NiO, CoO and α-Fe 2 O 3 , and a brief introduction to the magnetic structureof these materials follows below.[001][010][100]Fig. 1.10. The magnetic structure of cubic bulk metal(2+)-oxides like NiO and CoO.From [Shull et al., 1951]. The direction of the sublattice magnetization may vary between theoxides and between samples.NiO and CoOThe antiferromagnetic metal(2+)-oxides like NiO and CoO have face-centred cubicstructures with cubic close-packing of the oxygen layers along the [111] direction [Shull etal., 1951]. Below T N , which is 525 K for bulk NiO and 293 K for bulk CoO, the cationsorder such that the magnetic coupling within the (111) planes is ferromagnetic, and thereis an antiferromagnetic modulation of the magnetic structure is along the [111] direction.The magnetic structure is illustrated on Fig 1.10. The direction of the sublatticemagnetization varies between the metal(2+)oxides and apparently also between differentsamples of the same metal(2+)oxides as recorded from the varying directions given in theliterature. The magnetic structure of NiO nanoparticles has been suggested to be morecomplicated than a two-sublattice structure shown in Fig. 1.10, i.e. a structure with eightsublattices is a more appropriate description [Kodama et al., 1997]. We will for simplicitykeep the two-sublattice structure of the NiO nanoparticles in this treatise.

8 Nanomagnets and their interactions – Part 1α-Fe 2 O 3The crystal structure of α-Fe 2 O 3 (hematite) can be described in terms of alternating ironand oxygen layers stacked along the [001] axis of the hexagonal unit cell (a review on α-Fe 2 O 3 is given in [Morrish, 1994]). The Fe-layers order antiferromagnetically below T N ,which is ~ 955 K in bulk, such that the magnetization directions of neighbouring Fe-layersbecome antiparallel. The direction of the sublattice magnetization of α-Fe 2 O 3 is confinedto lie within the (001) plane (see Fig. 1.11a) above the temperature of the Morin transition,T M . In bulk α-Fe 2 O 3 , T M ~263 K. Between T N and T M , the antiferromagnetic structure isslightly canted away from the [001] axis by about 0.1 degrees. At T M , the sublatticemagnetization directions rotate 90 degrees out of the (001) plane, such that their directionsbecome parallel to the [001] axis and perfectly antiparallel to each other (Fig. 1.11b). Thetransition temperature decreases with decreasing particle size and it is found that there isno Morin transition above liquid helium temperature in α-Fe 2 O 3 particles with diameterssmaller than ~20 nm. Therefore, in nanoparticles of α-Fe 2 O 3 , the sublattice magnetizationsshould lie within the (001) plane at all temperatures below their Néel temperature. Theabsence of a Morin transition in α-Fe 2 O 3 nanoparticles is an example of the magneticstructure in nanoparticles being different from that in bulk. It has been suggested that thesuppression is caused by additional surface stress [Morrish, 1994] or surface anisotropy innanoparticles [Néel, 1954].[001](a)(b)Fig. 1.11. The magnetic structure of α-Fe 2 O 3 (a) above the Morin transition and (b)below the Morin transition. From [Lebech and Sikora, 2004].In nanoparticles of α-Fe 2 O 3 , the (001) plane is the plane of low anisotropy and thereforerelaxation of the spin structure begins within this plane until the temperature is highenough to cause a more isotropic relaxation. The anisotropy energy within the (001) planemay be described by [Bødker et al., 2000a]E = K Bu Vsin 2 φ, (Eq. 1.3)

Chapter 1: Introduction 9where K Bu is the in-plane anisotropy constant, and φ is the angle between an in-plane easyaxis and the in-plane direction of the sublattice magnetization. The out-of-plane anisotropyenergy may be described as [Morrish, 1994]E = K 1 Vsin 2 θ, (Eq. 1.4)where K 1 is the out-of-plane anisotropy constant and θ represents the angle between thesublattice magnetization and the [001] axis of α-Fe 2 O 3 . In accordance with the absence ofthe Morin transition in nanoparticles of α-Fe 2 O 3 , K 1 < 0 and K Bu

10 Nanomagnets and their interactions – Part 1The microstructure of the samples of agglomerated nanoparticles is expected to beimportant for the magnetic properties. Studies of e.g. TiO 2 nanoparticles revealed thatparticles under hydrothermal conditions (100-250 °C, 15-40 bar) may assemble withoriented attachment [Lee Penn and Banfield, 1998; Lee Penn and Banfield, 1999] (Fig.1.12). In case magnetic nanoparticles also assemble with preferred orientation, it is likelyto have a significant influence on their magnetic properties.Fig. 1.12. Electron microscopy image showing oriented attachment of TiO 2nanoparticles. From [Lee Penn and Banfield, 1999].A few recent studies have addressed the issue of the effects of exchange interactions incomposite systems of nanoparticles, where the individual components equals (~ 10 nm) 3[Sort et al., 1999; Zeng et al., 2002; Anhøj et al., 2004]. It has been shown hownanoparticles of FePt and Fe 3 O 4 , which are self-assembled into a 3-D structure, can beoxidized and annealed together as FePt and Fe 3 Pt, creating a significant increase incoercivity; a principle which can be used to create very strong magnets [Zeng et al., 2002].Studies of particles of Co and NiO or FeS, and of Fe and FeMn, ball-milled together havealso shown effects of exchange coupling [Sort et al., 1999; Anhøj et al., 2004]. Growingmagnetic materials layer by layer is a tedious way to make e.g. permanent magnets.Instead, if effects of strong exchange interactions can be achieved by mixingnanoparticles, this may be an efficient way to create new magnetic materials.1.1.6 Ring-shaped magnetsOne of the difficulties in the development of high-density magnetic data storage andmagneto-resistive memory devices is to reduce the cross-talk, in form of dipoleinteractions, between adjacent elements, which may influence the performance of the bitse.g. by leading to a distribution in and non-reproducibility of switching fields [Natali etal., 2002]. A way to get around the problem of dipole interactions between the magneticelements would be to use ring-shaped magnets, which could be magnetised clockwise orcounter-clockwise, such that all flux lines are enclosed in the rings, e.g. [Rothman et al.,2001]. Ring magnets of sub-millimetre dimensions were already used in the 1950’s tostore data (see Fig. 1.13a). Today, nano-scale lithography may lead to a renaissance ofring magnets, but on a much smaller scale (examples are shown in Fig. 1.13b).Lithography also allows for making layered ring structures e.g. for MRAMs [Zhu et al.,2000]. Potentially, even tiny self-assembled nanoparticles (Fig. 1.13c) may eventually finduse as suggested in [Tripp et al., 2003].

Chapter 1: Introduction 111 mm25050(a)(b)(c)Fig. 1.13. Ring-shaped magnets. (a) Rings threaded on thin wires used to write themagnetization of the individual rings. From [Parkin, 2003]. (b) Scanning electron micrograph oflithographically patterned rings prepared by F.J. Castaño and co-workers at MIT. These rings aresimilar to those studied in Chapter 6. (c) Electron micrograph (upper image) shows nanoscalestructures of Co particles, which have assembled due to dipole interactions; lower left imageshows close-up of a ring-shaped structure. The lower right image in (c) shows an electronholography image of the “flux-closed” magnetic state in the self-assembled ring (from [Tripp etal., 2003]).In order to make use of lithographically patterned rings, it is important to reveal theirmagnetic domain states, and to quantify the switching fields between states for rings ofdifferent dimensions. Studies on lithographically patterned rings by Rothman et al. [2001]and Li et al. [2001], using the magneto-optical Kerr effect (MOKE) and magnetic forcemicroscopy (MFM), have shown that the flux-closed “vortex” state existed in thin-films ofmicron-sized rings, and by applying a saturating in-plane field, they showed that it waspossible to switch between the vortex state and a bi-domain state, the so-called “onion”state, where the magnetization runs like the leaves of an onion forming domain walls atopposite sides of the rings. Both the vortex and the onion state were found to exist atremanence. Recent studies have provided information on switching fields for differentdomain states. A switching field phase diagram is given e.g. by Yoo et al. [2003].Rings have also been found to be very interesting objects for more fundamental studies,e.g. for investigating pinning of domain walls [Klaüi et al., 2003a] and current-induceddomain wall movements [Klaüi et al., 2003b, Tatara and Kohno, 2004].1.2 Outline of the thesisThis thesis deals with experimental studies on the magnetic properties of nanomagnets(particles and rings), such as their dynamics, coercivity, magnetic spin structure, andmagnetic domain structure, and it deals with the influence on the properties due to interparticleinteractions. The magnetic properties of antiferromagnetic nanoparticles havebeen studied by Mössbauer spectroscopy, inelastic neutron scattering, and magnetizationmeasurements. The use of these techniques has revealed novel aspects of the properties ofantiferromagnetic nanoparticles, and moreover they have showed that samples ofagglomerated nanoparticles are strongly influenced by inter-particle exchange interactions.

12 Nanomagnets and their interactions – Part 1In order to elucidate in further detail such exchange coupling between the particles, wewere looking for other techniques. Neutron powder diffraction turned out to be a keytechnique, and together with high-resolution electron microscopy and high-energysynchrotron x-ray diffraction it was possible to reveal both magnetic and structuralcorrelation between the particles. The resolution of magnetic force microscopy is too lowfor studying antiferromagnetic nanoparticles, but it has been used successfully to study themagnetic domain states of nanorings.Chapter 2 gives an overview of the experimental methods applied. Chapters 3-5 treatresults obtained on nanoparticles. Chapter 3 is devoted to studies, which have revealedinformation about particles of antiferromagnetic materials (Papers II and III), whileChapters 4 and 5 treat results obtained on respectively pure and composite systems ofantiferromagnetic nanoparticles, which are dominated by exchange interactions (PapersIV-IX). Chapter 6 deals with results from studies on ring magnets (Papers X and XI).

Chapter 2: Experimental methods 132. Experimental methods2.1 TechniquesThe following sections give brief introductions to the techniques used in this work. Theprinciples are described in much more detail in numerous text books and articles, e.g.[Greenwood and Gibb, 1971; Kopcewicz, 1994; Mørup, 1994] (Mössbauer spectroscopy),[Pynn, 1990; Squires, 1978] (neutron scattering), [Williams and Carter, 1996] (electronmicroscopy), and [Grütter et al., 1992; Wiesendanger, 1994] (scanning probe microscopyincluding atomic and magnetic force microscopy).2.1.1 Mössbauer spectroscopyMössbauer spectroscopy allows for studies of static and dynamic properties of a magneticcompound by detecting the electric and magnetic hyperfine interactions between thenucleus of a studied Mössbauer isotope, here 57 Fe, and its electronic environment. 57 Feconstitutes ~2 % of natural Fe.The principle of 57 Fe-Mössbauer spectroscopy is to obtain resonant absorption between theground state and the first excited state of the nucleus by a gamma-ray with a well-definedenergy similar to the excitation energy. For 57 Fe-Mössbauer spectroscopy, the gamma rayis typically produced from the decay of an excited Fe-nucleus, which is produced fromdecay of 57 Co. The hyperfine interactions give rise to splitting and shifts of the groundstate and excited states of the nuclei. In order for the energy of the gamma-ray, E γ, toprecisely match the energy gaps between the ground states and excited states of thenucleus, the source of the gamma rays is moved forth and back (see Fig. 2.1) whereby itsenergy is Doppler shifted by the amount ∆E. The number of absorption lines and theirpositions in the spectra thus provide information on the environment of the nucleus. It isconvention to plot the absorption directly as a function of the velocity, v, by which theenergy of the gamma-ray of the source is Doppler shifted (v=(∆E/E γ )c; c being thevelocity of light).Mössbauerspectrumsourceγ•sampledetectorabsorptionvelocityFig. 2.1. Schematic illustration of Mössbauer spectroscopy.There are three hyperfine interactions which can be studied by Mössbauer spectroscopy:The electric monopole interaction, the magnetic hyperfine interaction, and the electricquadrupole interaction.

14 Nanomagnets and their interactions – Part 1The electric monopole interaction originates from the Coulomb interactions between thenucleus and the electrons with a certain probability of being at the nuclear site. Thisinteraction causes shifts of the energy levels in the nucleus and thus a shift in absorptionenergy, which is seen as an overall shift of the spectrum. This effect is known as the“isomer shift” and provides information on the spin state and valency of Fe-ions.The hyperfine interactions, which are of most interest for the present work, are themagnetic hyperfine interaction and the electric quadrupole interaction.The magnetic hyperfine interaction is due to the interaction between the magnetic momentof the Fe-nucleus and the magnetic field at the site of the nucleus. This is the nuclearZeeman effect and it gives rise to splitting of the energy levels in the nuclei. In an 57 Fenucleus,where the ground state has nuclear spin I=1/2, and the first excited state has spinI=3/2, the splittings are such that there are 6 possible transitions between the excited stateand the ground state (a photon may change its spin quantum number by 0, and ±1), thussix absorption lines appear in the Mössbauer spectra (Fig. 2.2). In a magnetically orderedcompound, e.g. a ferromagnet or an antiferromagnet, the spin of the electrons is the majorcontributor to the field. The splitting is proportional in size to the hyperfine field, B hf .For a magnetic ordered material with one type of Fe-site environment, the Mössbauerspectrum consists of a six-line spectrum, a sextet. For random orientation of grains in apowder, the relative absorption areas of the six lines are 3:2:1:1:2:3 (see Fig. 2.2).The electric quadrupole interaction originates from the interaction between the electricquadrupole moment of nuclei and the electric field gradient acting at the nuclei e.g. from anon-spherical electronic charge distribution or surrounding ligands in a non-cubicstructure. For magnetically ordered compounds, the quadrupole interaction is aperturbation to the magnetic hyperfine interaction and it is seen in the magnetically splitspectra as a shift, ε, of the lines (see Fig. 2.2). In case of a compound for which thespectrum is not magnetically split the quadrupole interaction can split the excited state ofthe Fe-nucleus giving rise to a doublet in the spectra.For cubic materials such as NiO, CoO and γ-Fe 2 O 3 , the quadrupole interaction is zero. Forα-Fe 2 O 3 , which is hexagonal, the quadrupole shift is non-zero. The quadrupole shift, ε, ofα-Fe 2 O 3 is correlated to the angle θ between the direction of the sublattice magnetizationand the [001] direction byε = ε 0 (3cos 2 θ-1)/2, (Eq. 2.1)where ε 0 =0.200 mm/s. Above the Morin transition, where the sublattice magnetizations liewithin the (001) plane, ε = -0.100 mm/s while it is 0.200 mm/s below the Morin transition.The difference in line positions for bulk α-Fe 2 O 3 can be seen in Fig. 2.3.

Chapter 2: Experimental methods 15εεεεεεεεεεFig. 2.2. The magnetic hyperfine splitting and the combined magnetic andquadrupole interaction. Adapted from [Mørup, 1994].Relative absorption300 K20 K-12 -8 -4 0 4 8 12Velocity (mm/s)Fig. 2.3. Mössbauer spectra of bulk α-Fe 2 O 3 above and below the Morin transition.

16 Nanomagnets and their interactions – Part 1Sometimes the magnetic field at the nucleus fluctuates, such that the nucleus experiencesdifferent hyperfine fields during its lifetime. In the case where the time scale for thefluctuations are long compared to the time scale of Mössbauer spectroscopy, τ M ~10 -8 s,which is determined by the nuclear Larmor precession time, the spectrum will have wellresolved lines. If the time scale for the fluctuations is comparable to τ M , the lines willbroaden and the spectra will be rather complex. If the time scale for the fluctuations isshort compared to τ M , then the time average of the hyperfine field acting on the nucleuscan be replaced by an effective field. If this average is negligible, i.e. ~ 0, then thespectrum collapses to a singlet or a doublet, depending on whether the quadrupoleinteraction is zero or not.In nanoparticles, where collective magnetic excitations are prevalent (k B T

Chapter 2: Experimental methods 17SampleSpectrumStablemagnetizationCollectivemagneticexcitationsSuperparamagnetismdynamics.Fig. 2.4. Schematic illustration of influence on Mössbauer spectra from magnetic2.1.2 Neutron scatteringNeutron scattering allows for studies of structural and dynamical magnetic properties. Inthat respect, it may appear to resemble Mössbauer spectroscopy, but since the principles ofthe techniques are completely different, it allows for complementary studies.In a neutron scattering experiment, an incoming neutron with momentum ħk may bescattered by the nuclei of the sample as well as by the magnetic field from the spins in thesample, such that an out-going neutron has momentum hk’. Hereby the momentum andenergy of the neutron change by the amounts ħq=ħ(k-k′) and ε= ħ 2 (k 2 -(k′) 2 )/2m,respectively. 1 The concept of neutron scattering is to measure the intensity of the scatteredneutrons as a function of q and ε. Two types of neutron scattering will be considered here:neutron powder diffraction and inelastic neutron scattering.qk’elastic scattering (│k│= │k’│)kFig. 2.5. Incoming neutrons with wave vector k, elastically scattered by the sample.Outgoing neutrons have wave vector k’.In neutron powder diffraction (NPD) (i.e. elastic scattering, where│k│=│k’│, on amicro-crystalline powder), the atomic lattices of the crystals will Bragg scatter theneutrons giving rise to diffraction for the scattering vectors q=k-k’=τ. τ is a reciprocallattice vector (│τ │=2π/d, where d is the distance between lattice planes). This is similarto x-ray powder diffraction, but since neutrons have a magnetic moment which can1 Note: In relation to neutron scattering experiments, ε denotes the energy, while in connection withMössbauer studies, ε represent the quadrupole shift. For consistency with the Papers, these quantities havenot been relabelled. It should be clear from the text which quantity we are dealing with.

18 Nanomagnets and their interactions – Part 1interact with magnetic fields from the spins in magnetic compounds, neutron powderdiffraction can reveal the magnetic structure in addition to the crystalline structure. Forferromagnetic structures the magnetic peaks occur at the same scattering vectors as thestructural reflections, but for an antiferromagnet, where the periodicity of the magneticstructure is different from the crystal structure, additional reflections are observed. Due tothe anisotropic nature of the magnetic dipole interaction between neutrons and themagnetic field in the sample, the magnetic scattering is anisotropic and the intensity of amagnetic scattering is proportional to the component of the magnetic momentperpendicular to the scattering vector q. In α-Fe 2 O 3 , this gives rise to a change inintensities for the magnetic reflections at the Morin transitions (see e.g. Fig. 2.6, where thescattering vector from the (003) plane vanishes as the sublattice magnetizations are rotatedout of the (001) plane at low temperature). With increasing temperature the intensities ofthe magnetic peaks decreases, as the magnetic order parameter is reduced, and theydisappear at the magnetic ordering temperature (i.e. at T N or T C ).300 KIntensity(003)(101)(10-2)20 K(104)1.0 1.5 2.0 2.5Scattering vector (Å -1 )Fig. 2.6. Neutron powder diffraction data of bulk α-Fe 2 O 3 above and below theMorin transition. The magnetic reflections (003) and (101) change intensity due to the spinrotation. The (10-2) and (104) reflections are structural.For nanoparticles with sizes of ~10 nm, a broadening of the structural and magnetic Braggreflections typically occur due to a short correlation length B, in the directionperpendicular to the reflecting planes. B can be deduced from the full width half maximum(FWHM) of the reflections by B=2π/(FWHM 2 -d I 2 ) ½ , where d I is the instrumentalbroadening. This formula is the Scherrer equation (without corrections) in q-space forreflections with Gaussian line shapes.Inelastic neutron scattering (k ≠ k’) may occur due to excitations or de-excitations ofphonons and magnons. Similarly, in magnetic nanoparticles, the neutrons may excite orde-excite the precession state of the uniform mode of the collective magnetic excitations.For a given q, this energy transfer in nanoparticles gives rise to peaks at the positions ± ε 0,with the value of the excitation energy depending on the effective anisotropy field in theparticle [Hansen et al., 1997; Hansen, 1998]. An example of this is shown in Fig. 2.7. Asthe population of states increases with temperature, the intensities of the inelastic peaksincrease correspondingly. Superparamagnetic relaxation, which follows Eq. 1.2, is seen asa quasielastic broadening around ε=0 [Hansen et al., 1997].

Chapter 2: Experimental methods 19Fig. 2.7. Inelastic neutron scattering of 16 nm α-Fe 2 O 3 particles at the (003)reflection. The broad peaks (indicated by arrows) on the both sides of the central peak arises fromtransition between precession states close to an energy minima. From [Hansen et al., 1997].Neutron powder diffraction data was obtained on the DMC diffractometer at SINQ SwissSpallation Neutron Source, Paul Scherrer Institute, Villigen, Switzerland using awavelength of 4.21 Å. The instrumental resolution for this wavelength is about 0.018 Å -1at 1.37 Å -1 . The resolution varies 10-20 % over the q-range at which data was obtained,but this variation make only insignificant contributions to our data analysis and can bedisregarded. Inelastic neutron measurements were obtained at the RITA2 spectrometer atthe same institute. The measurements were obtained at temperatures between 6 and 300 Kand at high fields using cryogenic equipment similar to that used for Mössbauerspectroscopy.For the neutrons scattering experiments, large quantities (preferably grams) of material areneeded. For neutron powder diffraction, we used 0.3 - 2 g of material. For inelasticneutron scattering experiments about 10 g of material was used. The powders are pouredand compacted into aluminium containers. Due to large incoherent scattering fromhydrogen, particles suspended in H 2 O could not be measured by neutrons. Fornanoparticles, incoherent scattering is also rather strong due to adsorbed H 2 O, howevergood spectra could still be obtained over times varying from a few hours to one day perspectrum.2.1.3 X-ray diffractionεX-ray diffraction (XRD) was performed using a PW 1390 Philips diffractometer with aCuK α radiation source. About 0.5 g of material was used to obtain diffraction patterns.XRD was used to identify crystalline phases in the samples and to estimate particle sizesfrom line broadening.High-energy synchrotron x-ray diffraction (HES-XRD) measurements were obtained fromthe BW5 beam-line at HASYLAB at DESY, Hamburg, Germany using 100 keV photons(wavelength equal to 0.12536 Å). For this, a few mg of material is needed.

20 Nanomagnets and their interactions – Part 12.1.4 Magnetization measurementsMagnetic hysteresis loops, i.e. measurements of magnetic moment as a function of appliedfield, were measured at DTU by use of a vibrating sample magnetometer (VSM) with asuperconducting coil magnet. The principle of the VSM is that the sample is vibratedwhereby the magnetic flux through nearby pick-up coils changes, inducing a detectablecurrent in the coils. The instrument was calibrated using the known magnetic saturationmoment of a cobalt sample. The instrument has a geometry and sensitivity which allow forstudying powder samples with magnetizations of 0.5 Am 2 /kg.Measurements were performed in applied fields up to 1 T. Field cooled hysteresis curveswere obtained at 5 K by cooling in a field of 1 T from 310 K in less than 30 minutes andthen recording the loop starting from 1 T. The time per measurement point is of the orderof ~1 second.The samples of the studied powders were enclosed in copper cylinders with typical samplemasses of 125 mg. The powders were densely compacted to a coherent solid with the aimof avoiding rotation of the particles during measurements. No binding materials such asepoxy were added to the powders in order not to affect the inter-particle interactions.2.1.5 Electron microscopyHigh-resolution electron microscopy (HREM) allows for imaging, almost like an opticalmicroscope, but with a much higher resolution (a few Å). By this, size and shapes ofnanoparticles can be assessed directly. Also, atomic lattice planes can be imaged and it ispossible to reveal the relative orientation of neighbouring particles.HREM images were obtained on a Jeol 3000F FEG TEM, at Risø National Laboratory,Roskilde, Denmark and on a Philips EM 430 at DTU, both using an acceleration voltageof 300 keV and lacey carbon on 200 mesh Cu grids as sample supports. The particles weretypically deposited onto the grids from dilute suspensions.2.1.6 Magnetic force microscopyMagnetic force microscopy (MFM) allows for imaging of stray fields from domainstructures with a lateral resolution down to ~ 25 nm by scanning a sharp magnetic tipmounted on an oscillating cantilever over the sample surface. A sketch of the MFM isshown on Fig. 2.8a. The interaction between the tip and the sample is detected bymeasuring the phase shift in the oscillation of the cantilever. Close to the sample surfacevan der Vaals forces dominate the tip-sample interaction, and this can be used to firstobtain a topographic image (an AFM image) of the sample surface. At tip-sampleseparations of 20 nm, long-range forces such as magnetic dipole forces becomedominant. Knowing the topography of the sample, an MFM image can be obtained byscanning the tip at a constant tip-sample separation (Fig. 2.8b). Corresponding AFM andMFM images are thereby obtained.Images were obtained by a Digital Instrument (DI) scanning force microscope of the typeDimension at the NanoScienceLaboratory, MIT, using magnetic low-moment tips with

Chapter 2: Experimental methods 21magnetic coating and tip radii of about 25 nm from DI. The tip-sample separation waskept constant at 35 nm during imaging. The tip was oscillated with a frequency of ~70kHz. Typical scan rates were about two seconds per line, so scanning two correspondingAFM and MFM images of 256 lines each takes about 20 minutes.Fig. 2.8. Principle of MFM. (a) Interaction between tip and sample. (b) AFM andMFM images obtained at different tip-sample separations.The rings could be imaged as they were prepared. A fixture with two screws containingpermanent magnets was applied to provide an in-plane magnetic field. The field wasremoved before imaging, so the rings were imaged in their remanent states. The magneticstray field of the tip may indeed influence the magnetization of the sample. However, forCo rings with the dimensions given in Section 2.2.2, we observed no perturbations fromthe stray field of the low moment tips (inferred from the domain states being independentof scan direction and from the states of repeated scans being similar). Attempts were madeto image NiFe rings of similar sizes, but they were found to be too magnetically soft.2.2 Samples2.2.1 NanoparticlesSamples of nanoparticles of α-Fe 2 O 3 , γ-Fe 2 O 3 , NiO, and CoO have been prepared andstudied. Below follows for reference a short overview of the different samples and theirpreparation techniques. The samples have been characterized with x-ray diffraction,Mössbauer spectroscopy, and electron microscopy after preparation. This has lead to theestimate of the particle sizes and shapes, which are given below, and which are referred toin the text.α-Fe 2 O 3 nanoparticles9 nm α-Fe 2 O 3 particles: Most studies in this thesis on α-Fe 2 O 3 nanoparticles have beenconducted on a sample of pseudo-spherical 9 nm particles, which was prepared by a gelsolmethod similar to that described by Sugimoto et al. [1998]. Measurements of particles

22 Nanomagnets and their interactions – Part 1from this batch are presented throughout Chapters 4 and 5, and in Papers I, IV, VII andVIII.11 nm α-Fe 2 O 3 particles: A precipitate from a gel-sol sample preparation similar to thatdescribed by Sugimoto et al. [1998] consisting of 11 nm particles has been used in PaperIX and studies of it are also referred to in Section 4.1.5.16 nm α-Fe 2 O 3 particles: A sample of 16 nm particles was prepared by heating ofFe(NO 3 )·9H 2 O at 60-90 °C over 20 days [Hansen et al., 1997]. Studies of the sampleappear in Paper III and in Section 3.1.2.In Paper VIII a number of α-Fe 2 O 3 samples with mean particle diameters of 6-20 nm havebeen studied. Details are given therein and in [Bødker and Mørup, 2000].γ-Fe 2 O 3 nanoparticles7 nm γ-Fe 2 O 3 particles were prepared by oxidation of Fe 3 O 4 nanoparticles obtained byprecipitation of Fe 2+ and Fe 3+ from an aqueous solution (Paper V). Studies of the 7 nm γ-Fe 2 O 3 particles are presented in Sections 4.1.1 and 5.1.1 and in Papers V and VI.NiO nanoparticlesDisc-shaped nanoparticles of NiO, 2-3 nm thick and 12-17 nm in diameter, were preparedby annealing Ni(OH) 2 at 300-325 °C [Bødker et al., 2000b; Papers I, IV, and V].CoO nanoparticlesCoO particles with a diameter of 20 nm were prepared by annealing (CH 3 COO) 2 Co·4H 2 Oat 350 °C for 4 hours in an argon atmosphere (Papers IV and V), while smaller particles –about 10 nm in diameter – were prepared by ball milling (Papers V and VI).2.2.1.1 Samples and sample treatmentsFor reference, ferrofluids of non-interacting 9 nm α-Fe 2 O 3 and of 7 nm γ-Fe 2 O 3 particleswere prepared by keeping a part of the particles in suspension during the wet-chemistrysample preparations and then coating them with oleic acid. The remaining parts of theparticles from the same batches were freeze-dried (dried by sublimation at low pressureand temperature).The freeze-dried samples have been treated in different ways by ball milling, grinding, andultrasonic treatment, as well as by varying the drying procedure. These treatments aredescribed in more detail in Section 4.1.5 and in the Papers, especially Papers VII and IX.Composite samples of nanoparticles were prepared from dried samples of α-Fe 2 O 3 , γ-Fe 2 O 3 , CoO or NiO. The composites were prepared by treating an aqueous suspension ofthe particles with ultrasound using a “horn” for about 15 minutes in order to obtain ahomogeneous mixture. 50 mg of each compound was suspended in 100 mL H 2 O persample preparation. The suspensions were subsequently dried in open petri dishes

Chapter 2: Experimental methods 23allowing the particles to agglomerate. One preparation of sample material providedsufficient material for Mössbauer spectroscopy. However, several similar samplepreparations were carried out, in order to achieve enough material for neutron powderdiffraction and magnetization measurements.2.2.2 RingsArrays of 8x8 Co rings were made on wafers by electron-beam lithography (details aboutthe fabrication are given in Papers X and XI). The rings were approximately 10 nm thickand made from polycrystalline films with a grain size of about 10 nm. The rings had outerdiameters of 520 nm and widths of 170, 135, and 110 nm and outer diameters of 360 nmand widths of 110 nm. Fig. 2.9 shows the definition of the dimensions. When referring to aring with certain diameter (d) and width (w), we often give the dimensions as d/w, e.g. as520/170 nm.dwtwidth, w.Fig. 2.9. Sketch of ring, defining its dimensions: thickness, t, outer diameter, d, andNote on UnitsIn Chapters 3-5 on fine particle magnetism, SI units are used, while in Chapter 6 on ringmagnets Gaussian units are used. These conventions are adopted from the related papers inPart 2.

24 Nanomagnets and their interactions – Part 13. Antiferromagnetic nanoparticlesIn Paper I, a review is found on studies of antiferromagnetic nanoparticles conducted inour group up to spring 2002. In particular, this paper treats results from Mössbauerspectroscopy and inelastic neutron scattering on collective magnetic excitations andsuperparamagnetic relaxation in α-Fe 2 O 3 nanoparticles, and it provides a combinedmeasure of the anisotropy (K Bu ) governing the dynamics within the easy plane ofmagnetization. In the next sections, two examples of different character are reported,showing recent highlights from our group on understanding the properties ofantiferromagnetic nanoparticles. First it is found - by a general model (presented in PaperII) - that there is a thermoinduced contribution from the uniform modes to the magneticmoment of nanoparticles of antiferromagnetic materials. Then, it is shown (Paper III) thata high-frequency uniform mode, equivalent of an out-of-easy-plane excitation of the spinstructure, in 16 nm α-Fe 2 O 3 particles has been detected by use of inelastic neutronscattering experiments. In Paper I, some effects of inter-particle exchange interactions arereported. These effects and further studies of interactions are treated in detail in Chapters 4and 5 and in Papers IV-IX.3.1 Results3.1.1 Thermoinduced magnetismFor ferromagnetic nanoparticles, the magnetic excitations can be considered as uniformprecessions with all ionic spins parallel. Similarly, in ferrimagnetic nanoparticles, thedynamics can be described in terms of precession of two antiparallel sublattices. However,in antiferromagnetic materials, the excited states are more complex than this, because inthe uniform mode, the two sublattices are not strictly antiparallel, but precess in such away that they make slightly different angles with the easy direction of magnetization.Theoretical deriviation of this is found in [Kittel, 1951, Keffer and Kittel, 1952]. In bulk,this mode can be excited by an ac-field, giving rise to a net moment. In Paper II, wepropose that this mode can be thermally excited in nanoparticles, giving rise to a netmoment. This principle is illustrated in Fig. 3.1.(a)(b)Fig. 3.1. Principle of thermoinduced magnetism in nanoparticles ofantiferromagnetic materials. (a) In a nanoparticle of antiferromagnetic material, the magneticmoments may compensate each other giving rise to a zero net magnetization at low temperatures.However, with increasing temperature (b), thermal energy may be sufficient to excite uniformprecession, where the moments no longer cancel due to different precession angles for the twosublattice magnetizations, giving rise to a net magnetization.

Chapter 3: Antiferromagnetic nanoparticles 25We have used Bolzmann statistics to calculate the population of precession states at finitetemperatures and find that a non-zero magnetic moment is induced by thermal excitationof the uniform precession mode (Paper II). The increase is linear and typically of about 0.5µ B /K. This implies that antiferromagnetism, strictly speaking, is non-existent innanoparticles of antiferromagnetic materials at finite temperatures, even if all spins arecompensated. Our results are in accordance with several experimental observations. Werefer intensively to these studies in Paper II. We have, however, not measured the effectourselves, but experimental work is in progress at DTU to assess the model.3.1.2 High-frequency excitation in α-Fe 2 O 3 nanoparticlesWe have used inelastic neutron scattering to study the dynamics of 16 nm α-Fe 2 O 3particles. Previous studies revealed observations of both superparamagnetic relaxation andcollective magnetic excitations in nanoparticles of α-Fe 2 O 3 [Hansen et al., 1997; Klausenet al., 2003; Paper I]. From the elastic scan at the antiferromagnetic (003) scatteringvector, the collective magnetic excitations are seen (Fig. 2.7) as broad side peaks centredat about ε 0 =±0.2 meV at room temperature.(b)Fig. 3.2. (a) Inelastic neutron data on 16 nm α-Fe 2 O 3 particles at the (101)antiferromagnetic scattering vector obtained at the indicated temperatures. The spectra show theelastic peak and the side peaks, on a logarithmic scale. The arrows indicate the position of the sidepeaks representing the high-frequency collective magnetic excitation. (b) The temperaturedependence of the out-of-plane anisotropy constant, K 1 , of the nanoparticles (continous line)calculated from the position of side peaks. The dotted line shows the temperature dependence ofK 1 for bulk α-Fe 2 O 3 . (κ 1 is the anisotropy per Fe ion). Both parts of the figure are from Paper III.Recently, a new mode of magnetic dynamics in α-Fe 2 O 3 nanoparticles was discovered(Paper III). Its signal is visible as inelastic peaks around ±1.2 meV at theantiferromagnetic (101) scattering vector (see Fig. 3.2a). Paper III treats the results indetail. In brief, the results show that two collective magnetic excitation modes withdifferent transition energies exist in α-Fe 2 O 3 nanoparticles, a low-frequency mode[Hansen et al., 1997; Klausen et al., 2003; Paper I] and a high frequency mode (Paper III).

26 Nanomagnets and their interactions – Part 1In the low-frequency mode, the precession is mainly in the easy plane. The new highfrequencymode is found to have mainly out-of-plane precession (Paper III).Experiments performed in the temperature range 6-300 K show that the precession energyof the newly observed mode is found to decrease with decreasing temperature (Fig. 3.2a),reflecting changes in the out-of-plane anisotropy (Paper III). This helps in elucidating theabsence of the Morin transition in α-Fe 2 O 3 nanoparticles.The cause of the Morin transition, which ideally is a first order phase transition, can beexplained as follows [Morrish, 1994]: With the magnetic anisotropy energy of an α-Fe 2 O 3particle described by Eq. 1.4, the transition occurs as a first order transition because K 1changes sign from negative to positive. This change of sign has been measured for bulk α-Fe 2 O 3 [Morrish, 1994] and is shown with a dotted line in Fig. 3.2b. From the inelasticneutron measurements on 16 nm α-Fe 2 O 3 particles we see that K 1 (calculated from thepositions of the side peaks, Paper III) increases with decreasing temperature, but it neverchanges its sign from negative to positive (see data points in Fig. 3.2b). The neutronstudies do not provide information on the origin of the anisotropy of nanoparticles beingdifferent to that of bulk.3.2 Conclusions and outlookThe examples above (Papers II and III) have provided further knowledge on the propertiesof nanoparticles of antiferromagnetic materials. Calculations have interestingly shown thata thermoinduced moment exists in nanoparticles of antiferromagnetic materials. Inelasticneutron studies of α-Fe 2 O 3 nanoparticles have revealed the existence of a high-frequencyuniform mode and have led to a measure of the out-of-plane anisotropy, K 1 . This result isof importance for understanding the suppression of the Morin transition in nanoparticles ofα-Fe 2 O 3 .The model on thermoinduced magnetization presented in Paper II is general; in principle,it applies to nanoparticles of all antiferromagnetic materials. The model is supported by anumber of earlier measurements on nanoparticles of antiferromagnetic materials of e.g.NiO, Cr 2 O 3 and ferritin. It will, however, be interesting, now that an explanation isavailable, to prepare samples with the aim to investigate thermoinduced magnetismfurther. One may consider how thermoinduced magnetism appears in nanoparticles ofdifferent antiferromagnetic materials, and how big a moment can be achieved per particle.Also, does the model break down when the assumption KV>>kT (Paper II) is violated?And can there be other explanations for the experimental results? Moreover, sinceinteractions can significantly affect the properties of nanoparticles (see e.g. next chapter),it will be interesting to study effects of interactions between nanoparticles withthermoinduced moments, for instance, to assess if the interactions lead to stabilization ofthe moments. For applications, thermoinduced magnetism gives a new class of magneticmaterials, which might prove useful for e.g. medical applications if some of them (e.g. theiron storage protein ferritin?) are more biocompatible than traditional magnetic materials.Antiferromagnetic particles with thermoinduced moments may also be useful in highfrequencymaterials and devices, because they allow for very fast magnetic fluctuations,see e.g. [Kimel et al., 2004], and for relaxation with no energy barrier to be overcome(Paper II) in contrast to relaxation in nanoparticles of ferro- or ferrimagnetic materials.

Chapter 4: Inter-particle exchange interactions in pure systems 274. Inter-particle exchange interactions in pure systemsThis Chapter reports on findings related to inter-particle exchange interactions in puresystems. The text mainly concentrates on samples of α-Fe 2 O 3 nanoparticles (Papers I, IV,and VII-IX), having the sample of 9 nm α-Fe 2 O 3 particles as a basis. The text focuses to alesser extent on the sample of 7 nm γ-Fe 2 O 3 particles (reported in Paper V).4.1 Results and discussions4.1.1 Effects on dynamicsFigure 4.1a shows Mössbauer spectra of the ferrofluid of 9 nm α-Fe 2 O 3 particles (PaperIV). The measurements show that the particles in this sample possess fastsuperparamagnetic relaxation: The magnetically split low-temperature spectrum collapseswith increasing temperature to a doublet. The superparamagnetic blocking temperature,T B , defined as the temperature where the spectral absorption area is equally dividedbetween the sextet and the doublet, is about 70 K.180 K295 K120 K250 KRelative absorption100 K80 K180 K120 K50 K80 K25 K25 K-12 -8 -4 0 4 8 12Velocity (mm/s)(a)-12 -8 -4 0 4 8 12Velocity (mm/s)(b)Fig. 4.1. Mössbauer spectra obtained at the indicated temperatures of (a) a frozenferrofluid of 9 nm α-Fe 2 O 3 particles and (b) a dried sample of uncoated α-Fe 2 O 3 nanoparticlesfrom the same batch.Figure 4.1b shows Mössbauer spectra of 9 nm α-Fe 2 O 3 particles from the same batch asthose in Fig. 4.1a, but the particles measured in Fig. 4.1b were left uncoated and driedfrom suspension. For these agglomerated particles, the hyperfine field is seen to decrease

28 Nanomagnets and their interactions – Part 1with increasing temperature and the absorption lines become asymmetrically broadened.However, the sextet does not collapse to a doublet, suggesting that the superparamagneticrelaxation is suppressed by the agglomeration of the particles (Paper IV). This spectralbehaviour is similar to that found for samples of agglomerated antiferromagneticnanoparticles of α-FeOOH [Mørup et al., 1983] and NiO [Bødker et al., 2000b], and for20 nm α-Fe 2 O 3 particles [Hansen et al., 2000b] and 8 nm and 11 nm α-Fe 2 O 3 particles(Papers VIII and IX). Similar effects on the relaxation are observed for agglomeratedferrimagnetic γ-Fe 2 O 3 nanoparticles in [Mørup et al., 1995] and in (Paper V). See Paper Vfor detailed discussion of the effect in 7 nm γ-Fe 2 O 3 particles compared to that in the α-Fe 2 O 3 particles.The influence on relaxation in samples of agglomerated antiferromagnetic particles hasbeen ascribed to exchange coupling between surface atoms of the uncoated particles[Mørup et al., 1983]. The energy of a particle i, which interacts with several neighbours j,may be written [Mørup et al., 1983; Mørup, 1983; Hansen et al., 2000b]E=KVsin 2 θ – M i·∑ j K ij M j . (Eq. 4.1)The first term represents the magnetic anisotropy energy of the particle i (Eq. 1.1), thesecond term represents the interaction energy. In the second term, M i and M j denote thesublattice magnetizations of the interacting particles, and K ij denotes the effectiveexchange coupling constant. In a way Σ j K ij M j defines an effective interaction field actingon particle i, such thatE=KVsin 2 θ – B eff M i Vcos(θ-θ 0 ), (Eq. 4.2)where B eff denotes the effective exchange field acting on the particle, and (θ-θ 0 ) is theangle between the directions of the exchange field and the sublattice magnetization. If theanisotropy term dominates, superparamagnetic relaxation may take place between the twoenergy minima at temperatures T KV/k B , but if the interaction term is dominant, therewill only be one energy minimum. In this case, superparamagnetic relaxation issuppressed, but the sublattice magnetizations may fluctuate around the exchange fielddirection. For the 9 nm α-Fe 2 O 3 nanoparticles, the suppression of the superparamagneticrelaxation is quite strong (Fig. 4.1b and Paper IV). In 7 nm γ-Fe 2 O 3 particles the effect onrelaxation is less significant (Paper V). This does not necessarily mean that the interparticleexchange coupling in the sample of γ-Fe 2 O 3 particles is smaller than in the sampleof α-Fe 2 O 3 particles. It may also imply that the anisotropy energy is larger for the γ-Fe 2 O 3particles than for the α-Fe 2 O 3 particles. Moreover, dipole interactions can play a role inthe samples of γ-Fe 2 O 3 particles.For interacting magnetic nanoparticles, Eq. 2.2 describing the decrease in hyperfine fieldat low temperatures due to collective magnetic excitations, may be replaced by [Mørup,1983; Mørup et al., 1983; Mørup and Ostenfeld, 2001]B hf ≈ B 0 [1 – k B T/(2KV + E int )], (Eq. 4.3)

Chapter 4: Inter-particle exchange interactions in pure systems 29where E int is related to the strength of the interactions (E int =B eff M i V). We have measuredthe hyperfine fields at low temperatures by Mössbauer spectroscopy of samples ofagglomerated 9 nm α-Fe 2 O 3 particles. The temperature dependence of B hf is shown in Fig.4.2. From the linear fit to the data, by use of Eq. 2.2, and assuming that KV/k B ~ 300 K forthe 9 nm α-Fe 2 O 3 particles [Bødker and Mørup, 2000], we find that E int ~1000 K. This issimilar to what has been found for interacting 8 nm α-Fe 2 O 3 particles in Paper VIII, wherethe decrease in B hf was measured at low temperatures for both coated and non-coatedsamples. It has been suggested that only a few well established exchange bridges areneeded to account for interaction energies of some hundred K [Hansen et al., 2000b].Hyperfine field (T)535251500 20 40 60 80 100Temperature (K)Fig. 4.2. The magnetic hyperfine field, B hf , of dried, non-coated 9 nm α-Fe 2 O 3particles, found from Mössbauer spectra obtained in the temperature range 20-80 K. The solid lineis a linear fit to the data points.In many respects it can seem surprising that it is possible to achieve exchange interactionsbetween particles simply by letting the particles agglomerate, and there have been somediscussions in the literature whether the influence on the Mössbauer spectra really couldbe ascribed to interactions between the particles [Hansen and Mørup, 1998; Dormann etal., 1999]. It could be argued that the difference in the Mössbauer spectra is due to adifference in the particle size, resulting from the chemical treatments during the coatingwith oleic acid. The difference might also be related to a change of the surfacecontribution to the magnetic anisotropy energy constant because of the coating. However,a change of the volume or the anisotropy energy constant should mainly change the valueof the energy barrier, KV, and this would have an influence on the superparamagneticblocking temperature. If the only difference between the samples were different energybarriers, the spectrum of the uncoated particles should be qualitatively similar to those ofthe coated particles, i.e. they should consist of a superposition of a sextet and a doublet ina broad temperature range, but at elevated temperatures. The broadening of the sextet inFig. 4.1b and the absence of a doublet up to relatively high temperatures suggest that thisis not the case.In order to further elucidate this discussion, we have performed inelastic neutronexperiments on samples of non-coated and coated 8 nm α-Fe 2 O 3 particles. Detailed dataanalysis is in progress. Preliminary analysis shows, however, that for the coated particles,the expected spectrum with inelastic side peaks is found, but for the uncoated samples, theside peaks have diminished intensities and are smeared out, and not simply shifted tohigher energies. This is in qualitative agreement with the interpretation of the Mössbauerdata based on inter-particle exchange interactions.

30 Nanomagnets and their interactions – Part 1Moreover, we find that the agglomeration process is more or less reversible (Paper VII), inthe sense that effects ascribed to suppression of relaxation (Fig. 4.3a) can be removed bysuspending interacting uncoated particles in water by intense ultrasonic treatment for 6hours. After such treatment, the Mössbauer spectra of the suspended particles (Fig. 4.3b)show relaxation behaviour similar to that of the coated particles in the ferrofluid (Fig.4.1b, 180 K). If the particle suspensions are allowed to dry again, then the suppression ofthe superparamagnetic relaxation is to a large extent re-induced (Fig. 4.3c). This stressesthat the difference in the spectra for interacting and non-interacting samples is not due tocoating itself.(a)Relative absorption(b)(c)-12 -8 -4 0 4 8 12Velocity (mm/s)Fig. 4.3. Mössbauer spectra obtained at 180 K of 9 nm α-Fe 2 O 3 nanoparticles (a) inthe as-prepared dry powder sample, (b) in frozen suspension after treatment with ultrasound, and(c) in powder after drying of the suspension. From Paper VII.4.1.2 Direct observation of exchange coupling between α-Fe 2 O 3 nanoparticlesAlthough many observations, including those of Mössbauer spectroscopy [Mørup et al.,1983, Mørup 1983; Hansen et al., 2000b; Bødker et al., 2000b; Papers IV and V) andinelastic neutron scattering (with detailed data analysis in progress), strongly suggest thatexchange coupling exists between the agglomerated particles, the first more directobservation of it came from neutron powder diffraction (NPD) measurements of the aspreparedpseudo-spherical 9 nm α-Fe 2 O 3 particles as reported in Paper VII. From thesmall width of the antiferromagnetic (003) reflection (see Fig. 4.4), NPD data showed thatthe magnetic correlation along the [001] axis exceeds the particle dimensions in thatdirection.From NPD data, we inferred that, in order for the magnetic correlation to exceed theparticle size along [001], the particles had to be assembled with preferred orientation suchthat (001) layers of neighbouring particles are parallel and such that the inter-(001)-planedistanceis the same across the particle interface as inside the particles. The sublatticemagnetizations of neighbouring particles are aligned within the (001) planes, which havesmall in-plane anisotropy. Fig. 4.4b shows an illustration of assembled α-Fe 2 O 3 particleswith magnetic and crystalline correlation along the [001] direction.

Chapter 4: Inter-particle exchange interactions in pure systems 31I 0kNTE 5kNSI 0kTY(003)(101)-_(102)Neutronsb(a)_(210)5k1.00 1.25 1.50 1.75 2.00 2.25 2.50Scattering vector (Å -1 )(104)(b)[001](c)Fig. 4.4. (a) Neutron powder diffraction data of α-Fe 2 O 3 particles obtained at roomtemperature. The solid lines represent the fits to data (green denotes individual Bragg peaks, redthe sum of Bragg peaks). (b) Schematic illustration of the antiferromagnetic correlation across theparticle interfaces in the as-prepared sample. (c) Scherrer “ellipse” showing correlation lengthsfound from the reflections in (a).The (003) reflection in the NPD data can adequately be described as having two Gaussiancontributions (see fit to data in Fig. 4.4a). The first contribution, which covers two thirdsof the peak area, has a width corresponding to a magnetic correlation length which issimilar to the average particle size. The other contribution, which covers the last third ofthe peak area, has a correlation length of about three times the particle size. This suggeststhat about one third of the particles in the sample are assembled into chains of about threeparticles.We have been able to verify the inferred crystalline order along [001] by high-energysynchrotron XRD (HES-XRD) and high-resolution electron microscopy (HREM)measurements. In XRD, (00l) reflections of α-Fe 2 O 3 are forbidden, except (006), which isa low-intensity peak and thus difficult to resolve in normal XRD measurements. However,HES-XRD data obtained on the sample showed that the (006) peak is narrower than theother reflections in accordance with the interpretation of the NPD data (Paper VII). HREMmicrographs showed correspondingly that there is a tendency for the particles to alignalong a common [001] axis (see Fig. 4.5).It is possible that the particles are assembled such that the ordering sequence of the six Felayersof the crystal structure (Fig. 1.11) in one particle is not continued into theneighbouring particle, i.e. stacking faults may exist. There is little indication of acrystalline correlation exceeding the particle size in other directions than [001] (see Fig.4.4.c), but it is difficult to quantify this further from diffraction data, because thosediffraction planes, which give rise to diffraction in the NPD and HES-XRD data, andwhich make the smallest angle with the (001) planes, make angles of about 40 degree with(001). HREM shows particles aligned along [001] both with the other crystal planes than(001) being parallel (Fig. 4.5a) and being non-parallel (Fig. 4.5b).Regardless of what the exact orientations of the parallel (001) planes for neighbouringparticles may be, including the possibility of stacking faults, NPD data shows that thesublattice magnetizations of neighbouring particles are aligned within the (001) planessuch that the antiferromagnetic structure is continued across the particle interface. Thisshows that exchange coupling exist between the particles. Subsequently, NPD

32 Nanomagnets and their interactions – Part 1measurements of other samples of α-Fe 2 O 3 particles (e.g. of agglomerated 11 nm particlesstudied in Paper IX) have revealed spectra, which also have a narrow (003) reflection.(112)(102)[001]52°(a)(213) ° [001](213)(113) 48(b)52°(102)(112)Fig. 4.5. HREM images of α-Fe 2 O 3 nanoparticles showing that the particles areattached to one another along their common [001] axis. The arrows and angles indicate thedirection of the [001] axis of the particles relative to the plane of the paper (the [001] axis points~50° into the paper). In (a) the crystal planes of neighbouring particles are parallel. In (b) thecrystal planes other than (001) are non-parallel. From Paper VII.4.1.3 Effects on magnetic structure of α-Fe 2 O 3 nanoparticlesFrom Mössbauer studies of interacting and non-interacting nanoparticles, we noticed thatthe quadrupole shift, ε, differed. We performed a comparative study by Mössbauerspectroscopy on the value of ε (presented in Paper VIII) in order to investigate the possibleinfluence from exchange interaction on the magnetic spin structure. For samples ofinteracting α-Fe 2 O 3 nanoparticles, we find that ε deviates from the “in-(001)-plane”-valueof -0.100 mm/s found for samples of non-interacting particles and for bulk α-Fe 2 O 3 aboveits Morin transition. This deviation indicates that an out-of-plane rotation of the sublatticemagnetizations occurs in the samples of agglomerated particles. The deviation is largestfor particles smaller than 10 nm. For 9 nm particles, ε=-0.085 mm/s. This corresponds toan out-of-plane rotation of ~13 degrees. An estimate of B hf at 0 K (shown in Paper VIII)for the interacting and non-interaction particles supports the results obtained from ε. Weexplain this spin rotation as being due to exchange coupling between particles with nonparallel(001) planes, whereby the sublattice magnetizations of neighbouring particles tryto align themselves by slightly rotating out of the (001) plane (see Fig. 4.6).FromE=K 1 Vsin 2 θ – E int cos(θ-θ 0 ), (Eq. 4.4)where θ 0 is the angle between the direction of the interaction field and the [001] axis of α-Fe 2 O 3 , we can estimate the interaction energy, E int , related to this spin rotation, to be about600 K for the 9 nm particles (Paper VIII). This value is, although smaller, of the sameorder of magnitude as that found for E int from the decrease in hyperfine field by Eq. 4.3.The results imply interestingly that the magnetic structure is sensitive to inter-particleexchange interactions in the sense that the sublattice magnetization direction may deviatefrom the easy direction as defined by magnetic anisotropy.

Chapter 4: Inter-particle exchange interactions in pure systems 33[001][001]Fig. 4.6. Illustration showing α-Fe 2 O 3 nanoparticles with non-parallel [001] axes,where the sublattice magnetizations rotate slightly out of the (001) plane to minimize exchangeenergy.It is possible that the influence on the magnetic structure is caused by an orientedassembly of particles along directions other than [001], but we have not found evidencesupporting this.A similar, but larger, spin-reorientation effect on the magnetic structure of α-Fe 2 O 3resembling the Morin transition is observed for α-Fe 2 O 3 nanoparticles when in compositewith NiO nanoparticles. This is described in Section 5.1.2 and in Paper IV.4.1.4 Network of interacting α-Fe 2 O 3 nanoparticlesThe studies presented above on α-Fe 2 O 3 nanoparticles provide insight into different kindsof exchange interactions existing in the sample. By neutron powder diffraction we haveobserved a tendency for the particles to be aligned into small chains along their common[001] axis. Hereby the sublattice magnetizations of neighbouring particles may rotate inplanesuch that their directions become parallel. By Mössbauer spectroscopy we havefound that particles also agglomerate and couple with non-parallel [001] axes, whereby thesublattice magnetizations may rotate slightly out of the (001) planes.The strong suppression of the superparamagnetic relaxation is likely to be due to acombination of the different kinds of exchange interactions observed. The coupling ofparticles with parallel (001) planes may be stronger than those with non-parallel (001)planes but preferred assembly and coupling of about one third of the particles into smallchains of about three particles, as found from NPD, is not expected to be enough to giverise to the strong suppression of the superparamagnetic relaxation, which has beenobserved for all particles in the sample (Fig. 4.1b). A chain of three 9 nm particles isexpected to have a blocking temperature of about three times that of the individualparticles, i.e. about 210 K for the 9 nm particles. We suggest that the strong suppression isdue to existence of larger networks of particles in the samples with both parallel and nonparallel(001) planes. A part of such network is schematically illustrated in Fig. 4.7. Thisillustration shows particles that have assembled into small chains such that their [001] axesare parallel, but the neighbouring chains have non-aligned [001] directions. Since eachparticle in a powder only interacts with a limited number of neighbours (e.g less thanabout six) and since the coupling strengths are likely to be different between a particle andits different neighbours, there will be a net effective exchange field acting on each particle.

34 Nanomagnets and their interactions – Part 1The picture of the magnetic structure and dynamics of particles as being governed by anetwork of exchange coupled, aligned and non-aligned particles is in good agreement withthe model proposed in [Hansen et al., 2000b]. In order to fit Mössbauer data of interacting20 nm α-Fe 2 O 3 particles, the model in [Hansen et al., 2000b] assumed that the easy axesof the particles were parallel to the effective exchange field. This described most of thespectra well. The parts of the spectra, which the model could not describe, were ascribedto interacting particles with non-parallel easy axes. Here we have obtained more directobservations of the arrangement of particles assumed by the model.[001][001][001]Fig. 4.7. Illustration of network of interacting α-Fe 2 O 3 nanoparticles in powder.4.1.5 Influence of sample treatmentsThe influences on the magnetic properties e.g. by simply drying the samples from theaqueous suspension seemed significant, and we have conducted a number of experimentsrelated to sample handling in order to investigate the influence on the magnetic propertiesin more detail.Grinding and ball millingWe actually found that the grinding led to faster relaxation in the samples, i.e. to aseparation of particles, without reducing particle size. This was discovered, when we triedto dry-mix particles in a mortar to see if we could achieve effects of inter-particleexchange interactions in such samples. Thus instead of inducing inter-particle interaction,the interaction had been reduced. The effect is more significant in samples, which aremixed with non-magnetic particles than in pure samples (probably because the nonmagneticparticles act as spacers). Increasing the duration of the treatment also increasesthe effect. A systematic study on the effect on relaxation by grinding a sample ofagglomerated 11 nm α-Fe 2 O 3 particles is presented in Paper IX. Similar effects are seen insamples of 9 nm α-Fe 2 O 3 , which have been gently ball-milled (Paper VII). In Paper VII itis shown that this treatment can also lead to separation of locally aligned particles (seen asa significant line broadening solely of the (003) reflection in NPD data), and in Paper VIIIit is found that the grinding also acts to separate particles with non-parallel (001) planes(seen as a decrease in quadrupole shift ε in the Mössbauer spectra). This shows thatmacroscopic treatments can influence the local arrangement of nanoparticles.

Chapter 4: Inter-particle exchange interactions in pure systems 35Ultrasonic treatmentAs mentioned in Section 4.1.1 ultrasonic treatment of agglomerated particles can also leadto a faster relaxation. 9 nm α-Fe 2 O 3 particles have been suspended in water (50 mg in 80mL), and then treated with ultrasound. Mössbauer spectra of these particles showed a cleartendency of increasing relaxation (as well as a decrease in ε), with increasing intensity andduration of the ultrasonic treatment (Fig. 4.8). If the suspension was only treated for 15min in an ultrasonic bath and then frozen in a sample holder by immersion in liquidnitrogen immediately after treatment, the spectrum in Fig. 4.8a obtained at 180 K is verysimilar to that of the untreated sample (Fig. 4.1b). This shows that neither the suspensionin water nor this ultrasonic bath treatment affect the inter-particle interactionssignificantly. Contrary, application of a more intense treatment of the sample byimmersing an ultrasonic “horn” into the suspension of particles for 15 min led to a fasterrelaxation of the particles (Fig. 4.8b). Using the horn for 6 hours (and keeping thesuspension cold by a surrounding, ice-cooled water bath) led to an even faster relaxationof the particles since in this case the Mössbauer spectrum obtained at 180 K (Fig. 4.8c)consist solely of a doublet. These results strongly suggest that the inter-particleinteractions can be reduced by intense and durable ultrasonic treatments. However, wededuce from T B of the samples that the reduction although significant, is less than thatobtained due to grinding or ball milling with non-magnetic particles (Paper VII).(a)Relative absorption(b)(c)Fig. 4.8. Mössbauer spectra obtained at 180 K of frozen suspensions of 9 nm α-Fe 2 O 3 particles after ultrasonic treatment of increasing duration and intensity: (a) 15 minutes in abath, (b) 15 minutes by horn, and (c) 6 hours by horn.Drying-12 -8 -4 0 4 8 12Velocity (mm/s)Figures 4.9a-c show room temperature Mössbauer spectra of samples, which afterexposure to intense ultrasonic treatment by use of the horn for six hours, have been driedwith increasing duration and consequently show stronger interaction (seen as suppressionof the superparamagnetic relaxation and an increase in ε). If the suspensions are frozenimmediately after the ultrasonic treatment and then freeze-dried, the particles show lessinteraction (a sextet is absent in the spectrum in Fig. 4.9a), compared to drying the

36 Nanomagnets and their interactions – Part 1particles under ambient conditions in an open petri dish over a couple of days (Fig. 4.9b).However, in both cases the interaction is significantly stronger than for the particles frozenin suspension. If the suspensions are dried at ambient conditions, but under a perforated lidover a couple of weeks, the area of the sextet increases at the expense of the centraldoublet showing that the particles achieve even stronger interaction (Fig. 4.9c). Thus,drying the particles from suspension with increasing duration of the drying process leadsto a stronger coupling between the particles. The suppression of the superparamagneticrelaxation is not quite as strong in Fig. 4.9 as in the as-prepared sample (Fig. 4.1b, 295 K).This may be due to differences in sample preparation, e.g. the concentration of particlesduring drying. In the as-prepared sample (Fig. 4.1b) about 15 g is dried in 500 mL water,while for the treated sample (Fig. 4.9) it is about 50 mg per 100 mL water.We have directly observed the oriented alignment of particles in the as-prepared sample of9 nm α-Fe 2 O 3 particles (Figs. 4.4 and 4.5). One should note that there are many steps inthe sample preparation, which may influence the assembly of the particles [Park et al.,1996; Sugimoto et al., 1996; Sugimoto et al., 1998]. The particles are prepared by a gelsolmethod, where β-FeOOH nanoparticles are nucleated from an alkaline solution of Fe 3+and Cl - ions. The β-FeOOH particles are then aged to α-Fe 2 O 3 , and from this a seedsolution of α-Fe 2 O 3 particles is prepared. The process is then repeated using the seedsolution as a precursor and later the sample is washed several times with differentsolutions e.g. acetone, then ball milled, centrifuged and finally freeze-dried. The samplepreparation including all steps takes about a month, so the influence of time may also bean issue to consider.It is promising if nanoparticles simply assemble with preferred orientation in water, but amore comprehensive study is needed to verify this further. It is of particular importance toestablish whether the particles, when they re-agglomerate, as observed by Mössbauerspectroscopy, assembly in such a way that the particles have common [001] axes.Additional HREM, NPD and HES-XRD experiments would elucidate this matter.(a)Relative absorption(b)(c)-12 -8 -4 0 4 8 12Velocity (mm/s)Fig. 4.9. Mösbauer spectra obtained at room temperature of samples dried withincreasing duration from aqueous suspension after 6 hours of ultrasonic treatment. (a) Freezedried.(b) Dried at ambient condition over a couple of days. (c) Dried at ambient conditions over acouple of weeks.

Chapter 4: Inter-particle exchange interactions in pure systems 374.1.6 Magnetic assembly?Until recently, the general understanding was that crystals in solutions grow by addition ofatoms, but interestingly, recent HREM studies by Banfield and co-workers onnanoparticles of TiO 2 and iron oxyhydroxides have revealed that crystals, under certaincircumstances, can also grow by oriented attachment of nanoparticles [Lee Penn andBanfield, 1998; Lee Penn and Banfield, 1999; Banfield et al., 2000]. In their work, it hasbeen suggested that reduction of surface energy of nanoparticles is the driving mechanismfor this type of crystal growth. The preferred attachment of the 9 nm α-Fe 2 O 3 particles is,however, surprising because the particles are nominally equidimensional (spherical) [LeePenn et al., 2001] and the (001) planes of α-Fe 2 O 3 are generally considered to be theplanes of low surface energy, although hydration as well as oxygen vs. iron termination ofthe planes can alter the surface energies [Jones et al., 2000; Wang et al., 1998]. The (001)surface energy of α-Fe 2 O 3 has been calculated to have values between 0.75 and 1.65 J/m 2depending on the environment, see [Jones et al., 2000; Wang et al., 1998].Since the α-Fe 2 O 3 particles are magnetic and since exchange coupling is establishedbetween the particles, it is worth considering if exchange interaction between particles canaffect the assembly. Magnetic coupling mechanisms make it favourable for the α-Fe 2 O 3particles to assemble along [001]: The superexchange coupling across the oxygen-layers isdominant compared to in-plane exchange interaction [Morrish, 1994], and the (001) planeis the plane where all spins are parallel such that coupling of two (001) planes will lead toleast spin frustration. We have calculated the exchange energy across the (001) planes ofα-Fe 2 O 3 and we find it to be 0.2 J/m 2 (Paper VII). The contribution from the exchangeenergy between aligned particles may thus be a small extra driving force for the assembly.4.2 ConclusionsWe have studied samples of antiferromagnetic nanoparticles, in particular 9 nm α-Fe 2 O 3particles. Mössbauer spectroscopy has shown that agglomeration of the particles can leadto suppression of superparamagnetic relaxation. This effect has been ascribed to interparticleexchange interactions, in accordance with results obtained on other systems[Mørup et al., 1983; Hansen et al., 2000b]. By use of neutron powder diffraction we havefound the magnetic correlation length to exceed the particle size along the [001] directionof the 9 nm α-Fe 2 O 3 particles, and from this we conclude that exchange coupling is moredirectly observed to exist between particles. This result further implies that the particlesare assembled with preferred orientation along the [001] direction; an implication, whichhas been confirmed by HES-XRD and HREM. Moreover, we find that inter-particleinteractions between α-Fe 2 O 3 particles with non-parallel [001] axes influence the magneticspin structure since the sublattice magnetization is observed to rotate up to ~15 degreesout of the (001) plane. These results together show that the powder of agglomerated α-Fe 2 O 3 particles can be described as networks of exchange interacting particles both withaligned and non-aligned [001] axes. Macroscopic treatments of the powders influence thecoupling between the particles (i.e. the structure of the network). For instance, grindingand ultrasonic treatment leads to a separation of particles, while drying aqueoussuspensions brings particles together. The results imply the magnetic properties areextremely sensitive to almost any handling of the samples. Thus, interestingly, theproperties of samples are controllable by sample treatments.

38 Nanomagnets and their interactions – Part 14.3 OutlookIt is interesting that strong exchange coupling can be achieved between particles driedfrom aqueous suspensions. For future work the key issue to address is to understand themechanisms behind the coupling, such that inter-particle interactions and assembly can becontrolled.α-Fe 2 O 3 (hematite) is one of the most common iron-containing minerals. It comes invarious forms (e.g. on Earth as kidney ore or as specularite, and recently it has been foundas blueberries on Mars [JPL, 2004]) but the environmental conditions and themechanisms, which give rise to the different forms, are not very well understood. Theassembly of α-Fe 2 O 3 nanoparticles under controlled conditions in the laboratory may be ofrelevance for understanding crystal growth in natural environments.For studies of assembly of α-Fe 2 O 3 nanoparticles, NPD seems to be the key technique.However, large samples are needed for NPD and for that reason, HES-XRD may be amore appropriate technique although the structural (006) reflection appears much lessintense than the magnetic (003) reflection of NPD. HES-XRD also allows for studying wetsamples such as aqueous suspensions of particles. This might prove helpful in revealing ifpreferred assembly takes place, and at what moment the assembly may take place, e.g.whether the particles are brought together in the liquid due to Brownian motions or if theyassemble during the drying process.One may speculate that exchange coupling plays a role for the assembly of nanoparticles.To establish this idea is a challenge. It would be interesting to examine in further detail theinfluence of exchange coupling on self-assembly by selecting a system of very fineparticles with a Néel temperature, which matches the experimental conditions, such thatthe strength of the coupling can be controlled by varying the temperature.Assembled systems may also allow for more detailed physics studies on relaxation ofcoupled nanoparticles. One interesting issue to address is the possible existence of spinwaves over several particles (“super-spin waves”). In one scenario one could imagine thatthe sublattices of neighbouring particles relax collectively in a uniform mode. Anotherpossibility is that the sublattice magnetizations of neighbouring particles could decouplefrom one another with increasing temperature due to very fast relaxation [Hansen et al.,2000b]. The sublattice magnetization of neighbouring particles may also relax in acorrelated, non-uniform mode.

Chapter 5: Inter-particle exchange interactions in composites 395. Inter-particle interactions in compositesWe have complemented the studies on exchange interactions in pure systems with studieson nanoparticle composites. This Chapter treats results obtained on nanoparticle compositeof α-Fe 2 O 3 /CoO and α-Fe 2 O 3 /NiO (Papers I and IV) and γ-Fe 2 O 3 /CoO and γ-Fe 2 O 3 /NiO(Papers V and VI). The results in Sections 5.1.2-4 have not been published elsewhere.5.1 Results and discussion5.1.1 Effects on dynamics and coercivityFigure 5.1a shows Mössbauer spectra of 9 nm α-Fe 2 O 3 particles, which have been treatedwith intense ultrasound for 15 minutes and then dried at ambient conditions. Figures 5.1band 5.1c show spectra of similarly prepared samples of α-Fe 2 O 3 particles, but which havebeen mixed with CoO and with NiO nanoparticles. From these spectra, we find thatmixing the α-Fe 2 O 3 nanoparticles with CoO particles lead to a stronger suppression of thesuperparamagnetic relaxation of α-Fe 2 O 3 nanoparticles than in the pure sample. Contrary,the effect of the NiO particles on α-Fe 2 O 3 particles is a faster relaxation. Similar effects byCoO particles on γ-Fe 2 O 3 and 57 Fe-doped NiO nanoparticles and by NiO nanoparticles onγ-Fe 2 O 3 particles have been observed (Paper IV and V).300 K295 K250 K250 K250 K180 KRelative absorption180 K120 K180 K120 K120 K100 K80 K80 K80 K25 K20 K20 K-12 -8 -4 0 4 8 12Velocity (mm/s)-12 -8 -4 0 4 8 12Velocity (mm/s)(a) (b) (c)-12 -8 -4 0 4 8 12Velocity (mm/s)Fig. 5.1. Mössbauer spectra obtained at the indicated temperatures of dried samplesof (a) α-Fe 2 O 3 nanoparticles, (b) α-Fe 2 O 3 and CoO nanoparticles, and (c) α-Fe 2 O 3 and NiOnanoparticles. Similar spectra are found in Paper IV.

40 Nanomagnets and their interactions – Part 1The difference in the spectra of α-Fe 2 O 3 particles when mixed with CoO and NiO particleshas been ascribed to the difference in anisotropy of the CoO and NiO particles (Papers IVand V). CoO has a larger anisotropy constant than NiO, and the studied particles of CoOalso have larger volumes than the studied NiO particles (For the spectra in Fig. 5.1b, theCoO particles are 20 nm in diameter, while the NiO particles have average diameters of ~5nm). We note that in the spectra of α-Fe 2 O 3 nanoparticles mixed with CoO particles (Fig.5.1b) the lines are much sharper than in the spectra of α-Fe 2 O 3 particles (Fig. 5.1a). Thiscan be explained by the relaxation of the α-Fe 2 O 3 particles in the α-Fe 2 O 3 /CoO compositebeing dominated by relaxation over an energy barrier due to the coupling with CoO(compare to Eq. 4.2). By measuring the hyperfine field of the pure α-Fe 2 O 3 and the α-Fe 2 O 3 /CoO composite at low temperatures (Fig. 5.2), we find from Eq. 4.3 that in thecomposite E int ~8000 K.54Hyperfine field (T)535251α-Fe 2O 3/CoOα-Fe 2O 3500 20 40 60 80 100Temperature (K)Fig. 5.2. The temperature dependence of the magnetic hyperfine fields, B hf , of 9 nmα-Fe 2 O 3 particles and of 9 nm α-Fe 2 O 3 particles in composite with 20 nm CoO particles. The solidlines are linear fits to the data points. From Paper I.We cannot conclude that the exchange coupling between α-Fe 2 O 3 and NiO nanoparticlesis less than that between α-Fe 2 O 3 and CoO nanoparticles. The difference in the effect onthe relaxation in the Mössbauer spectra is merely ascribed to the anisotropy of the NiOnanoparticles being much smaller than that of CoO.In the sample of α-Fe 2 O 3 particles mixed with NiO particles, we have observed anintriguing phenomenon at low temperatures, namely that a Morin-like phase transitionoccurs in the α-Fe 2 O 3 nanoparticles. It is possible that this effect can be ascribed toexchange coupling between particles. This phenomenon is treated in detail in Section5.1.2. Due to this transition, which affects B hf , we cannot derive E int for the α-Fe 2 O 3 /NiOcomposite by use of Eq. 4.3.The effects observed on α-Fe 2 O 3 in the composites have only been found when thecomposites are prepared from aqueous suspension. For instance, they have not been foundwhen mixing dry particles. Nor do we see it for samples mixed in heptane, nor in α-Fe 2 O 3nanoparticles dried in ionic solutions of Co 2+ or Ni 2+ (Paper IV).Exchange interactions between different phases are often associated with effects on thehysteresis loops, e.g. seen as an increased coercivity and a shifted loop due to exchange

Chapter 5: Inter-particle exchange interactions in composites 41bias. In order to assess the interpretation that exchange interactions were responsible forthe influence on the relaxation in the composites, we measured the hysteresis loops of the“ferrimagnetic” samples of γ-Fe 2 O 3 , γ-Fe 2 O 3 /CoO, and γ-Fe 2 O 3 /NiO at 5 K (Paper V).From these measurements, it was found that mixing the γ-Fe 2 O 3 nanoparticles with CoOnanoparticles resulted in an increased coercivity (about three times larger) compared to asample consisting solely of γ-Fe 2 O 3 nanoparticles (see Fig. 5.3). On the contrary, mixingof γ-Fe 2 O 3 nanoparticles with NiO nanoparticles resulted in a slightly reduced coercivity(Fig. 5.3). These results show that the effective anisotropy is larger for γ-Fe 2 O 3 particlesinteracting with CoO nanoparticles than for those interacting with NiO nanoparticles. Thisstrongly supports the interpretations of the relaxation behaviour observed by Mössbauerspectroscopy, and that exchange interactions exist between the particles. In Paper VI, weshow accordingly, by use of Mössbauer spectroscopy, how the spin structure of γ-Fe 2 O 3nanoparticles with applied field is pinned by interaction with CoO nanoparticles. In PaperVI, we also discuss the possible influence from localized spin canting at the interfaces, butwe find it unlikely that the results can be explained by localized spin canting. We foundfrom the magnetization measurements that no exchange bias was induced in the samples(Paper V). This is probably due to the small anisotropies, on an absolute scale, of theantiferromagnetic nanoparticles, which allow the ferrimagnetic particles to drag thesublattice magnetization of the antiferromagnets around. Similar behaviour fornanoparticle composites is found in [Anhøj et al., 2004].Moment (Am 2 /kg)100500-50γ-Fe 2O 3/NiOγ-Fe 2O 3γ-Fe 2O 3/CoO-100-1.0 -0.5 0.0 0.5 1.0Applied field (T)Fig. 5.3. Hysteresis loops obtained at 5 K of samples containing γ-Fe 2 O 3nanoparticles. From Paper V. Note: The reasons for the differences in moment at 1 T are probablythat the plate-shaped NiO nanoparticles have significant uncompensated moments (due to an oddnumber of (111) layers in the plate-shaped particles) and that the sample containing CoO is lesssaturated than the pure sample of γ-Fe 2 O 3 at 1T in agreement with Mössbauer results presented inPaper VI.We have investigated by neutron powder diffraction whether the Néel temperature of theCoO nanoparticles increases due to inter-particle interaction with iron oxides, which havemuch higher ordering temperatures than CoO, such as it has been observed for thin films(

42 Nanomagnets and their interactions – Part 1effects in nanoparticle composites, because Mössbauer spectra of α-Fe 2 O 3 /CoOnanocomposites had shown effects on the relaxation, even at temperatures ~30 K abovethe Néel temperature of bulk CoO [Ostenfeld and Mørup, 2002; also mentioned in PaperI]. By NPD we measured T N in pure samples of CoO nanoparticles to be close to bulkvalue of ~293 K. However by NPD, we were not able to resolve any increase in T N of theCoO nanoparticles in composites above this value. For the samples, which included α-Fe 2 O 3 , it could be seen that the antiferromagnetic (½½½) peak of CoO had vanished at300 K. In the case of CoO/γ-Fe 2 O 3 , overlapping diffraction lines made it impossible todetermine the critical temperature of CoO in this composite. In [van der Zaag et al., 2000]it was found that the effect on T N was most pronounced in very thin films. The reason thatwe do not observe an effect on T N of CoO may be due to the small volume fraction ofCoO that the interface regions constitute in the powder samples.Although the effects observed in nanoparticles composites due to exchange coupling insome ways are different from those observed for e.g. thin film systems, the results showinterestingly that exchange coupling can be achieved in composites of particles preparedby drying aqueous suspensions of particles.5.1.2 A Morin-like phase transition induced in α-Fe 2 O 3 nanoparticlesIn nanoparticles of α-Fe 2 O 3 mixed with NiO nanoparticles, it is found by Mössbauerspectroscopy that ε for α-Fe 2 O 3 takes values of about 0.15 mm/s at low temperatures,suggesting that a spin-reorientation similar to the Morin transition takes place [Ostenfeldand Mørup, 2002; Papers I and IV]. We have observed the phenomenon in a number of α-Fe 2 O 3 /NiO composites, where the particles have sizes smaller than ~ 15 nm. Here wepresent studies of the 9 nm α-Fe 2 O 3 particles mixed with NiO particles, which are discshapedwith diameters of about 12 nm and thicknesses of about 2 nm.The Morin-like transition is seen in the Mössbauer spectra obtained at low temperatures ofthe α-Fe 2 O 3 /NiO composite (Fig. 5.1c) as the distance between lines 5 and 6 of the sextetbeing larger than the distance between lines 1 and 2. With increasing temperature thesextet becomes asymmetric: lines 2 and 6 become broader and less intense than lines 5 and1. This is in contrast to spectra of other samples containing the 9 nm α-Fe 2 O 3 particles(e.g. those in Figs. 5.1a and 5.1b). The simplest but still sufficient fit of the lowtemperaturespectra in Fig. 5.1c is made up of two sextets which each have pair wise equalareas like 3:2:1:1:2:3. The fits to data obtained at 20 K and 80 K are seen on Fig. 5.4. Thedata can only be fitted up to ~ 130 K; at higher temperatures, the spectra are too severelyinfluenced by the relaxation. The quadrupole shifts found for the two sextets as a functionof temperature are plotted in Fig. 5.5. From this we see that at 20 K one sextet (whichconstitute 65 % of the spectral area) has ε = 0.16 mm/s, corresponding to an angle, θ,between the [001] axis and the direction of the sublattice magnetization of only 21degrees. This value of ε is close to the value of 0.20 mm/s found for bulk α-Fe 2 O 3 belowits Morin transition and reflects the existence in part of the sample of a quite significantspin reorientation, which resembles the Morin transition. The other sextet (with a spectralarea of 35 %) has a quadrupole shift of about 0.08 mm/s at 20 K, corresponding to θ=39°.With increasing temperature the quadrupole shifts of both sextets increase and at 130 K, εtake values of ~ 0.00 mm/s for both sextets. Quadrupole shifts of ~0.08 mm/s and ~0.00

Chapter 5: Inter-particle exchange interactions in composites 43mm/s strongly suggest that the sublattice magnetizations in a temperature range neither arefixed in the [001] direction nor in the (001) plane but makes oblique angles with the [001]-axis. We have tried other fitting procedures than using two sextets and found that they donot produce significantly different results or they give less good fits. Also, the spectracannot be described solely by a superposition of two sextets for α-Fe 2 O 3 being truly aboveand below the Morin transition.α-Fe 2 O 3 /NiO300 KRelative absorption80 K20 K-12 -8 -4 0 4 8 12Velocity (mm/s)temperatures.Fig. 5.4. Mössbauer spectra of α-Fe 2 O 3 /NiO fitted with two sextets at low0.20QBulk α-Fe 2 O 3 below MT21ºuaSextet 1drSextet 2up 0.10 39ºolesplitt 0.00ing(m α-Fe 2 O 377º-0.10Bulk α-Fe 2 O 3 above MTQuadrupole splitting (mm/s)0 50 100 150 200 250 300Temperature (K)Fig. 5.5. Quadrupole shifts, ε, as a function of temperature obtained fromMössbauer spectra of α-Fe 2 O 3 /NiO nanoparticles. The horizontal solid lines show the values of εfor bulk α-Fe 2 O 3 above and below the Morin transition (MT). The dashed blue line shows thevalue of ε obtained for the interacting 9 nm α-Fe 2 O 3 particles (Section 4.1.3 and Paper XIII).NPD data (Fig. 5.6) of α-Fe 2 O 3 /NiO nanoparticles shows from the changing intensities ofthe magnetic reflections that, in accordance with the interpretation of the Mössbauer data,a spin-reorientation transition takes place at low temperatures. The changes in intensitiesare shown in Fig. 5.7. Neutron data does not directly give the spin orientation if different

44 Nanomagnets and their interactions – Part 1states co-exist, as we have found from Mössbauer spectroscopy, because the lines from thedifferent states overlap. But if it is assumed, based on Mössbauer results, that 65 % of theparticles have performed an almost complete Morin transition at 20 K, then analysis ofneutron data tell us that for the last 35 % of the particles, the sublattices make an angle θof ~ 40° in accordance with Mössbauer results.(003)(101)300 KINTENSITY80 K20 K1.2 1.4 1.6 1.8 2.0 2.2 2.4SCATTERING Scattering vector VECTOR q (Å -1 )Fig. 5.6. Neutron powder diffraction data of nanocomposite of α-Fe 2 O 3 /NiOobtained at the indicated temperatures. The solid lines show fit to data. The (“green”) reflection at1.31 Å -1 is the (½½½) reflection of NiO. The other reflections are due to α-Fe 2 O 3 . The black line issum of fit.Analysis of the line width of the neutron data shows that there is no increase in widths ofthe peaks with decreasing temperature. This excludes the possibility that the particles mayhave a domain-like structure due to the spin-reorientation, where the direction of thesublattice magnetization in one corner of a particle point out of the (001) plane, in theother corner lays within the (001) plane, and in between there is a domain wall regionwhere the sublattice magnetization direction takes intermediate angles, as suggested in[Ostenfeld and Mørup, 2002] as a possible explanation for the oblique angles found byMössbauer spectroscopy. This exclusion of domain wall formation is also in goodagreement with the general perception that nanoparticles are too small to have domains.One may ask if the effects could be caused by e.g. spin canting at the interfaces, but theeffects are too large to be explained by this. Instead, it can be positively concluded that,since the particles are single domain particles at all temperatures, the sublatticemagnetization of individual α-Fe 2 O 3 particles (or agglomerates of them) rotates coherentlyout of the (001) plane during the transition.In addition to interaction between α-Fe 2 O 3 nanoparticles and NiO nanoparticles, α-Fe 2 O 3nanoparticles also interact with other α-Fe 2 O 3 particles in the α-Fe 2 O 3 /NiO composite.This can be seen, for instance, from the NPD data in Fig. 5.6, where the (003) reflection is

Chapter 5: Inter-particle exchange interactions in composites 45still fairly narrow compared to that of the other reflections. It is therefore likely that bothindividual particles and small agglomerates of α-Fe 2 O 3 and of NiO particles interact withone another.The observation that the transition occurs in the same temperature range (170 K - 30 K) inboth Mössbauer and neutron measurements, which have different experimental timescales, suggest that relaxation within the particles between states above and below theMorin transition is not prevalent (i.e. an average value measured due to relaxation betweenstates cannot explain the apparent intermediate angles). This result has been furtherverified by in-field Mössbauer measurement of the α-Fe 2 O 3 /NiO nanocomposite at 50 K.In case of relaxation between states it is expected that applying a field of 6 T would favourthe state above the Morin transition, which has a small magnetic moment due to cantedantiferromagnetism, but this was not observed.1.1.Normalized peak areaNormalizedpeakar0.0.0.0.0.(46°) 33(003)(101)0 100 200 300Temperature (K)Fig. 5.7. Integrated intensities of magnetic reflections of α-Fe 2 O 3 nanoparticles incomposite with NiO nanoparticles.This, in all, leads us to draw the following picture of the spin structure (for illustration seeFig. 5.8). With decreasing temperature (170 – 30 K) the sublattice magnetizations of theindividual particles rotate coherently out of the plane. Neither domain wall formation norrelaxation between states has been observed to otherwise explain the data. At ~ 30 K, allthe particles seem to have acquired their final state, but we do not know if the sublatticemagnetizations of the individual particles flip directly into their low temperature states orif they gradually turn with temperature. Distinct intermediate states have previously beenproposed existing in more bulk-like α-Fe 2 O 3 during the Morin transition [Vandenberghe etal., 2001], and they are not prohibited for symmetry reasons [Lebech and Sikora, 2004],but usually they do not occur because the magnetic anisotropy does not favour it.TFig. 5.8. Schematic illustration showing coherent out-of-(001)-plane rotation in α-Fe 2 O 3 nanoparticles with decreasing temperatures.

46 Nanomagnets and their interactions – Part 1Origin of the transitionThe origin of the spin reorientation at low temperatures in the α-Fe 2 O 3 /NiO compositemay be due to exchange interactions between particles, similar to the spin reorientationobserved in the pure α-Fe 2 O 3 system (Section 4.1.3, Paper VIII). We propose thefollowing model for explaining the spin reorientation based on interactions. A schematicdrawing of two interacting particles is shown in Fig. 5.9. The magnetic energy of an α-Fe 2 O 3 particle which interacts with a NiO particle may be written asE = K 1 V sin 2 θ - E int cos(θ-θ 0 ). (Eq. 5.1)Here, θ 0 denotes the angle between the sublatttice magnetization of NiO and the [001] axisof α-Fe 2 O 3. If the expression is differentiated with respect to θ in order to find possibleenergy minima, we obtain∂E/∂θ = 2K 1 V sinθ cosθ + E int sin(θ-θ 0 ) = 0 (Eq. 5.2)In order to simplify this, we choose θ 0 = 0, and find the following solutionssinθ = 0 or | cosθ | = | E int / K 1 V |, (Eq. 5.3)which shows that both a complete Morin transition and a partial transition are possible.From the second solution we see that θ decreases with decreasing temperature, since | K 1 |gradually decreases with decreasing temperature (Paper III/Section 3.1.2), and that θmight vary due to a distribution among the particles of the parameters E int , K 1 , and V.These results are qualitatively in accordance with our observations.We, however, do not fully understand the origin of the transition. One of the puzzling factsis that the transition is not observed for the α-Fe 2 O 3 /CoO composite, where E int is large(Section 5.1.1). In connections with this, we note that we neither observe the transition forα-Fe 2 O 3 nanoparticles in composite with NiO particles, which are larger than ~15 nm,suggesting that a large anisotropy or volume do not lead to the effect. It may be that largerparticles are not so likely to assemble in a way which gives rise to the effect. We areinvestigating the origin of the effect further. Below are stated other properties, whichcould play a role for the effect if it is caused by inter-particle interactions:• The ordering temperatures. (The blocking temperature of the NiO particles is about120 K (Paper IV), which is the intermediate temperature for the induced Morintransition. The CoO particles are expected to have an ordering temperature close toits Néel temperature, which is close to the temperature where the particlesassemble.)• The direction of the sublattice magnetization in NiO and CoO nanoparticles.• The coupling (e.g. the directions of the sublattice magnetizations of neighbouringparticles may be either parallel or perpendicular, e.g. [Finazzi et al., 2004])• The interface between the particles and the number of uncompensated spins at theinterface, e.g. [Finazzi et al., 2004]

Chapter 5: Inter-particle exchange interactions in composites 47One may consider other possibilities than the transition being caused by inter-particleexchange interaction. The general lack of a Morin transition in α-Fe 2 O 3 nanoparticles hasbeen suggested to be due to the large stress and surface anisotropy in the nanoparticles. Itis possible that an assembly of α-Fe 2 O 3 and NiO nanoparticles may change the surface ofthe α-Fe 2 O 3 nanoparticles in such a way (e.g. by structural relaxation of the surfacestructure) that it allows the Morin transition to take place. However, if this was the casewe would expect the particles to be either above or below the Morin transition and not totake the observed intermediate states (where θ ≠ 0 and θ ≠ 90 degrees). So, it is notexpected that this alone can explain the spin rotation.θθ 0Fig. 5.9. Illustration of α-Fe 2 O 3 nanoparticle (white) assembled with NiOnanoparticle (grey).In conclusion of this section, it has been shown that when α-Fe 2 O 3 nanoparticles are wetmixedwith NiO nanoparticles, a spin reorientation transition akin to the Morin transitioncan be induced in the α-Fe 2 O 3 particles. The spin-reorientation occurs coherently withinthe particles. The spin-reorientation has similarities with the out-of-(001)-plane sublatticemagnetization observed in pure samples of interacting α-Fe 2 O 3 nanoparticles. We proposethat the magnetic coupling between NiO and α-Fe 2 O 3 nanoparticles is important forinducing the Morin-like transition. Certainly, there are still unresolved aspects related tothe understanding of this intriguing phenomenon.5.1.3 Assembly of α-Fe 2 O 3 and NiO nanoparticlesWe considered the possibility that the particles in the α-Fe 2 O 3 /NiO and in the α-Fe 2 O 3 /CoO systems might have a tendency to assemble themselves with a preferredorientation, when mixed in water. If they are to assemble with preferred orientations, itseems likely that this will be such that hexagonal “ABABAB…” close-packing of oxygenionsin α-Fe 2 O 3 is continued into the cubic “ABCABC…” close-packing of NiO or ofCoO, i.e. the (001) planes of α-Fe 2 O 3 become parallel to the (111) planes of NiO or CoO(see Fig. 5.10). By doing so, epitaxial attachment can be achieved because the inter-atomicdistances between the oxygen atoms in these plane are very similar for the compounds.Moreover, by doing so, antiferromagnetic modulation vectors are parallel, and this maylead to least spin frustration.

48 Nanomagnets and their interactions – Part 1Fig. 5.10. Illustration of nanoparticles with hexagonal close packing (like α-Fe 2 O 3 )and cubic close packing (like NiO) assembling together.Revealing the exact relative orientation of the particles calls for HREM studies. Weanticipated that it would be very difficult to achieve detailed information on a composite.However, we found several examples, which supported the existence of preferredattachment of α-Fe 2 O 3 and NiO nanoparticles. A HREM image is shown in Fig. 5.11. It isa very interesting result because it shows assembly with preferred orientation in acomposite sample where the particles have been brought together in water. In the α-Fe 2 O 3 /CoO system we have not yet been able to reveal preferred attachment between thedifferent types of particles by HREM.α-Fe 2 O 3(006)(030)(111)(022)NiOFig. 5.11. HREM image of α-Fe 2 O 3 nanoparticle and a small agglomerate of NiOnanoparticles, which have assembled such that the (006) planes of α-Fe 2 O 3 are parallel to the (111)planes of NiO (i.e. the [001] axis of α-Fe 2 O 3 is parallel to the [111] axis of NiO).5.1.4 Controlling the assembly?In Chapter 4 it was proposed that it would be interesting to investigate if exchangecoupling really is a driving force for the assembly of antiferromagnetic magneticnanoparticles by letting particles agglomerate above and below their Néel temperature. Weconducted a few preliminary experiments where suspensions of α-Fe 2 O 3 and CoO

Chapter 5: Inter-particle exchange interactions in composites 49nanoparticles were mixed and dried at temperatures approximately 15 degrees below andabove the Néel temperature of CoO. Mössbauer spectra of these samples did not showdistinct differences. However, there are many parameters which are varied during thistreatment in addition to temperature, e.g. drying time is significantly longer for thecomposites dried at 5 °C than at 35 °C. Brownian motion may also be different. Moreover,a temperature difference of 30 degree may not be sufficient. Also, since we have notobserved preferred assembly between α-Fe 2 O 3 and CoO nanoparticles, this system maynot be the most appropriate. So, although this particular experiment did not show effectsof assembly being driven by exchange coupling, the experiment does not rule out that thepossibility may exist.5.2 ConclusionsWe have shown that effects of inter-particle exchange coupling can be achieved betweendifferent types of magnetic nanoparticles dried from aqueous suspensions. Mixing 9 nm α-Fe 2 O 3 or 7 nm γ-Fe 2 O 3 particles with CoO particles lead to a suppression of thesuperparamagnetic relaxation, while mixing the same particles with NiO nanoparticleslead to a faster relaxation. Magnetization measurements showed that the γ-Fe 2 O 3 particlesmixed with CoO particles had their coercivity three times enlarged, while if mixed withNiO particles, their coercivity was slightly reduced. The differences on relaxation andcoercivity from mixing with CoO and NiO nanoparticles are ascribed to the differences inanisotropy of the CoO and NiO particles. For α-Fe 2 O 3 nanoparticles mixed with NiOnanoparticles, a Morin-like phase transition was observed induced. Moreover, the α-Fe 2 O 3and NiO nanoparticles have been found by HREM to assemble in water with preferredorientation such that the [001] axis of α-Fe 2 O 3 is parallel to the [111] axis of NiO. Wehave considered possible explanations for the Morin-like transitions including that it couldbe caused by inter-particle exchange interactions.5.3 OutlookThe results have shown that composites of magnetic nanoparticles prepared by dryingaqueous suspension can achieve properties, which differ significantly from those of theindividual constituents. This may have implications for how new magnetic materials canbe fabricated. Although many details of the origin of the effects are not fully understoodyet, one may start thinking about tailoring magnetic materials from different types ofnanoparticles to be prepared from aqueous suspensions.One may envisage building objects such as nanostructured devices from assembly ofindividual nanoparticles. For instance one could imagine ultra-small MRAMs being buildby self-assembly of different types of nanoparticles. Therefore the preferred assembly ofnanoparticles in the α-Fe 2 O 3 /NiO composite is particularly interesting because it showsthat different types of nanoparticles can be made to assemble.For further studies in order to understand the assembly of nanoparticles, it could beprofitable to prepare suspensions of α-Fe 2 O 3 and NiO nanoparticles, which can be studiedby Mössbauer. This may elucidate whether the assembly takes place already in thesuspension (indicated as a Morin-like transition in the frozen suspension) or whether ittakes place during the drying (only the Morin-like transition in the dried samples).

50 Nanomagnets and their interactions – Part 16. Ring-shaped magnetsIn this Chapter results obtained on ring-shaped Co magnets by use of magnetic forcemicroscopy are reported. Domain structures have been revealed and magnetic switchingfields quantified for rings with given dimensions (Papers X and XI). The reader may liketo review Section 1.1.6 prior to reading further.6.1 Results and discussions6.1.1 Domain states of magnetic ringsAfter saturation in a field of 10 kOe, the studied Co rings were found to be in the “onion”state [Rothman et al., 2001] at remanence (Paper X and XI). As an example of this, Fig.6.1a shows an AFM image of the lower part of the array of 520/170 nm rings and Fig.6.1b shows the corresponding MFM image. The MFM image shows dark and lightcontrasts on opposite sides of the rings for every single ring. These contrasts arise from thetwo 180-degree domain walls in the bi-domain onion state. Looking closely at the rings,we notice that the contrasts are displaced toward the edge of the rings (Figs. 6.2a-b). Thisis because an in-plane 180-degree domain wall in a narrow ring (Fig. 6.2c) resembles thatof a radially distributed “dipole” (see schematic drawing of spin structure in Fig. 6.2d).When imaged by MFM with the tip some tens of nanometers above sample surface, thewall ends up looking more like a “monopole” displaced towards the edge of the ring [Zhu,2002; Paper X].(a)(b)Fig. 6.1. (a) AFM image and (b) corresponding MFM image of lower part of arrayof 520/170 nm rings after saturation. The direction of the applied field was along the rows, to theright. All states are onion states. The dark and light MFM contrasts represent domain walls.Widths of scans are 9 µm.(a)(d)(b)(c)Fig. 6.2. Onion state. (a)AFM image and (b) MFM image of oneof the rings in the onion state in Fig. 6.1.(c) Illustration of the two domainmagnetizations of the onion state withtwo in-plane 180-degree domain wallsopposing each other. The magnetizationis in the plane of the ring. The dottedlines represent the centre of the 180-degree domain walls. (d) Schematicillustration of the magnetic spins in theonion state.

Chapter 6: Ring-shaped magnets 51By applying a reverse field of increasing strength, and measuring the states at remanence,we find that the contrasts disappear indicating the switching from onion state to vortexstate (see Fig. 6.3). The mechanism of the onion to vortex transition is explained as thatone of the two domain walls of the onion state will unpin and then move around the ringuntil it meets the other domain wall, where they annihilate [Rothman et al., 2001]. Withincreasing reverse field, domain walls will nucleate within the vortex state and a reverseonion state forms [Rothman et al., 2001]. However, after we had imaged a number ofarrays over a range of reverse fields, we noticed that prior to vortex formation the domainwalls often stabilized next to one another forming a 360-degree domain wall (such domainwall configuration is pointed out by the arrows in the MFM image in Fig. 6.3b andillustrated in Fig. 6.4). This configuration appeared to be a metastable state, which wecalled the “twisted state” (Paper X).(a)(b)Fig. 6.3. (a) AFM image and (b) corresponding MFM image of lower part of arrayof 520/170 nm rings after applying a reverse field (pointing to the left) of -108 Oe. The MFMcontrasts have disappear in a number of the rings, e.g. in the two rings in the upper left corner,compared to image of the same rings in Fig. 6.1b, signifying vortex formation. The white arrowspoint out apparent stabilization of domain walls next to one another before vortex formation (i.e.ring in the twisted state). Widths of scans are 9 µm.(a)(d)(b)(c)Fig. 6.4. Twisted state. (a)AFM image and (b) MFM image of one of therings in the twisted state in Fig. 6.3. (c)Illustration of the domain magnetizations inthe twisted state, where the two domain wallsare stabilized next to one another forming a360-degree domain wall. (d) Illustration of thespins of the magnetic ions in the twisted state.The state is probably stabilized by the dipole interaction between the two domain wallsand the exchange energy in between the walls (Paper X). The domain walls may attractone another due to the dipole interaction, but at the same time the exchange interactionbetween Co-ions in the region between the walls, keep the walls apart. This leads to anenergy barrier needed to be overcome in order for the spin of Co ions to flip and the vortexstate to be achieved. If such stabilization occurs, the states should be distinct. In the

52 Nanomagnets and their interactions – Part 1following section, a detailed characterization of the state in Co rings addressing this issueis provided. Many of the details reported below are also found in Papers X and XI. PaperX reports the discovery of this metastable state and Paper XI gives a more detailed accounton the state. The present Chapter can be considered as the author’s report on resultsobtained while at MIT and from subsequent data analysis. The existence of the twistedstate in small, narrow rings has been confirmed by micromagnetic simulations (Papers Xand XI). Later studies have revealed the state in magnetic ellipses, too [Castaño et al.,2003].6.1.2 Characteriztion of the twisted stateThe twisted state was found to occur in a considerable number of the studied Co rings. Foran array of 520/170 nm rings, MFM images were recorded at 28 different fields up to 496Oe and the twisted state was found in 15 different rings out of an array of 64 rings.Imaging the same array only at 17 fields over the same field range revealed only 8 ringswith a twisted state. The 520/135 nm rings, sampled at 7 fields up to 828 Oe, showed atwisted state in 5 out of 60 rings; the 520/110 nm rings were sampled at 13 fields up to992 Oe and showed a twisted state in 8 out of 62 rings. The results are summarized inTable 6.1 together with those of 360/110nm rings. Dense sampling rate is clearlyimportant to resolve the existence of the state.dimensions# offieldsrange(Oe)# ofRings520/170 28 -496 64 15520/135 7 -828 60 5520/110 13 -992 61 8360/110 17 -910 62 20# oftwistedstatesTable 6.1. Appearance of twisted state in four arrays of rings with differentdimensions (diameter/width). MFM images were recorded at a number of fields (# of fields) over afield range (range) for each array. Only those rings (# of rings), which were fabricated withoutmajor defects, have been studied. In a number of the studied rings the twisted state occurred (# oftwisted states).The twisted state has typically been found to occur before the formation of the vortex stateas the series of MFM images in Fig. 6.5 show. Sometimes the vortex state is not observedbefore the reverse onion state occurs. Only once has the twisted state been found to occurafter annihilation of the vortex state.One can identify four variants of the twisted state depending on which of the two domainwalls has moved around the ring and which direction it has chosen. All four variants havebeen observed and are shown on Figs. 6.6a-d. In Figures 6.6a, and 6.6d, the direction ofthe magnetization is clockwise, while in Figs. 6.6b and 6.6c, the direction ofmagnetization is counter clockwise. A neat thing about the twisted state is that due to itsstray fields, it is possible to "see" the direction of magnetization in the rings and from thatone can deduce the direction of magnetization in the succeeding vortex state. In symmetricrings and aligned fields, none of the states should be preferred over one another. Indeed,we find experimentally that there is 50 % chance of either direction of magnetization.

Chapter 6: Ring-shaped magnets 53(a)250 nm(b)-28 Oe(c)-162 Oe(d)-267 Oe(e)-299 Oe -496 Oe(f)Fig. 6.5. (a) AFM image of 520/170 nm Co ring. The ring was saturated by an inplanefield pointing to the right. MFM images of the ring showing the evolution of remanentmagnetic states as a function of reverse field. (b) Onion state. The grey arrows in this imageindicate the magnetization directions in the ring. (c) Twisted state forms at -162 Oe: The adjacentlight and dark contrasts indicate that the domain wall to the right in (b) has depinned and movedaround the ring until it has stabilized next to the other wall. (d) The twisted state is stable over afield range of about 100 Oe. (e) Vortex state: The two domain walls have annihilated and theresulting flux-closed state produces no MFM contrast. (f) Reverse onion state: Two domain wallshave nucleated producing an MFM contrast, which is roughly a negative image of that in (a).θ(a)(b)(c)(d)(e)(fθFig. 6.6. MFM images of states in 520/170 nm rings. (a-d) Four variations of thetwisted state. In (b) it is seen how the angle (θ) between the domain walls is measured. (e)Example of pinned state. (f) Example of onion state, where the domain walls are not separated byexactly 180 degrees.We find that the field range stability of the twisted state in the rings can be large, up toseveral hundred Oe, but often the twisted state in a certain ring was only observed at onefield. The stability ranges for the twisted states of the 520 nm-diameter Co rings withdifferent widths are shown in Fig. 6.7. The plot shows that, on average, the twisted statesoccur at lower fields for the wider rings and that the distribution of fields, at which thetwisted states occur, is largest for the narrow rings.Repeated measurements, which have only been obtained with different sampling rate,show that the probability for the twisted state to occur in the same rings is less than 30 %,and it often occurs at different fields.

54 Nanomagnets and their interactions – Part 1170135110-1000 -750 -500 -250 0Field (Oe)Fig. 6.7. Plot showing the field range where twisted states exist in 520 nm-diameterCo rings of width 110, 135 and 170 nm. Each bar represent the range over which the twisted statewas seen in an individual ring.In the MFM images of twisted states, the adjacent light and dark contrasts appear distinctand representative of domain walls being stabilized next to one another. In order toquantify this observation, the angle between the domain walls was found by measuring theangle (θ) between the two lines going through the centre of the ring and through the twoMFM contrasts, as indicated on Fig. 6.6b. The angles of the 15 twisted states in the520/170 nm rings, are plotted on the histogram in Fig. 6.8. For these rings the averagevalue is found to be 33 (±8) degrees. This well defined angle makes it unlikely thatstabilization of the twisted state is merely controlled by random pinning of the wallsaround the ring. Random pinning of walls occurs in the arrays, but this gives a differentMFM contrast; one example is shown on Fig. 6.6e. In the array of 520/170 nm rings,which were sampled at 28 different fields, random pinning occurred in four rings and theangles between the walls varied between 50 and 130 degrees as seen on the histogram inFig. 6.8. In rings showing no twisted or pinned states, the angle between the domain wallsin the onion state was measured and plotted in Fig. 6.8, to give an impression of thevariations in domain wall positions of this well-defined state and of the precision by whichthe angle measurements could be performed. The angle between the walls in the onionstate is around 180 degrees, as expected, but some variation is certainly found, see e.g.Fig. 6.6f where the walls in the onion state are not exactly opposing each other.Number of occurrences108642Twisted statesPinned statesOnion states00 50 100 150 200 250Angle between domain walls (degree)Fig. 6.8. Histogram of the angles between the domain walls in Co rings, 520 nm indiameter and 170 nm wide. The angles between the walls in the twisted state are grouped around30 degrees. The angles between the walls in the onion state are close to 180 degrees while the wallseparations in randomly pinned states are found in the range between 50 and 130 degrees.

Chapter 6: Ring-shaped magnets 55The angles between the walls in twisted states in arrays of 520 nm-diameter rings, 170,135 and 110 nm wide, and in one array of smaller rings (320 nm in diameter, 110 nmwide) were measured and the results are summarized in Table 6.2. In all four cases, theangle between the domain walls in the twisted state is well defined within some degrees,while pinned states occurred only in a few rings in each array and with distinctly differentangles. It can be seen from Table 6.2 that the angle between the walls in the twisted stateincreases with increasing width of the rings and with decreasing diameter of the rings.dimensions angle (deg.)520/170 33(±8)520/135 24(±6)520/110 20(±2)360/110 39(±11)Table 6.2. The mean angle between the domain walls in the twisted state and itsvariance for rings with given dimensions.Based on this investigation of the twisted state, where we have found that the state isabundant and has a well-defined inter-wall angle, which depends on ring dimensions, weconclude that the twisted state is a distinct state being stabilized in the rings by the dipoleinteraction between the walls competing with the exchange interaction in the regionbetween the walls. Although random pinning cannot explain the existence of the twistedstate, the fact that the state is observed only in some of the rings and with a varyingstability makes it likely that its existence is sensitive to small variations in the morphologyof the rings.6.1.3 Remanent hysteresis loops of the ring arraysFigures 6.5b-f show MFM images of the evolving remanent states as a function of reversefield in a 520/170 nm ring. For this particular ring, the field required to destruct the onionstate, H C1 , is -162 Oe, while the field for creation of the reverse onion state, H C2 , is -496Oe. Figure 6.9 shows the remanent hysteresis loop of the ring constructed from MFMimages by attributing the value +1 to the onion state, 0 to the vortex state as well as to thetwisted state (since in normal magnetization measurements they are likely to beindistinguishable), and -1 to the reverse onion state. A complete loop is drawn as a guideto the eye.1.0Remanence0.50.0-0.5-1.0-600 -400 -200 0 200 400 600Field (Oe)Fig. 6.9. Hysteresis loop of the ring constructed from MFM images of the 520/170nm ring in Fig. 6.5.

56 Nanomagnets and their interactions – Part 1By superposition of the hysteresis loops of the individual rings, it is possible to obtaininformation about the variations of the magnetization reversals within an array of similarsized rings. Moreover, one can compare general trends in behaviour between differentarrays. Figure 6.10 shows the collective hysteresis loops for three arrays of Co rings, 520nm in diameter and 170, 135, and 110 nm wide. We see that due to variations in H C1 andH C2 between different rings, the hysteresis loop of the array of the 170 nm wide rings inFig. 6.10 is smeared out and the vortex plateau is lacking in contrast to the loop of a singlering seen in Fig. 6.9. Comparison of the three collective hysteresis loops in Fig. 6.10shows that the average switching fields, and , are larger for narrower rings: and are around -170 and -410 Oe, -330 and -690 Oe, and -470 and -850 Oefor the 170 nm, 135 nm, and 110 nm wide rings, respectively. Moreover, from the loops inFig. 6.10, we observe that the variation in H C1 within the arrays is larger for the narrowrings, and the variation in H C1 is larger than the variation in H C2 in all three arrays.1.00.5110 nm135 nm170 nmRemanence0.0-0.5-1.0-1200 -800 -400 0 400 800 1200Field (Oe)Fig. 6.10. Remanent hysteresis loops of three arrays of Co rings. The rings are 520nm in diameter and 110, 135, or 170 nm wide. The hysteresis loops are constructed from MFMimages taken at reverse fields and normalized to 1 at saturation. Complete loops are drawn asguides to the eye.6.1.4 Domain wall creation and annihilation: MicromagneticsIn order to create the vortex state from the onion state, a domain wall has to unpin andmove around the ring [Rothman et al., 2001]. The dependence of on the width ofthe rings is likely to be related to the size of the dipole moment of the domain walls,because it influences the strength of magnetostatic interaction with an applied field. Forthe narrower rings the dipole moments of the domain walls are smaller and thus it requiresa larger field to move the domain walls. It is known that notches and other asymmetriescan pin domains walls [Kläui et al., 2002a; Rothman et al. 2001]. Surface defects andmicrostructural variations will inevitable form during lithographic processing. These maycause an increase in H C1 but are also likely to cause variations in H C1 , especially in thenarrow rings, where surface to volume ratio is largest.During the vortex annihilation process, a reverse domain is nucleated on the inside of thering [Lopez-Diaz et al., 2000]. This process has been found to be strongly dependent onthe inner-curvature of the rings [Lopez-Diaz et al., 2000; Kläui et al., 2002b]. Inagreement with this we see from Fig. 6.10 that increases with decreasing ring

Chapter 6: Ring-shaped magnets 57width. This has been explained as follows: When the width is decreased, the spins in therings are more strongly aligned and rotation of the spins is harder. Correspondingly, it hasbeen found in [Castaño et al., 2003] that domain wall nucleation in elliptical rings ishardest in the least sharply curved parts of the rings.Our results of the dependence on ring width are in good agreement with resultsfrom [Kläui et al., 2002b], who studied magnetization curves of 1.6 µm- and 0.8 µmdiameterCo rings, which were in the vortex state at remanence. By MOKE measurementsand micromagnetic simulations, they found that the field for transition from the vortexstate into the onion state was increasing with decreasing width; in particular for 10 nmthick Co rings, they found the switching fields (H C2 ) of 225 and 100 nm wide rings to beabout 600 and 980 Oe. Since we find similar switching field values for smaller rings withsimilar widths, our results support the findings that vortex annihilation is more sensitive tothe widths of the rings than to the diameters [Kläui et al., 2002b].It is noticeable that within each array we find that the distribution of H C1 is wider than thedistribution of H C2 . These differences in switching field distributions of H C1 and H C2 arelikely to be linked to the different processes causing the transitions. In the onion-to-vortexstate-transition,a domain wall has to unpin, and this makes the process very sensitive tosurface defects such as notches. On the contrary, the vortex-to-reverse-onion-statetransitionoccurs through domain nucleation which might be more dependent on the“intrinsic” properties of the ring such as magnetic shape anisotropy.6.2 ConclusionsWe have measured the remanent states of Co rings by MFM and discovered a metastablestate. This so-called twisted state is a stabilization of two adjacent 180-degree domainwalls, formed from movement of a domain wall of the onion state, prior to vortexformation. The state is stabilized by dipole interactions between the walls and by theexchange energy in the region between the walls. We have characterized the twisted statewith respect to domain wall separation, occurrence, and stability, and from this weconclude that the state is distinct. By obtaining collective remanent hysteresis loops forarrays of 64 rings, we were able to gain information on the size and distribution inswitching fields. We found that the narrow rings switch at higher fields and have largerdistributions in switching field from onion to vortex state. The distribution in switchingfields appears larger for the vortex formation than for the vortex annihilation.6.3 OutlookIt may seem surprising that even simple symmetric magnetic objects can attain a range ofdifferent domain structures. Indeed, the existence of the twisted state was not anticipated.While it is beyond the scope of this work to address in detail questions regarding magneticrings for data storage, a few comments on the potential use of the states, related to resultspresented here, seem appropriate.In order to use the vortex state in data storage devices it is of crucial importance to be ableto attain this state in a controllable way. The nucleation of the vortex state is a complicatedprocess seen from a micromagnetic perspective [Lopez-Diaz et al., 2000]. The existence

58 Nanomagnets and their interactions – Part 1of the metastable twisted state stresses this. Assessing the twisted state in more detailmight help to shed more light on the process or to achieve better control. The twisted stateis well-defined state which may also allow for more general studies of domain wallannihilation.For applications, the vortex state may be reached by applying a circumferential field froma current running through the core of the ring, rather than by applying an in-plane field.This also allows for better control of the chirality of the vortex magnetization.Although we observed no strong influence of dipole interactions between the rings, it isworth examining in further detail the possible influence of dipole interaction, e.g. on thestability of the states. It is anticipated that the stray fields of a twisted state is smaller thanthat of an onion state, because adjacent walls have more constricted stray fields thanseparated walls.If dipole-interactions between narrow rings are insignificant, one may consider using theonion or the twisted state instead of the vortex state for data storage. When using an inplanefield, the creation of the onion state seems to be less dependent on defects than theformation of the vortex state and since is rather small (

References 59References[Ambrose and Chien, 1996] T. Ambrose and C.L. Chien, Phys, Rev. Lett. 76 (1996) 1743.[Anhøj et al., 2004] T. Anhøj, C.S. Jacobsen, and S. Mørup, J. Appl. Phys. 95 (2004)3649.[Banfield et al., 2000]. J.F. Banfield, S.A. Welch, H. Zhang, T.T. Ebert, and R. Lee Penn,Science 289 (2000) 751.[Barbara and Chudnowsky, 1990] B. Barbara and E. M. Chudnovsky, Phys. Lett. A 145(1990) 205.[Berkowitz and Takano, 1999] A.E. Berkowitz and K. Takano, J. Magn. Magn. Mater. 200(1999) 1.[Borchers et al., 1995] J.A. Borchers, R.W. Erwin, S.D. Berry, D.M. Lind, J.F. Ankner, E.Lochner, K.A. Shaw, and D. Hilton, Phys. Rev. B 51 (1995) 8276.[Brown, 1963] W.F. Brown Jr., Phys. Rev. 130 (1963) 167.[Butter et al., 2003] K. Butter, P.H.H. Bomans, P.M. Frederik, G.J. Vroege, andA.P. Philipse, Nat. Mater. 2 (2003) 88.[Bødker and Mørup, 2000] F. Bødker and S. Mørup, Europhys. Lett. 52 (2000) 217.[Bødker et al., 2000a] F. Bødker, M.F. Hansen, C.B. Koch, K. Lefmann, and S. Mørup,Phys. Rev. B 61 (2000) 6826.[Bødker et al., 2000b] F. Bødker, M.F. Hansen, C.B. Koch, and S. Mørup, J. Magn. Magn.Mater. 221 (2000) 32.[Castaño et al., 2003] F.J. Castaño, C.A. Ross, and A. Eilez, J. Phys. D: Appl. Phys. 36(2003) 2031.[Chudnowsky and Günther, 1998] E.M. Chudnowsky and L. Günther, Phys. Rev. Lett. 60(1998) 661.[Coey, 1971] J.M.D. Coey, Phys. Rev. Lett. 27 (1971) 1140.[DI, 2001] Digital Instruments, www.di.com, 2001.[Dickson and Frankel, 1992] D.P.E. Dickson and R.B. Frankel, p. 393-402 in J.L.Dormann and D. Fiorani (editors), Magnetic Properties of Fine Particles, North-Holland,Amsterdam, 1992.[Djurberg et al., 1997] C. Djurberg, P. Svedlindh, P. Nordblad, M.F. Hansen, F. Bødker,and S. Mørup, Phys. Rev. Lett. 79 (1997) 5154.

60 Nanomagnets and their interactions – Part 1[Dormann and Fiorani, 1992] J.L. Dormann and D. Fiorani (editors), Magnetic Propertiesof Fine Particles, North-Holland, Amsterdam, 1992.[Dormann et al., 1997] J.L. Dormann, D. Fiorani, and E. Tronc, Adv. Chem. Phys. 98(1997) 283.[Dormann et al., 1999] J.L. Dormann, D. Fiorani, and E. Tronc, J. Magn. Magn. Mater.202 (1999) 251.[Dunlop and Özdemir, 1997] D.J. Dunlop and Ö. Özdemir, Rock magnetism:fundamentals and frontiers, Cambridge, 1997.[Finazzi et al., 2004] M. Finazzi, M. Portalupi, A. Brambilla, L. Duò, G. Ghiringhelli, F.Parmigiani, M. Zacchigna, M. Zangrando, and F. Ciccacci, Phys. Rev. B. 69 (2004)014410.[Ghazali and Lévy, 2003] A. Ghazali and J-C. Lévy, Phys. Rev. B 67 (2003) 064409.[Greenwood and Gibb, 1971] N.N. Greenwood and T.C. Gibb, Mössbauer spectroscopy,Chapman and Hall, 1971.[Grütter et al., 1992] P. Grütter, H.J. Mamin, and D. Rugar, Magnetic force microscopy(MFM), in Scanning tunneling microscopy II, Editors: R. Wisendanger and H.-J.Güntherodt, Springer, 1992.[Hansen et al., 1997] M.F. Hansen, F. Bødker, S. Mørup, K. Lefmann, K.N. Clausen, andP.-A. Lindgård, Phys. Rev. Lett. 79 (1997) 4910.[Hansen, 1998] M.F. Hansen, Ph.D. Thesis, Technical University of Denmark, 1998.[Hansen and Mørup, 1998] M.F. Hansen and S. Mørup, J. Magn. Magn. Mater. 184 (1998)262.[Hansen et al., 2000a] M. F. Hansen, F. Bødker, S. Mørup, K. Lefmann, K.N. Clausen,and P.-A. Lindgård, J. Magn. Magn. Mater. 221 (2000) 10.[Hansen et al., 2000b] M.F. Hansen, C.B. Koch, and S. Mørup, Phys. Rev. B 62 (2000)1124.[Harris et al., 1999] J. G. E. Harris, J. E. Grimaldi, D. D. Awschalom, A. Chiolero, and D.Loss, Phys. Rev. B 60 (1999) 3453.[Hendriksen et al., 1993] P.V. Hendriksen, S. Linderoth, and P.-A. Lindgård, Phys. Rev. B48, (1993) 7259.[IBM, 2001] www.research.ibm.com/thinkresearch/pages/2001/20010202_mram.shtml

References 61[Jones et al., 2000] F. Jones, A.L. Rohl, J.B. Farrow, and W. van Bronswijk, Phys. Chem.Chem. Phys. 2 (2000) 3209.[Jonsson et al., 1998] T. Jonsson, P. Svedlindh, and M.F. Hansen, Phys. Rev. Lett. 81(1998) 3976.[JPL, 2004] Webster, G. & Brown, D. Mineral in Mars 'Berries' Adds to Water Story.http://www.jpl.nasa.gov/releases/2004/88.cfm (March 18, 2004).[Keffer and Kittel, 1952] F. Keffer and C. Kittel, Phys. Rev. 85 (1952) 329.[Kimel et al., 2004] A.V. Kimel, A. Kirilyuk, A. Tsvetkov, R.V. Pisarev, and Th. Rasing,Nature 429 (2004) 850.[Kittel, 1951] C. Kittel, Phys. Rev. 82 (1951) 565.[Kläui et al., 2002a] M. Kläui, C.A.F. Vaz, J.A.C. Bland, W. Wernsdorfer, G. Faini, andE. Cambril, Appl. Phys. Lett. 81 (2002) 108.[Kläui et al., 2002b] M. Kläui, L. Lopez-Diaz, J. Rothman, C.A.F. Vaz, J.A.C. Bland, andZ. Cui. J. Magn. Magn. Mater. 240 (2002) 7.[Kläui et al., 2003a] M. Kläui, C.A.F. Vaz, J. Rothman, J.A.C. Bland, W. Wernsdorfer, G.Faini, and E. Cambril, Phys. Rev. Lett. 90 (2003) 097202.[Kläui et al., 2003b] M. Kläui, C.A.F. Vaz, J.A.C. Bland, W. Wernsdorfer, G. Faini, andE. Cambril, L.J. Heyderman, Appl. Phys. Lett. 83 (2003) 105.[Klausen et al., 2002] S.N. Klausen, P.-A. Lindgård, K. Lefmann, F. Bødker, and S.Mørup, Phys. Stat. Sol. A 189 (2002) 1039.[Klausen et al., 2003] S. N. Klausen, K. Lefmann, P.-A. Lindgård, K. N. Clausen, M. F.Hansen, F. Bødker, S. Mørup, and M. Telling, J. Magn. Magn. Mater. 266 (2003) 68.[Kodama et al., 1997] R.H. Kodama, S.A. Makhlouf, and A.E. Berkowitz, Phys. Rev.Lett. 79 (1997) 1393.[Kopcewicz, 1994] M. Kopcewicz, Mössbauer effect, Encyclopedia of applied physics,vol. 11, p. 1-22. Editor: G.L. Trigg. 1994.[Kündig et al., 1966] W. Kündig, K.J. Ando, G. Constabaris, and R.H. Lindquist, Phys.Rev. 142 (1966) 327.[Lebech and Sikora, 2004] B. Lebech and W. Sikora, to be published.[Lee Penn and Banfield, 1998] R. Lee Penn and J.F. Banfield, Science 281 (1998) 969.

62 Nanomagnets and their interactions – Part 1[Lee Penn and Banfield, 1999] R. Lee Penn and J.F. Banfield, Geochim. Cosmochim.Acta 63 (1999) 1549.[Lee Penn et al., 2001] . R. Lee Penn, G. Oskam, T.J. Strathmann, P.C. Searson, A.T.Stone, and D.R. Veblen, J. Phys. Chem. B 105 (2001) 2177.[Lefmann et al., 2001] K. Lefmann, F. Bødker, S.N. Klausen, M.F. Hansen, K.N. Clausen,P.-A. Lindgård, and S. Mørup, Europhys. Lett. 54 (2001) 526.[Li et al., 2001] S.P. Li, D. Peyrade, M. Natali, A. Lebib, Y. Chen, U. Ebels, L.D. Buda,and K. Ounadjela, Phys. Rev. Lett. 86 (2001) 1102.[Lopez-Diaz et al., 2000] L. Lopez-Diaz, J. Rothman, M. Kläui, and J.A.C. Bland, IEEEtransactions on magnetics 36 (2000) 3155.[Luo et al., 1991] W. Luo, S.R. Nagel, T.F. Rosenbaum, and R.E. Rosensweig, Phys. Rev.Lett. 67 (1991) 2721.[Meiklejohn and Bean, 1956] W.H. Meiklejohn and C.P. Bean, Phys. Rev. 102 (1956)1413.[Menon and Gupta, 1999] A.K. Menon and B.K. Gupta, NanoStructured Materials 11(1999) 965.[Morrish, 1966] A.H. Morrish, The physical principles of magnetism, John Wiley & Sons,New York, 1966.[Morrish, 1994] A.H. Morrish, Canted antiferromagnetism: Hematite, World Scientific,Singapore, 1994.[Mørup and Topsøe, 1976] S. Mørup and H. Topsøe, Appl. Phys. 11 (1976) 63.[Mørup, 1983] S. Mørup, J. Magn. Magn. Mater. 37 (1983) 39.[Mørup et al., 1983] S. Mørup, M.B. Madsen, J. Franck, J. Villadsen, and C.J.W. Koch, J.Magn. Magn. Mater. 40 (1983) 163.[Mørup, 1994] S. Mørup, Mössbauer spectroscopy and its applications in materialsscience, Technical University of Denmark, 1994.[Mørup and Tronc, 1994] S. Mørup and E. Tronc, Phys. Rev. Lett. 72 (1994) 3278.[Mørup et al., 1995] S. Mørup, F. Bødker, P.V. Hendriksen, and S. Linderoth, Phys. Rev.B 52 (1995) 287.[Mørup and Ostenfeld, 2001] S. Mørup and C.W. Ostenfeld, Hyp. Interact. 136 (2001)125.

References 63[Natali et al., 2002] M. Natali, I.L. Prejbeanu, A. Lebib, L.D. Buda, K. Ounadjela, and Y.Chen, Phys. Rev. Lett. 88 (2002) 157203.[Néel, 1949] L. Néel, Ann. Geophys. 5 (1949) 99.[Néel, 1954] L. Néel, J. Phys. Radium. 15 (1954) 225.[Néel, 1961] Compes Rendus 252 (1961) 4075.[Nogues and Schuller, 1999] J. Nogues and I.K. Schuller, J. Magn. Magn. Mater. 192(1999) 203.[O’Reilly, 1984] W. O’Reilly, Rock and mineral magnetism, Blackie, 1984.[Ostenfeld and Mørup, 2002] C.W. Ostenfeld and S. Mørup, Hyperfine Interact. C5 (2002)83.[Pankhurst et al., 2003] Q.A. Pankhurst, J. Connolly, S.K. Jones, J. Dobson, J. Phys. D.:Appl. Phys. 36 (2003) R167.[Park et al., 1996] G.S. Park, D. Shindo, Y. Waseda, and T. Sugimoto, J. Colloid InterfaceSci. 177 (1996) 198.[Parkin, 2003] Presentation by S.S.P. Parkin, IBM, at Boulder Summer School 2003.[Puntes et al., 2004] V.F. Puntes, P. Gorostiza, D.M. Aruguete, N.G. Bastus, andA.P. Alivisatos, Nat. Mater. 3 (2004) 263.[Pynn, 1990] R. Pynn, Neutron scattering – a primer, Los Alamos Science Summer 1990.[Robinson et al., 2002] P. Robinson, R.J. Harrison, S.A. McEnroe, and R.B. Hargraves,Nature 418 (2002) 517.[Ross et al., 1999] C.A. Ross, H.I. Smith, T. Savas, M. Schattenburg, M. Farhoud, M.Hwang, M. Walsh, M.C. Abraham, and R.J. Ram, J. Vac. Sci. Tech. B 17 (1999) 3168.[Rothman et al., 2001] J. Rothmann, M. Klaui, L. Lopez-Diaz, C.A.F. Vaz, A. Bleloch,J.A.C. Bland, Z. Cui, and R. Speaks, Phys. Rev. Lett. 86 (2001) 1098.[Shull et al., 1951] C.G. Shull, W.A. Strauser, and E.O. Wollan, Phys. Rev. 83 (1951)333.[Skinner and Porter, 1987] B.J. Skinner and S.C. Porter, Physical Geology, Wiley andSons, 1987.[Skumryev et al., 2003] V. Skumryev, S. Stoyanov, Y. Zhang, G. Hadjipanayis, D.Givord, and J. Nogués, Nature 423 (2003) 850.

64 Nanomagnets and their interactions – Part 1[Sort et al., 1999] J. Sort, J. Nogués, X. Amils, S. Surinach, J.S. Munoz, and M.D. Baro,Appl. Phys. Lett. 75 (1999) 3177.[Squires, 1978] G.L. Squires, Introduction to the theory of thermal neutron scattering,Cambridge University Press, Cambridge (1978).[Sugimoto et al., 1996] T. Sugimoto and A. Muramatsu, J. Colloid Interface Sci. 184(1996) 626.[Sugimoto et al., 1998] T. Sugimoto, Y. Wang, H. Itoh, and A. Muramatsu, Colloids Surf.A 134 (1998) 265.[Tatara and Kohno, 2004] G. Tatara and H. Kohno, Phys. Rev. Lett. 92 (2004) 086601.[Tripp et al., 2003] S.L. Tripp, R.E. Dunin-Borkowski, and A. Wei, Angew. Chem. Int.Ed. 42 (2003) 5591.[Vandenberghe et al., 2001] R.E. Vandenberghe, E. Van San, E. De Grave, G.M. DaCosta, Czech. J. Phys. 51 (2001) 663.[van der Zaag et al., 2001] P.J. van der Zaag, Y. Ijiri, J.A. Borchers, L.F. Feiner, R.M.Wolf, J.M. Gaines, R.W. Erwin, and M.A. Verheijen, Phys. Rev. Lett. 84 (2001) 6102.[Vine and Matthews, 1963] F.J. Vine and D.H. Matthews, Nature 199 (1963) 947.[Wang et al., 1998] X.-G. Wang, W. Weiss, Sh.K. Shaikhutdinov, M. Ritter, M. Petersen,F. Wagner, R, Schlögl, and M. Scheffler, Phys. Rev. Lett. 81 (1998) 1038.[Wiesendanger, 1994] R. Wiesendanger, Scanning probe microscopy and spectroscopy:methods and applications, Cambridge, 1994.[Williams and Carter, 1996] D.B. Williams and C.B. Carter, Transmission ElectronMicroscopy, Plenum Press, 1996.[Yoo et al., 2003] Y.G. Yoo, M. Kläui, C.A.F. Vaz, L.J. Heyderman, and J.A.C. Bland.Appl. Phys. Lett. 82 (2003) 2470.[Zeng et al., 2002] H. Zeng, J. Li, J.P. Liu, Z.L. Wang, and S. Sun, Nature 420 (2002)395.[Zheng et al., 1997]. Y. Zheng and J. Zhu, J. Appl. Phys. 81 (1997) 5471.[Zhu et al., 2000] J.-G. Zhu, Y. Zheng, and G.A. Prinz, J. Appl. Phys. 87 (2000) 6668.[Zhu, 2002] X. Zhu, Ph.D. thesis, McGill University, Canada, 2002.

Summary 65SummaryThe thesis deals with the magnetic properties of nm-sized antiferromagnetic nanoparticlesand ring-shaped ferromagnets. The results obtained have a character of basic science, butsince both types of nanomagnets are of interest for applications due to their small sizes andthe limited degree of dipole interactions, the results may be relevant for development ofnew magnetic materials and devices.In antiferromagnetic materials, the magnetic moments of the ions are pair wiseantiparallel, and therefore antiferromagnetic materials appear non-magnetic on the outside.However, when the size of the materials is reduced, compensation of magnetic momentsmay not be complete, giving rise to an external moment of the magnet. We have proposedthat for antiferromagnetic nanoparticles, regardless of their uncompensated moments, thethermal energy may excite the magnetic structure such that a thermoinduced magneticmoment appears. This is a new type of nanomagnetism where the magnetization increaseswith increasing temperature in contrast to the behaviour of traditional magnetic materials,which loose their magnetization with temperature. At room temperature thethermoinduced magnetization can be similar in magnitude to that originating fromuncompensated moments.Despite the external magnetic moment of antiferromagnetic nanoparticles - includingcontributions from uncompensated moments, canted antiferromagnetism, andthermoinduced magnetism - the magnetic dipole interaction is limited. This allows forstudies of the magnetic exchange coupling between the particles. We have prepared bothpure and composite systems of antiferromagnetic nanoparticles and have firmlyestablished that it is possible to achieve inter-particle exchange interactions in ensemblesof nanoparticles prepared from aqueous suspensions.In isolated nanoparticles of magnetic materials, the magnetization direction may fluctuatebetween the easy axes of magnetization. These fluctuations, termed superparamagneticrelaxation, are an example of the dramatic differences between bulk and nanoparticles.Superparamagnetic relaxation can make nanoparticles useless for data storage, becausethey forget whether they are “0” or “1”.From Mössbauer spectroscopy, we have found that agglomeration of antiferromagneticnanoparticles dried form aqueous suspensions can lead to a suppression of thesuperparamagnetic relaxation. The agglomeration process has been found to be reversible,in the sense that ultrasonic treatment of aqueous suspensions of the agglomerated particlescan lead to separation of the particles and reinduce fast superparamagnetic relaxation. Wealso find that grinding of the powders can lead to a separation of the particles and fasterrelaxation without decreasing particle sizes. All together, these results show that the interparticleinteractions between magnetic nanoparticles are extremely sensitive to simplemacroscopic treatments. This implies that the properties of magnetic powder samples canbe sensitive to almost any handling of the samples.By use of magnetization measurements and Mössbauer spectroscopy, we find that themagnetic stability of nanoparticles can be further increased by mixing with different typesof nanoparticles, which have larger magnetic anisotropies. This occurs due to inter-particle

66 Nanomagnets and their interactions – Part 1exchange coupling. We have used neutron powder diffraction, high-energy synchrotron x-ray diffraction, and high-resolution electron microscopy to assess the microstructure of thesamples. This revealed tendencies for the particles to assemble with preferred crystallineorientation when prepared from suspensions. Mössbauer spectroscopy has further revealedthat also the spin direction of the individual particles can be influenced by inter-particleinteractions.In all, the studies on ensembles of nanoparticles show that inter-particle exchangeinteraction can significantly influence the properties (relaxation, coercivity, and magneticstructure) of the particles. This stresses that the magnetic properties of nanoparticlescannot solely be described by considering individual particles, but they have to beunderstood in terms of interactions, too.Agglomerates of nanoparticles may be considered as intermediate states between singleparticles and bulk nanocrystalline materials. Understanding the interaction effects in theagglomerates as well as the assembly process itself may help understanding anddeveloping the magnetic properties of nanocrystalline materials. It may apply to hownanocrystalline magnetic materials with interesting properties can be tailored or perhapseven how nanostructured devices such as ultra-smal Magnetic Random Access Memories(MRAMs) can be build using nanoparticles as building blocks. It may also apply to e.g.understanding crystal growth and formation of geological sediments.Small magnetic ring structures have recently been proposed for use as bits in high-densitydata storage and in MRAMs, because the ring-shape can support a magnetic flux-closedstate with no stray fields such that dipole interactions between bits are avoided. The twopossible circulations of the flux lines are intended to represent binary information. In thethesis, sub-micron lithographically fabricated ring magnets have been studied by magneticforce microscopy (MFM) in order to illuminate the magnetic switching into the fluxclosure state. The MFM studies resulted in the identification of a metastable magneticstate, the “twisted” state, where domain walls do not annihilate, and thus the flux-closedstate is not readily formed. The MFM studies also provided quantitative information onthe switching fields between different domain states for rings with given dimensions. Theidentification and control of magnetic domain states are considered to be of importance forthe possible use of ring structures in data storage. The results also shed light on thecomplicated process of domain wall annihilation.

Resumé (summary in Danish)Ph.d. afhandlingen omhandler studier af de magnetiske egenskaber af nm-storenanopartikler af antiferromagnetiske materialer samt af ring-strukturer af ferromagnetiskematerialer. De opnåede resultater er af grundvidenskabelig karakter, men p.g.a. destuderede magneters nanoskala-dimensioner og deres begrænsede indbyrdes magnetiskedipol-vekselvirkning, kan resultaterne være relevante for udvikling af nye magnetiskematerialer og komponenter.I et antiferromagnetisk materiale er de magnetiske ioners momenter parvis modsatrettede.Derfor virker antiferromagneter typisk umagnetiske. Når magneterne bliver meget små(ca. 10 nm i diameter eller mindre) kan der opstå uparrede momenter og materialet bliverudadtil magnetisk. Vi har vist, at der tilmed kan findes et bidrag til en ydre magnetisering iantiferromagnetiske nanomagneter, som skyldes at den omgivende termiske energi kananslå den magnetiske struktur. Dette er en ny slags magnetisme som - modsat meretraditionelle former for magnetisme - øges med øget temperatur. Ved stuetemperatur kanbidraget fra denne termisk inducerede magnetisme være sammenligneligt med bidraget fraukompenserede magnetiske momenter.På trods af bidragene til antiferromagneters ydre moment fra ukompenserede momenter ogfra termisk induceret magnetisme, så er den magnetiske dipol-vekselvirkning imellemnanopartikler af antiferromagnetiske materialer beskeden. Af den grund er der mulighedfor, at den magnetiske exchange vekselvirkning imellem partiklerne kan studeresuforstyrret. Vi har fremstillet rene prøver samt blandinger af antiferromagnetiskenanopartikler og har observeret at det er muligt at opnå exchange vekselvirkning i mellempartikler som er tørret sammen efter opslemning i vand.I isolerede nanopartikler af magnetiske materialer kan magnetiseringsretningen fluktuere imellem dens foretrukne retninger. Disse fluktuationer kaldes superparamagnetisme og eret eksempel på de dramatisk anderledes egenskaber, som nanopartikler kan have i forholdtil almindelige magneter. Superparamagnetisme gør nanopartikler uegnede til datalagringpå hard diske, fordi de glemmer om de er ”0” eller ”1”.Ved brug af Mössbauer spektroskopi har vi set, at agglomerering af nanopartikler, når detørres fra vandige opslemninger, kan undertrykke superparamagnetismen. Mössbauerspektroskopi og magnetiseringsmålinger viser yderligere, at stabiliteten afmagnetiseringen kan forøges, når partiklerne blandes og vekselvirker med andre typer afpartikler, som har en større magnetisk anisotropi. Vi finder at processen er reversibel, sånår partiklerne skilles ad, er superparamagnetisme dominerende igen. Forsigtig formalingmed en morter eller i en kuglemølle samt behandling med ultralyd kan separerepartiklerne, mens tørring bringer partiklerne sammen. Disse studier viser at de magnetiskeegenskaber af prøver af partikler er meget følsomme overfor håndteringen.Vi har benyttet neutron pulver-diffraktion, høj-energi Røntgen-diffraktion samt højopløsnings-elektronmikroskopitil at undersøge mikrostrukturen af prøverne, og fundet atpartiklerne har en tendens til at sætte sig sammen med en foretrukken krystallinskorientering. Mössbauer spektroskopi har yderligere vist, at exchange vekselvirkningimellem partiklerne kan påvirke deres magnetiske struktur.

Alt i alt viser disse studier af nanopartikler, at exchange vekselvirkning imellempartiklerne kan ændre deres magnetiske egenskaber betydeligt. Dette betyder desuden atde magnetiske egenskaber af nanopartikler ikke alene kan beskrives udfra isoleredepartikler, men også må inkludere effekter af vekselvirkning mellem partiklerne.Agglomerater af nanopartikler kan opfattes som en tilstand imellem enkelte partikler ogstørre nanokrystallinske materialer. Forståelse af vekselvirkningseffekterne i agglomerateraf nanopartikler kan bidrage til forståelsen af nanokrystallinske materialers magnetiskeegenskaber. Desuden kan forståelse af de mekanismer, som bevirker samling afpartiklerne, have betydning for hvordan nye materialer og komponenter som f.eks. bittesmåmagnetiske RAM enheder kan opbygges med brug af nanopartikler som byggesten.Forståelse af disse mekanismer kan også have betydning for forståelsen af krystalvækst ogdannelsen geologiske sedimenter.Små magnetiske ring strukturer er blevet foreslået til brug som bits til datalagring påharddiske og til magnetiske RAM, fordi ringene, hvis de magnetiseres i en af de to muligeomløbsretninger (svarende til ”0” eller ”1”), ikke har et ydre magnetfelt, som kan påvirkenabomagneterne. Vi har undersøgt ring-formede nanomagneter med et magnetisk kraftmikroskop og set at der forekommer en metastabil magnetisk tilstand i ringene inden denflux-lukkede tilstand formes. Dette kan have betydning for brugen af ring-magneter tildatalagring.

Part 2

PapersFine particle magnetism (antiferromagnets)Review (as of spring 2002):Paper I: S. Mørup, C. Frandsen, F. Bødker, S.N. Klausen, K. Lefmann, P.-A. Lindgårdand M.F. Hansen, Magnetic properties of nanoparticles of antiferromagnetic materials,Hyperfine Interact. 144/145 (2002) 347.Antiferromagnetic nanoparticles:Paper II: S. Mørup and C. Frandsen, Thermoinduced magnetization in nanoparticles ofantiferromagnetic materials, Phys. Rev. Lett. 92 (2004) 217201.Paper III: S.N. Klausen, K. Lefmann, P.-A. Lindgård, L. Theil Kuhn, C.R.H. Bahl, C.Frandsen, S. Mørup, B. Roessli, N. Cavadini, and C. Niedermayer, Magnetic anisotropyand quantized spin waves in hematite nanoparticles, Phys. Rev. B (in press).Inter-particle interactions:Paper IV: C. Frandsen and S. Mørup, Inter-particle interactions in composites ofantiferromagnetic nanoparticles, J. Magn. Magn. Mater. 266 (2003) 36.Paper V: C. Frandsen, C.W. Ostenfeld, M. Xu, C.S. Jacobsen, L. Keller, K. Lefmann, andS. Mørup, Inter-particle interactions in composites of nanoparticles of ferrimagnetic (γ-Fe 2 O 3 ) and antiferromagnetic (CoO, NiO) materials, Phys. Rev. B (in press).Paper VI: C. Frandsen, H. K. Rasmussen, and S. Mørup, A Mössbauer study of themagnetization of γ-Fe 2 O 3 nanoparticles in applied fields: Influence of interaction withCoO, J. Phys.: Condens. Matter 16 (2004) 6977.Paper VII: C. Frandsen, C.R.H. Bahl, B. Lebech, K. Lefmann, L. Theil Kuhn, L. Keller,N. Hessel Andersen, M. v. Zimmermann, E. Johnson, S.N. Klausen, and S. Mørup, Selfassemblyand exchange coupling of antiferromagnetic nanoparticles, submitted (July2004).

Paper VIII: C. Frandsen and S. Mørup, Spin rotation in α-Fe 2 O 3 nanoparticles byinterparticle interactions, submitted (July 2004).Paper IX: M. Xu, C.R.H. Bahl, C. Frandsen, and S. Mørup, Inter-particle interactions inagglomerates of α-Fe 2 O 3 nanoparticles: Influence of grinding, J. Colloid Interface Sci.279 (2004) 132.Ring-magnetsPaper X: F.J. Castaño, C.A. Ross, C. Frandsen, A. Eilez, D. Gil, H.I. Smith, M. Redjdal,F.B. Humphrey, Metastable states in magnetic nanorings, Phys. Rev. B 67 (2003) 184425.Paper XI: F.J. Castaño, C.A. Ross, A. Eilez, W. Jung, and C. Frandsen, Magneticconfigurations in 160-520-nm-diameter ferromagnetic rings, Phys. Rev. B 69 (2004)144421.Other publications by the author, not included in the thesis:J.P. Merrison, P. Bertelsen, C. Frandsen, P. Gunnlaugsson, J.M. Knudsen, S. Lunt, M.B.Madsen, L.A. Mossin, J. Nielsen, P. Nørnberg, K.R. Rasmussen and E. Uggerhøj,Simulation of the Martian dust aerosol at low wind speeds, Journal of GeophysicalResearch - Planets 107 (2002) 5133.C. Frandsen, S.L.S. Stipp, S.A. McEnroe, M.B. Madsen, J.M. Knudsen, Magnetic domainstructures and stray fields of individual elongated magnetite grains revealed by magneticforce microscopy, Physics of the Earth and Planetary Interiors 141 (2004) 121.

Paper I

Hyperfine Interactions 144/145: 347–357, 2002.© 2003 Kluwer Academic Publishers. Printed in the Netherlands.347Magnetic Properties of Nanoparticlesof Antiferromagnetic MaterialsSTEEN MØRUP 1 , CATHRINE FRANDSEN 1 , FRANZ BØDKER 1,∗ ,STINE NYBORG KLAUSEN 2 , KIM LEFMANN 2 , PER-ANKER LINDGÅRD 2and MIKKEL FOUGT HANSEN 31 Department of Physics, Bldg. 307, Technical University of Denmark, DK-2800 Kgs. Lyngby,Denmark2 Materials Research Department, Risø National Laboratory, DK-4000 Roskilde, Denmark3 Mikroelektronik Centret, Bldg. 345E, Technical University of Denmark, DK-2800 Kgs. Lyngby,DenmarkAbstract. The magnetic properties of antiferromagnetic nanoparticles have been studied byMössbauer spectroscopy and neutron scattering. Temperature series of Mössbauer spectra of noninteracting,superparamagnetic hematite nanoparticles were fitted by use of the Blume–Tjon relaxationmodel. It has been found that the magnetic anisotropy energy constant increases significantlywith decreasing particle size. Neutron scattering experiments on similar samples give new informationon both superparamagnetic relaxation and collective magnetic excitations. There is goodagreement between the values of the parameters obtained from Mössbauer spectroscopy and neutronscattering. In samples of interacting hematite nanoparticles, the relaxation was significantly suppressed.The Mössbauer data for these samples are in accordance with a mean field model for anordered state of strongly interacting particles. Mixing nanoparticles of hematite with CoO nanoparticlesresulted in suppression of the superparamagnetic relaxation, whereas NiO nanoparticles had theopposite effect.Key words: Mössbauer spectroscopy, magnetic nanoparticles, superparamagnetic relaxation, neutronscattering.1. IntroductionMost experimental studies of the magnetic properties of nanoparticles have beenfocused on ferromagnetic and ferrimagnetic particles because of their importancefor magnetic data storage, in ferrofluids, etc. Furthermore, the theoretical modelsfor superparamagnetic relaxation have been derived for ferromagnetic particles.Antiferromagnetic nanostructured materials are interesting both from a fundamentalpoint of view and because they have important applications in devices in whichexchange bias is utilised, such as spin valves. In this paper, we give a brief review ofresults of studies of antiferromagnetic nanoparticles obtained by use of Mössbauerspectroscopy and neutron scattering.* Present address: Danfysik, Møllehaven 31, DK-4040 Jyllinge, Denmark.

348 S. MØRUP ET AL.2. Non-interacting particlesSeveral studies of both ferrimagnetic and antiferromagnetic nanoparticles haveshown that inter-particle interactions can have a strong influence on the magneticproperties of samples containing magnetic nanoparticles [1–5]. Therefore, in orderto study the magnetic properties of non-interacting nanoparticles it is necessaryto prepare samples with negligible inter-particle interactions. Since long rangedipole–dipole interactions are small because of the small magnetisation of antiferromagneticparticles, it may be sufficient to coat the particles with a thin layer ofnon-magnetic material such that short range exchange interaction can be avoided.Often the magnetic anisotropy energy of a nanoparticle is assumed to be uniaxialand given by the expressionE(θ) = KV sin 2 θ, (1)where θ is the angle between the (sublattice) magnetisation direction and an easydirection of magnetisation, K is the magnetic anisotropy constant, and V is the particlevolume. The superparamagnetic relaxation time, i.e. the average time betweentransitions between the minima of the anisotropy energy, is expected to follow theNéel–Brown expression [6, 7]:( ) Eτ = τ 0 exp , (2)k B Twhere k B is Boltzmann’s constant and T is the temperature. E is the heightof the energy barrier separating two minima corresponding to easy directions ofmagnetisation. For a particle with the magnetic energy given by Equation (1),E = KV. In ferromagnetic nanoparticles, τ 0 depends slightly on temperature[7] and is typically in the range 10 −12 –10 −9 s. No theoretical expressions for thevalue of τ 0 for antiferromagnetic particles have been published.As an example of Mössbauer spectra of non-interacting particles, Figure 1(a)shows spectra of 9 nm hematite nanoparticles coated with oleic acid and suspendedin heptane. At 25 K, the spectrum is dominated by a sextet with relatively sharplines, indicating a relaxation time τ 10 −7 s. At 180 K, the spectrum consists of adoublet, indicating relaxation times τ 10 −9 s. At intermediate temperatures, thespectra can be described as superpositions of sextets and doublets with relativelynarrow lines, and there is no significant contribution from particles with relaxationtimes in the range 10 −9 –10 −8 s, which should give contributions with considerableline broadening [1]. This can be explained by a relatively broad particle sizedistribution in conjunction with the exponential size dependence of the relaxationtime. For a particle with magnetic energy given by Equation (1) one finds fromEquation (2) that a small volume change V will give rise to a change in relaxationtime given by[ ( KVτ = τ(V + V ) − τ(V) = τ(V) expk B TVV) ]− 1 . (3)

ANTIFERROMAGNETIC NANOPARTICLES 349Figure 1. Mössbauer spectra of 9 nm hematite nanoparticles obtained at the indicated temperatures.(a) Particles coated with oleic acid and suspended in heptane. (b) Uncoated particles prepared bydrying an aqueous suspension.For non-interacting hematite nanoparticles, τ 0 is of the order of 10 −11 s [8]. Therefore,for a particle with a superparamagnetic relaxation time of the order of the timescale of Mössbauer spectroscopy (∼ 5 · 10 −9 s), we find from Equation (2) that thevalue of the parameter KV/k B T is approximately 6. According to Equation (3),a change of the particle diameter by only about 10% will then result in a changeof the relaxation time, which is sufficient to transform the spectrum to a doubletor a sextet. The samples of hematite nanoparticles studied by us typically have abroad size distribution [9]. Therefore, at a given temperature only a small fractionof the particles in a sample will have relaxation times in the range 10 −9 –10 −8 s,for which the spectra are substantially broadened. The spectra therefore appear assuperpositions of sextets and doublets with relatively sharp lines.We have fitted temperature series of spectra of non-interacting hematite nanoparticlessimultaneously [4, 8, 10] with the Blume–Tjon model [11] for Mössbauerrelaxation spectra. We assumed that the relaxation time is given by the Néel–Brown

350 S. MØRUP ET AL.Figure 2. The magnetic anisotropy constant for hematite nanoparticles as a function of the particlesize. Adapted from [8].expression (Equation (2)). In the fits, the values of E and τ 0 were free parameters.The volume distribution was estimated from electron micrographs, and in the fittingprocedure, it was approximated with a log-normal distribution. The fits showedunambiguously that the relatively broad size distribution and the small value ofτ 0 can explain the apparent absence of components with broad lines. The studiesshowed, as illustrated in Figure 2, that the magnetic anisotropy energy constantincreases by a factor of about 10, when the size decreases from about 25 nm toabout 6 nm [8]. It is likely that the major contribution to this increase is the surfaceanisotropy. The results also showed that the value of τ 0 decreases with decreasingparticle size.At low temperatures, where the superparamagnetic relaxation time is long comparedto the time scale of Mössbauer spectroscopy, the Mössbauer spectra of samplesof magnetic nanoparticles consist of sextets. However, the magnetic splitting isreduced compared to the bulk value because of the influence of collective magneticexcitations (i.e. fluctuations of the sublattice magnetisation in directions around aneasy direction of magnetisation) [12, 13]. These fluctuations can be described as acombination of precession of the (sublattice) magnetisation vector in the anisotropyfield and transitions between precession states with different precession angles. Ifboth processes are fast compared to the time scale of Mössbauer spectroscopy, theobserved magnetic hyperfine field is at low temperatures given by [13](B obs∼ = B0 1 − k )BT. (4)2κV

ANTIFERROMAGNETIC NANOPARTICLES 351Table I. The magnetic anisotropy parameters κV/k Band E/k Band the valueof τ 0 for 15 nm hematite particles obtained from superparamagnetic relaxation(SPM) and collective magnetic excitations (CME)κV/k B(K) E/k B(K) τ 0 (s) Ref.SPM (Mössbauer) 600 ± 150 6 · 10 −11 [10]CME (Mössbauer) 620 ± 50 – [10]SPM (neutron scatt.) 500 ± 200 1.4 · 10 −11 [15, 16]CME (neutron scatt.) 600 ± 200 – [15, 16]Here B 0 is the magnetic hyperfine field in the absence of collective magnetic excitations,and may be close to the bulk magnetic hyperfine field. The parameter κdepends on the magnetic anisotropy constant(s) and may also be influenced byinter-particle interactions. For a particle with magnetic energy given by Equation(1), κ = K. According to Equation (4), B obs /B 0 should depend linearly ontemperature, and this has in fact been found in experimental studies of nanoparticlesof, for example, magnetite [12] and hematite [4, 14]. (In hematite nanoparticles,the sublattice magnetisation is to a large extend confined in a plane and themagnetic energy is more complex than that given by Equation (1) [10].)It should be noticed that the fits of the whole temperature series of Mössbauerspectra are mainly sensitive to the superparamagnetic relaxation, which is governedby the height of the energy barriers, E (although the reduction of thehyperfine fields due to collective magnetic excitations was also included in thefitting model [4, 8, 10]). When analysing only the reduction of the hyperfine fielddue to collective magnetic excitations at low temperatures, one obtains informationon the parameter κV, which is related to the magnetic energy near the bottom ofthe minima. Therefore, if the magnetic anisotropy is different from that given inEquation (1), the results for the energy barriers, obtained using the two methods,may not be identical. The values, obtained using the two different types of analysisfor 15 nm hematite nanoparticles, are given in Table I. In this case there is goodagreement between the values.Another experimental technique, which is useful to study superparamagnetic relaxationand collective magnetic excitations, is neutron scattering [15–17]. Figure 3shows, as an example, energy scans from a triple-axis neutron spectrometer takenaround the pure (1 1 1) antiferromagnetic reflection for 15 nm hematite nanoparticles[15]. The zero field scans (a) show a relatively narrow quasielastic peakcentered at zero energy transfer and two broad inelastic peaks at energy transfersaround ε =±0.2 meV. The width of the quasielastic peak increases with increasingtemperature, because of the finite lifetime of the magnetisation orientations insuperparamagnetic particles. Thus the superparamagnetic relaxation time can beestimated from the line width of the quasielastic peak. It is notable that neutronscattering is sensitive to fluctuations at the time scale 10 −14 s >τ>10 −7 s. It isthus suitable for the study of superparamagnetic relaxation, which is so fast, that

352 S. MØRUP ET AL.Figure 3. Inelastic neutron scattering data obtained at the indicated temperatures at zero appliedmagnetic field (a) and at 268 K in various applied magnetic fields (b). Adapted from [15].Mössbauer spectroscopy becomes insensitive to the relaxation rate. The inelasticpeaks are caused by collective magnetic excitations and their positions correspondto the energy change associated with a transition between two neighbouring precessionstates. Thus the position of the inelastic peaks are at ε =±¯hω AF whereω AF is the antiferromagnetic resonance frequency [15, 16], which is related tothe parameter κ. It can be seen that the area of the inelastic peaks increases withincreasing temperature. This is due to the temperature dependence of the populationof the precession states. When magnetic fields are applied, the inelastic peaksmove to higher energies (Figure 3(b)), because the magnetisation vectors precessin an effective field, which has contributions from both the anisotropy field andthe applied field. The values of the parameters E, κV and τ 0 , obtained fromthe analysis of the neutron data, are given in Table I. There is a good agreementbetween the values of E and κV obtained from the analysis of the neutron dataand the Mössbauer data. The uncertainty of the estimated values of τ 0 is about oneorder of magnitude and therefore the values given in the table also agree within theexperimental uncertainty.

ANTIFERROMAGNETIC NANOPARTICLES 353Neutron scattering has also appeared very useful for studies of the temperaturedependence of the sublattice magnetisation in nanoparticles of, for example, NiO.It has been shown that the Néel temperature of NiO nanoparticles is lower thanthe bulk value and that the temperature dependence of the sublattice magnetisationfollows a mean-field model for finite-sized particles [18].3. Inter-particle interactionsInteractions between antiferromagnetic nanoparticles have in several cases beenfound to have a surprisingly strong influence on the superparamagnetic relaxation[1, 4, 14, 19–21]. Figure 1(b) shows Mössbauer spectra of interacting 9 nm hematiteparticles. These particles were taken from the same batch as those yielding thespectra in Figure 1(a), but they were uncoated, suspended in water and then allowedto dry at room temperature such that they may interact. The large differencesbetween the spectra in Figures 1(a) and (b) illustrate that inter-particle interactionsresult in much slower relaxation than seen in the sample of non-interacting particles.Moreover, the shapes of the spectra in the two figures differ significantly.Instead of the appearance of a doublet at relatively low temperatures as in Figure1(a), the lines of the sextet in Figure 1(b) become increasingly broadened asthe temperature is raised and the average hyperfine field decreases considerably.The magnetic energy of a particle i, which interacts with its neighbours j, maybe writtenE i = KV i sin 2 θ − M i · ∑K ij M j , (5)jwhere M i and M j represent the (sublattice) magnetisation of the particles i and j,respectively, and K ij is an effective exchange coupling constant due to exchangecoupling between surface atoms belonging to neighbouring particles. If the firstterm in Equation (5) is predominant, superparamagnetic relaxation may take placebetween the easy directions at θ = 0andθ = π. However, if the interaction isstrong such that the second term is predominant, there may be only one energyminimum for the particle i, and the interactions may result in an ordered (collective)state at low temperatures [1, 4, 13, 21]. At finite temperatures, the (sublattice)magnetisation may then fluctuate around the direction corresponding to this energyminimum. The magnetic properties of such samples have been calculated by use ofa mean field model in which the summation in the second term in Equation (5)is replaced by an average value [13, 21]. The properties of the sample can becharacterised by an order parameter, which describes the degree of ordering ofthe (sublattice) magnetisation directions of the particles [4, 21]. The temperaturedependence of the order parameter can then be calculated by use of Boltzmannstatistics [4, 13, 21]. If the fluctuations of the sublattice magnetisation directionsare fast compared to the time scale of Mössbauer spectroscopy, the magnetic splittingin the spectra will be proportional to the order parameter. In a sample of

354 S. MØRUP ET AL.more or less randomly packed nanoparticles one would expect a broad distributionof exchange coupling constants. Therefore, at a given temperature, the orderparameter is different in different parts of the sample. This variation can explainthe asymmetric line broadening of the lines in the sextet [4, 21]. The model hasbeen used to explain the Mössbauer data for interacting hematite [4] and goethitenanoparticles [21]. If the neighbouring particles are randomly oriented one mightexpect that the contributions from different neighbouring particles in the summationof Equation (5) partially cancel and therefore the interaction field should besmall. However, recent high resolution transmission electron micrographs of TiO 2nanoparticles have revealed that there can be a large tendency for neighbouringnanoparticles to align with parallel lattice planes [22]. It is possible that a similartendency is present in samples of hematite nanoparticles and this may explain thestrong magnetic coupling.An alternative explanation of the slower relaxation in samples of interactingparticles might be that the effective energy barrier, E, increases with increasingstrength of interactions [5, 23]. The shapes of the spectra of interacting particlesare, however, as illustrated in Figure 1, very different from those of non-interactingparticles. This suggests that the relaxation mechanism is fundamentally differentfrom that of particles with relaxation behaviour governed by Equation (2). Furthermore,the physical model [23], which has been used to explain the apparentincrease of the magnetic anisotropy, is based on assumptions, which may not befulfilled [24].The influence of interactions between hematite nanoparticles has also beenstudied by neutron scattering. The studies have shown a large reduction of therelative area of the inelastic peaks when the particles interact. Qualitatively thisis in accordance with the presence of an ordered state as discussed above. Theanalysis of the data is in progress [25].4. Interactions between nanoparticles of different materialsIn recent studies it has been found that interactions between nanoparticles of differentantiferromagnetic materials can have unexpected effects on the superparamagneticrelaxation time [20, 26]. The samples of interacting nanoparticles wereprepared by suspending mixtures of uncoated particles in water, exposing them toultrasound, and allowing them to dry at room temperature. Figure 4 shows spectraof hematite nanoparticles at 180 K for a sample consisting solely of hematite particlesand of hematite particles from the same batch mixed with similar amountsof NiO or CoO nanoparticles. It is clearly seen that NiO results in faster relaxationwhereas CoO results in suppression of the relaxation compared to the pure hematitesample.In the presence of inter-particle interactions, the expression for the reduction ofthe magnetic hyperfine field due to collective magnetic excitations may be written[4, 14]:

ANTIFERROMAGNETIC NANOPARTICLES 355Figure 4. Mössbauer spectra of 9 nm hematite nanoparticles obtained by drying aqueous suspensionsof particles of pure hematite and mixtures of hematite particles and CoO or NiO nanoparticles. Thespectra were obtained at 180 K.B obs = B 0(1 − k BTE a + E int), (6)where E a is related to the magnetic anisotropy energy (= 2KV if the anisotropyenergy is given by Equation (1)) and E int is proportional to the interaction strength.The temperature dependence of B obs at low temperature for the samples of purehematite nanoparticles and the mixture of hematite and CoO nanoparticles is shownin Figure 5. Data for the mixture with NiO are not included, because the sampleshowed a partial Morin transition at low temperatures [20, 26] and the hyperfinefields are therefore not comparable to those of the other two samples. For bothsamples, a linear temperature dependence of B obs is found, but the slopes differconsiderably. In the sample with CoO nanoparticles, the variation of B obs withtemperature is small and close to the bulk behaviour. In the sample consisting solelyof hematite nanoparticles, the slope is much larger indicating a smaller interaction

356 S. MØRUP ET AL.Figure 5. Temperature dependence of the magnetic hyperfine field of 9 nm hematite nanoparticlesmixed with CoO nanoparticles and pure hematite.energy. These results are in accordance with the differences in the strength ofinteractions, which were found from the analysis of the spectra at 180 K (Figure 4).The origin of the different influence of NiO and CoO on the relaxation ofhematite nanoparticles is not understood in detail. It is possible that a strong exchangecoupling between hematite and CoO nanoparticles prevent the relaxationof the hematite particles because their sublattice magnetisation is coupled to thesublattice magnetisation of the CoO particles, which have larger anisotropy energy[20, 26]. The smaller magnetic anisotropy of NiO particles may be the reason forthe faster relaxation of hematite particles when they are mixed with NiO [26].AcknowledgementsThe work was supported by the Danish Technical Research Council and the DanishNatural Science Research Council.References1. Mørup, S., Hyp. Interact. 90 (1994), 171.2. Mørup, S. and Tronc, E., Phys. Rev. Lett. 72 (1994), 3278.3. Mørup, S., Bødker, F., Hendriksen, P. V. and Linderoth, S., Phys. Rev. B 52 (1995), 287.4. Hansen, M. F., Bender Koch, C. and Mørup, S., Phys. Rev. B 62 (2000), 1124.5. Dormann, J. L., Fiorani, D. and Tronc, E., Adv. Chem. Phys. 98 (1997), 283.6. Néel, L., Ann. Geophys. 5 (1949), 99.7. BrownJr.,W.F.,Phys. Rev. 130 (1963), 167.8. Bødker, F. and Mørup, S., Europhys. Lett. 52 (2000), 217.

ANTIFERROMAGNETIC NANOPARTICLES 3579. Fisker, R., Carstensen, J. M., Hansen, M. F., Bødker, F. and Mørup, S., J. Nanoparticle Research2 (2000), 267.10. Bødker, F., Hansen, M. F., Bender Koch, C., Lefmann, K. and Mørup, S., Phys. Rev. B 61(2000), 6826.11. Blume, M. and Tjon, J. A., Phys. Rev. 165 (1968), 446.12. Mørup, S. and Topsøe, H., Appl. Phys. 11 (1976), 63.13. Mørup, S., J. Magn. Magn. Mater. 37 (1983), 39.14. Mørup, S. and Ostenfeld, C. W., Hyp. Interact. 136 (2001), 125.15. Hansen, M. F., Bødker, F., Mørup, S., Lefmann, K., Clausen, K. N. and Lindgård, P.-A., Phys.Rev. Lett. 79 (1997), 4910.16. Hansen, M. F., Bødker, F., Mørup, S., Lefmann, K., Clausen, K. N. and Lindgård, P.-A.,J. Magn. Magn. Mater. 221 (2000), 10.17. Lefmann, K., Bødker, F., Klausen, S. N., Hansen, M. F., Clausen, K. N., Lindgård, P.-A. andMørup, S., Europhys. Lett. 54 (2001), 526.18. Klausen, S. N., Lindgård, P.-A., Lefmann, K., Bødker, F. and Mørup, S., Phys. Stat. Sol. A 189(2002), 1039.19. Bødker, F., Hansen, M. F., Bender Koch, C. and Mørup, S., J. Magn. Magn. Mater. 221 (2000),32.20. Ostenfeld, C. W. and Mørup, S., Hyp. Interact. C 5 (2002), 83.21. Mørup, S., Madsen, M. B., Franck, J., Villadsen, J. and Koch, C. J. W., J. Magn. Magn. Mater.40 (1983), 163.22. Lee Penn, R. and Banfield, J. F., Geochim. Cosmochim. Acta 63 (1999), 1549.23. Dormann, J. L., Bessais, L. and Fiorani, D., J. Phys. C 21 (1988), 2015.24. Hansen, M. F. and Mørup, S., J. Magn. Magn. Mater. 184 (1998), 262.25. Klausen, S. N., Frandsen, C., Lefmann, K. and Mørup, S., J. Magn. Magn. Mater. (in press).26. Frandsen, C. and Mørup, S., J. Magn. Magn. Mater. (in press).

Paper II

VOLUME 92, NUMBER 21PHYSICAL REVIEW LETTERS week ending28 MAY 2004Thermoinduced Magnetization in Nanoparticles of Antiferromagnetic MaterialsSteen Mørup and Cathrine FrandsenDepartment of Physics, Building 307, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark(Received 7 November 2003; published 26 May 2004)We show that there is a thermoinduced contribution to the magnetic moment of nanoparticles ofantiferromagnetic materials. It arises from thermal excitations of the uniform spin-precession mode,and it has the unusual property that its magnitude increases with increasing temperature. This has theconsequence that antiferromagnetism is nonexistent in nanoparticles at finite temperatures and itexplains magnetic anomalies, which recently have been reported in a number of studies of nanoparticlesof antiferromagnetic materials.DOI: 10.1103/PhysRevLett.92.217201PACS numbers: 75.50.Ee, 75.75.+a, 76.50.+gCurrently, there is a rapid development in fabricationand applications of nanostructured magnetic devices suchas spin valves and magnetic random access memories. Inthis context, an understanding of the size-dependent magneticproperties of ferro-, ferri-, and antiferromagneticmaterials is crucial. The magnetic properties of mostferro- and ferrimagnetic nanostructured materials, includingthin film structures and nanoparticles, seem onthe whole to be well understood. However, several authorshave reported that nanoparticles of antiferromagneticmaterials show anomalies, which have not yet beenexplained.The magnetization of nanoparticles of antiferromagneticmaterials is often significantly larger than the bulkvalue [1–6]. Néel [7] suggested that the finite magneticmoment of nanoparticles of antiferromagnetic materialsis due to uncompensated spins at the surface or in theinterior of the particles. Still, the dependence of themagnetization on particle size and temperature has shownfeatures that are not fully understood. Several studieshave revealed that the temperature dependence is not inaccordance with the Langevin behavior, i.e., the magnetizationdoes not decrease with increasing temperature inthe expected way [8–15]. These results have been observedin several synthetic samples, in the iron storageprotein ferritin, and in ferrihydrite, which can be foundin sediments in nature. Some examples are given below.Seehra et al. [8] reported that the magnetic moment of4 nm particles of ferrihydrite increases consistently withincreasing temperature such that the room temperaturevalue is about twice the low-temperature value. Their dataare shown in Fig. 1. Harris et al. [9] found in a study offerritin samples with different particle sizes that themagnetic moment of the particles increases with temperature,and the authors remarked that ‘‘the reason for thistemperature dependence is not clear.’’ In another study offerritin particles with about 4000 iron atoms, Kilcoyneand Cywinski [10] noted that ‘‘above 120 K, is surprisinglyfound to increase slowly with increasing temperature.’’Makhlouf et al. [11] found that the magneticmoment of ferritin particles at finite temperatures wasconsiderably larger than expected from the low-temperaturevalue. Vollath et al. [12] observed a substantial increasewith increasing temperature of the magneticmoment of Cr 2 O 3 particles with diameters below 4 nm.A qualitatively similar temperature dependence of themagnetic moment was found in a study of 21 nm Cr 2 O 3nanoparticles [13]. In a study of NiO nanoparticlesMakhlouf et al. [4] found that ‘‘the magnetizations donot scale with H=T as found for very small ferri- andferromagnetic particles.’’In this Letter we show that there is a thermoinducedcontribution to the magnetic moment of nanoparticles ofantiferromagnetic materials, which can explain suchanomalies. We find that for particles of antiferromagneticmaterials with a size below a few nm, the thermoinducedmoment may be predominant at room temperature. Wealso point out that relaxation of the thermoinduced momentin some cases may be difficult to distinguish frommacroscopic quantum tunneling.FIG. 1. The magnetic moment of 4 nm ferrihydrite particlesas a function of temperature. The experimental data, shown bybold circles, are those obtained by Seehra et al. [8] frommagnetization measurements. The solid line is a linear fit tothe data in accordance with Eq. (4).217201-1 0031-9007=04=92(21)=217201(4)$22.50 © 2004 The American Physical Society 217201-1

VOLUME 92, NUMBER 21PHYSICAL REVIEW LETTERS week ending28 MAY 2004The magnetic energy of a nanoparticle with uniaxialanisotropy may be writtenE KVsin 2 ; (1)where K is the magnetic anisotropy energy constant, V isthe particle volume, and is the angle between themagnetization direction and the easy direction of magnetization.At finite temperatures, the (sublattice) magnetizationdirection fluctuates, because the magneticanisotropy energy is comparable to the thermal energy.At high temperatures, the magnetic properties are commonlydominated by superparamagnetic relaxation, i.e.,reversals of the (sublattice) magnetization directions. Atlower temperatures, the thermal energy may be insufficientto result in frequent magnetization reversals, butstill the (sublattice) magnetization direction may fluctuatein directions close to an energy minimum. Thesefluctuations, termed collective magnetic excitations, canbe described as a uniform precession of the magnetizationvector around an easy direction of magnetization in combinationwith transitions between these precession states[16,17]. In nanoparticles, the uniform precession mode,which can be described as a spin wave with wave vectorq 0, is predominant compared to other spin wave excitationswith q 0 [17]. In Mössbauer spectroscopy,these magnetic fluctuations result in a reduction of themagnetic hyperfine splitting because they can be consideredfast compared to the time scale of the experimentaltechnique [16,17]. In inelastic neutron scattering experiments,transitions between the q 0 precession statescan be studied [18,19].In ferromagnetic nanoparticles, the excitations can beconsidered as uniform precessions with all ionic spinsparallel. Similarly, in ferrimagnetic nanoparticles, thedynamics can be described in terms of precession oftwo antiparallel sublattices. However, in antiferromagneticmaterials, the excited states are more complex.Both classical and quantum mechanical calculations[20] show that the two sublattices are not strictly antiparallel,but precess in such a way that they make slightlydifferent angles, A and B , with the easy direction ofmagnetization. This leads to precession frequencies,which are much higher than the typical frequencies offerro- and ferrimagnetic resonances. The theoretical resultshave been confirmed in numerous experimentalstudies of antiferromagnetic resonance; see, for example,[21,22]. The relationship between the two angles can bewritten [20,21]sin A1 ; (2 )sin Bwhere 2B a =B 1=2 E . Here, B a K=M s is the anisotropyfield, where M s is the sublattice magnetization, andB E is the exchange field. Equation (2 ) is a good approximationfor 1. Because A B, the crystal has anonzero magnetic moment when the uniform mode isexcited by an external ac field. Similarly, a nanoparticleof an antiferromagnetic material will have a net magneticmoment when the uniform mode is thermally excited.When averaging over the precession motion, the absolutevalue of the magnetic moment of a particle is given byj j M s Vj cos B cos A j. This is illustrated schematicallyin Fig. 2. By use of Eq. (2 ) one finds for 1j j M s V sin2 B: (3)cos BUsing Boltzmann statistics one can calculate the thermalaverage of j j. Because A B, the magnetic energyis to a good approximation given by Eq. (1) withA B. Neglecting the quantization of the precessionstates, we obtain for k B T KV (corresponding to1)hj ji T M s V k BTKV2gBk B Th! 0; (4)where g is the Landé factor, B is the Bohr magneton, k Bis Boltzmann’s constant, T is the temperature, and wehave introduced the angular frequency of the precession[20,21] ! 0 h 1 g B 2B a B 1=2 E . The angular frequency! 0 of the uniform mode of antiferromagnetic materials istypically of the order of 10 12 s 1 [22], which gives a sizeindependentmoment hj ji T 200 B at room temperature.This is the same order of magnitude as the expectedmagnetic moment due to uncompensated spins in a typicalantiferromagnetic particle with diameter of the orderof 5 nm. For smaller particles, the thermoinduced magneticmoment may be predominant at room temperature.As opposed to the behavior of normal bulk magneticFIG. 2. Schematic illustration of thermoinduced magnetizationin nanoparticles of antiferromagnetic materials. M sA andM sB are the instantaneous sublattice magnetization vectors.M A and M B are the sublattice magnetization vectors afteraveraging over the precession in a state with precession anglesA and B. M M A M B is the net magnetization. Forclarity, the difference between A and B is exaggerated.217201-2 217201-2

VOLUME 92, NUMBER 21PHYSICAL REVIEW LETTERS week ending28 MAY 2004materials, the magnitude of the thermoinduced magneticmoment increases with increasing temperature untilit starts to decrease when the Néel temperature isapproached.Because the thermal average of the absolute value ofthe thermoinduced magnetization, hjMji hj ji T =V, isinversely proportional to the volume, it is significant onlyin nanoparticles. In bulk antiferromagnets, a large numberof other spin wave excitation modes with q 0 arepopulated at finite temperatures. For each of these modes,the probabilities for A > B and A < B are equal.Since a large number of positive and negative contributionsare added together the resulting net magnetizationwill be vanishingly small in bulk. In a nanoparticle thepopulation of modes with q 0 may be negligible at lowtemperatures because of the energy gap between the q0 state and the q 0 states [23]. The q 0 modes withA > B and A < B have equal probabilities, but, at agiven instant of time, only one precession state exists in agiven particle. Therefore the particle will have a nonzeromagnetic moment.In practice, there can be several contributions to themagnetic moment of nanoparticles of antiferromagneticmaterials. Apart from the contributions from uncompensatedspins, even a tiny amount of strongly magneticimpurity phases can have a decisive influence on themagnetization because of the small susceptibility of perfectantiferromagnetic materials [3]. Furthermore, themagnetic structure of nanoparticles may differ fromthat of bulk materials [6]. The Néel temperature of nanoparticlesmay differ from the bulk value [23,24], and thismust also be taken into account when analyzing magnetizationdata. The thermoinduced magnetization in nanoparticlesmay be distinguished from other contributions,because its magnitude increases with temperature.Moreover, it is proportional to d 3 , where d is the particlediameter, whereas the size dependence due to uncompensatedspins is expected to be smaller [3], e.g., approximatelyproportional to d 1 .We have fitted the data of Seehra et al. [8], shown inFig. 1, to the linear relation of Eq. (4). In the fit we haveneglected other possible contributions to the temperaturedependence of the magnetic moment, and we have nottaken into account the random orientation of easy axes ofthe particles in the sample. From the slope of the linear fitwe find an angular frequency, ! 0 0:52 10 12 s 1 ,which is the expected order of magnitude for the uniformmode. The intercept at 167 B canbeattributedtothe magnetic moment due to uncompensated spins. Thethermoinduced moment at room temperature is of theorder of 250 B in accordance with Eq. (4). The increasein magnetic moment with temperature in ferritin particleswith nominally 1000, 2000, and 3000 iron atoms,found by Harris et al. [9], also shows a linear temperaturedependence with a slope corresponding to ! 0 0:410 12 s 1 . For smaller particles a larger slope was found.Although other explanations for the anomalous behaviorof antiferromagnetic nanoparticles have been suggested[9,12,14,15], the experimental data and the fit, shown inFig. 1, together with a number of similar experimentalobservations, give experimental evidence for a temperaturedependent magnetic moment that is in accordancewith the model for thermoinduced magnetization. Thusthe thermoinduced magnetization can explain anomalousmagnetic properties of nanoparticles of antiferromagneticmaterials, which have been discussed in the literature[4,8–15].The magnitude and direction of the thermoinducedmagnetic moment fluctuates because of rapid relaxationbetween the precession states with different precessionangles. In zero applied field, the time average of themagnetic moment will be zero. However, in an appliedfield, the thermoinduced moments will to some extent bealigned as is the case for the magnetic moments of superparamagneticparticles of ferro- or ferrimagnetic materials.The magnetization, induced by a small magneticfield applied parallel to the easy direction of magnetization,can be calculated by using Boltzmann statistics, andone finds that the contribution to the initial susceptibilityfrom the thermoinduced magnetic moment is given byi8k B TVg 2 B : (5)h! 0We see that i like hj ji T increases with temperature.This is in accordance with experimental studies of, forexample, Cr 2 O 3 nanoparticles [12].It is noteworthy that fluctuations between precessionstates with net magnetization ‘‘up’’ and ‘‘down’’ can takeplace without surmounting any energy barrier. Therefore,the thermoinduced magnetization may respond quickly tovariations of an applied field, and the high-frequencysusceptibility of nanoparticles of antiferromagnetic materialscan thus be expected to be significant. Further,because magnetic relaxation between all populated q 0precession states can take place without thermal activation,the relaxation may be independent of temperature.Macroscopic quantum tunneling is also characterized bya temperature-independent magnetic relaxation at lowtemperatures. In antiferromagnetic nanoparticles, macroscopicquantum tunneling is expected to be more pronouncedthan in ferro- or ferrimagnetic particles [25,26].Temperature-independent relaxation at very low temperatureshas been observed in, for example, nanoparticles ofantiferromagnetic ferritin [27,28] and -Fe 2 O 3 [29], butin experimental studies it may be difficult to distinguishbetween macroscopic quantum tunneling and classicalmagnetic relaxation, such as the relaxation of the thermoinducedmoment.In the case where nanoparticles of antiferromagneticmaterials are exposed to a dc magnetic field, the thermoinducedmagnetic moment will be aligned with the217201-3 217201-3

VOLUME 92, NUMBER 21PHYSICAL REVIEW LETTERS week ending28 MAY 2004field. This will partially suppress the superparamagneticrelaxation, which otherwise may take place at high temperatures.Similarly, if a nanoparticle of an antiferromagneticmaterial is in close contact with another magneticmaterial, the exchange coupling between surface atoms ofneighboring particles can also have a significant influenceon the relaxation behavior [30]. Such an exchange couplingmay also result in a preferred direction of thethermoinduced magnetic moment, which then contributesto the permanent magnetization.In conclusion, we have shown that there is a thermoinducedcontribution to the magnetic moment of nanoparticlesof antiferromagnetic materials, which explains anumber of recently reported anomalies. Because nanostructuredmagnetic materials are produced at a growingrate due to their important technological applications weanticipate that thermoinduced magnetization will be encounteredmore frequently in the future and that it willplay a role in future applications of magnetic nanoparticlesin nanotechnology.The work was supported by the Danish TechnicalResearch Council and the Danish Natural ScienceResearch Council. We thank P. J. van der Zaag andJ. Nygård for valuable comments.[1] J.T. Richardson and W. O. Milligan, Phys. Rev. 102, 1289(1956).[2] J. Cohen, K. M. Creer, R. Pauthenet, and K. Srivastava,J. Phys. Soc. Jpn. Suppl. B-1 17, 685 (1962).[3] J.T. Richardson, D. I. Yiagas, B. Turk, K. Forster, andM.V. Twigg, J. Appl. Phys. 70, 6977 (1991).[4] S. A. Makhlouf, F. T. Parker, F. E. Spada, and A. E.Berkowitz, J. Appl. Phys. 81, 5561 (1997).[5] A. Punnoose, H. Magnone, M. S. Seehra, andJ. Bonevich, Phys. Rev. B 64, 174420 (2001).[6] R. H. Kodama, S. A. Makhlouf, and A. E. Berkowitz,Phys. Rev. Lett. 79, 1393 (1997).[7] L. Néel, Compes Rendus 252, 4075 (1961).[8] M. S. Seehra, V. S. Babu, A. Manivannan, and J.W. Lynn,Phys. Rev. B 61, 3513 (2000).[9] J. G. E. Harris, J. E. Grimaldi, D. D. Awschalom,A. Chiolero, and D. Loss, Phys. Rev. B 60, 3453 (1999).[10] S. H. Kilcoyne and R. Cywinski, J. Magn. Magn. Mater.140–144, 1466 (1995).[11] S. A. Makhlouf, F.T. Parker, and A. E. Berkowitz, Phys.Rev. B 55, R14 717 (1997).[12] D. Vollath, D.V. Szabó, and J. O. Willis, Mater. Lett. 29,271 (1996).[13] M. Bañobre-López, C. Vázquez-Vásquez, J. Rivas, andM. A. López-Quintela, Nanotechnology 14, 318 (2003).[14] C. Gilles, P. Bonville, K. K.W. Wong, and S. Mann, Eur.Phys. J. B 17, 417 (2000).[15] M. S. Seehra and A. Punnoose, Phys. Rev. B 64, 132410(2001).[16] S. Mørup and H. Topsøe, Appl. Phys. 11, 63 (1976).[17] S. Mørup, J. Magn. Magn. Mater. 37, 39 (1983).[18] M. F. Hansen et al., Phys. Rev. Lett. 79, 4910 (1997).[19] K. Lefmann et al., Europhys. Lett. 54, 526 (2001).[20] C. Kittel, Phys. Rev. 82, 565 (1951); F. Keffer andC. Kittel, Phys. Rev. 85, 329 (1952).[21] S. Chikazumi, Physics of Ferromagnetism (ClarendonPress, Oxford, 1997, 2nd ed., p. 574.[22] A. H. Morrish, The Physical Principles of Magnetism(John Wiley & Sons, Inc., New York, 1966), 2nd ed.,p. 623.[23] P.V. Hendriksen, S. Linderoth, and P.-A. Lindgård, Phys.Rev. B 48, 7259 (1993).[24] S. N. Klausen, P.-A. Lindgård, K. Lefmann, F. Bødker,and S. Mørup, Phys. Status Solidi (a) 189, 1039 (2002).[25] B. Barbara and E. M. Chudnovsky, Phys. Lett. A 145, 205(1990).[26] E. M. Chudnovsky, J. Magn. Magn. Mater. 140 –144, 1821(1995).[27] J. Tejada and X. X. Zhang, J. Phys. Condens. Matter 6,263 (1994).[28] M. Duran, E. del Barco, J. M. Hernández and J. Tejada,Phys. Rev. B 65, 172401 (2002).[29] E. del Barco et al., Phys. Rev. B 65, 052404 (2002).[30] C. Frandsen and S. Mørup, J. Magn. Magn. Mater. 266,36 (2003).217201-4 217201-4

Paper III

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Paper IV

ARTICLE IN PRESSJournal of Magnetism and Magnetic Materials 266 (2003) 36–48Inter-particle interactions in composites ofantiferromagnetic nanoparticlesCathrine Frandsen*, Steen M^rupDepartment of Physics, Technical University of Denmark, Bldg. 307, Lyngby DK-2800 KGS., DenmarkReceived 24 October 2002; received in revised form 19 December 2002AbstractWe have prepared mixtures of a-Fe 2 O 3 , CoO, and NiO nanoparticles by drying aqueous suspensions of the particles.The magnetic properties were studied by M.ossbauer spectroscopy. The measurements showed that interactions withCoO particles suppress the superparamagnetic relaxation of both a-Fe 2 O 3 and 57 Fe-doped NiO particles. The effect ofNiO particles on a-Fe 2 O 3 particles was a shorter relaxation time and an induced Morin transition, which usually isabsent in a-Fe 2 O 3 nanoparticles. Spectra of a-Fe 2 O 3 particles, prepared by drying suspensions with added Co 2+ andNi 2+ ions, showed that the suspension medium can affect the magnetic properties of the a-Fe 2 O 3 particles significantly,but not in the same way as the CoO or NiO nanoparticles. Therefore, a strong inter-particle exchange interactionbetween particles of different materials seems to be responsible for the magnetic properties of the nanocomposites.r 2003 Elsevier B.V. All rights reserved.PACS: 75.50.Tt; 76.80.+y; 75.70.CnKeywords: Nanoparticles; M.ossbauer spectroscopy; Inter-particle interactions; Superparamagnetic relaxation; Nanocomposite1. IntroductionMany studies have been undertaken on samplesof magnetic nanoparticles in order to characterisethe influence of inter-particle interactions on themagnetic properties. Both dipole–dipole interactionbetween ferro- or ferrimagnetic particles andexchange interaction between epitaxially grownferro- and antiferromagnetic thin films haveattracted considerable attention. Based on the*Corresponding author. Tel.: +45-45-25-31-68; fax: +45-45-93-23-99.E-mail address: cathrine.frandsen@fysik.dtu.dk(C. Frandsen).results of these studies, it also seems interesting toinvestigate the interaction between different antiferromagneticmaterials.Previous studies of samples of antiferromagneticnanoparticles have shown that the superparamagneticrelaxation of a-FeOOH [1], a-Fe 2 O 3 [2], and57 Fe-doped NiO [3] nanoparticles can be stronglyinfluenced by inter-particle interactions. The relaxationof the sublattice magnetisation is significantlysuppressed when the particles are allowed toaggregate. Because of the small dipole moment ofthe antiferromagnetic particles, the dipole–dipoleinteraction is negligible and the interaction isdominated by exchange interactions across theparticle interfaces [1,2]. Only a few exchange0304-8853/03/$ - see front matter r 2003 Elsevier B.V. All rights reserved.doi:10.1016/S0304-8853(03)00453-0

ARTICLE IN PRESSC. Frandsen, S. M^rup / Journal of Magnetism and Magnetic Materials 266 (2003) 36–48 37bridges between surface atoms of neighbouringcrystallites are needed to account for the interactionstrength [2].The results of studies of interaction betweenmagnetic nanoparticles of the same material openthe question of possible interaction effects insamples containing magnetic nanoparticles ofdifferent materials. Studies of multilayers ofdifferent magnetic materials have already showninteresting features. For example, van der Zaaget al. [4] have shown that the N!eel temperature ofthin antiferromagnetic CoO layers (o50 ( A) isenhanced above its bulk value (293 K), whenepitaxially grown on ferrimagnetic Fe 3 O 4 . Ifsimilar interaction effects are present in compositesof nanoparticles, it may be possible to designmagnetic materials with new properties by mixingnanoparticles of different materials.Here we present the results of a study ofinteractions in mixtures of antiferromagneticnanoparticles. By use of M.ossbauer spectroscopywe have studied how the magnetic dynamics of a-Fe 2 O 3 and 57 Fe-doped NiO nanoparticles isaffected by neighbouring antiferromagnetic nanoparticlesof other materials. The mixtures weinvestigated are a-Fe 2 O 3 +CoO, a-Fe 2 O 3 +NiO,and 57 Fe-NiO+CoO. The results of some preliminarystudies have been published elsewhere [5].In the present work, we have also assessed whetherthe effects seen in the spectra are solely caused by apure particle–particle interaction or as an effect ofthe mixing process, e.g. ion adsorption on theparticle surfaces.2. Experimental detailsA batch of several grams of 9 nm a-Fe 2 O 3(hematite) nanoparticles was synthesized by meansof a modified gel–sol method developed bySugimoto et al. [6]. NiO nanoparticles wereprepared by annealing chemically precipitatedNi(OH) 2 (with and without 57 Fe doping) [3,7] at300 C in air for 3 h. These particles are disc shapedwith an average diameter of 12 nm and a thicknessof about 2 nm [3]. Particles of CoO were synthesizedby annealing cobalt acetate in an argonatmosphere at 350 C for 4 h yielding a particle sizeof about 20 nm and a minor impurity (o10%) ofmetallic Co.Samples of pure particles (a-Fe 2 O 3 and 57 FedopedNiO) and mixtures of a-Fe 2 O 3 +NiO, a-Fe 2 O 3 +CoO, and 57 Fe-doped NiO+CoO (all inweight ratios 1:1) were prepared by pouring 50 mgof each compound into 100 ml of a ‘‘suspensionmedium’’. Within this liquid, the particles wereexposed to intense ultrasound for 15 min in orderto break apart agglomerates of particles and toobtain homogeneous mixtures. The particles werethen allowed to settle and dry at room temperaturein an open petri bowl. Initially, we had chosendemineralised water as the suspension medium.We also studied samples of a-Fe 2 O 3 nanoparticles,prepared by drying suspensions of particles inaqueous solutions of NiCl 2 or Co(NO 3 ) 2 . Samplesof a-Fe 2 O 3 particles were also prepared by dryingaqueous suspensions with a range of pH values(1–8). The suspensions with different pH valueswere prepared by first adjusting the pH value of asuspension of hematite particles to 13.5 by addingNaOH. This results in formation of a stablesuspension of the particles. Then in eight separatebatches the pH was decreased to 1, 2,y, or8byadding HNO 3 and the samples were allowed to dryat room temperature. As a reference for themeasurements of the interacting particles, asuspension of non-interacting a-Fe 2 O 3 particleswas made by coating the suspended particles witholeic acid and then permanently suspending themin heptane. The concentration of a-Fe 2 O 3 in thesuspension was 0.13 vol%. This corresponds to7mg a-Fe 2 O 3 ml1 . The amount of surfactant was12 mg ml1 . This sample will be referred to as the‘‘a-Fe 2 O 3 ferrofluid’’.The samples were studied by 57 FeM.ossbauerspectroscopy using constant-acceleration spectrometerswith sources of 57 Co in rhodium. Spectra inthe temperature range 17–300 K were obtainedusing a closed cycle helium refrigerator from APDCryogenics Inc and a temperature controlledliquid nitrogen cryostat. The spectrometers werecalibrated with a 12.5 mm thick a-Fe foil at roomtemperature. Isomer shifts are measured relative tothat of the calibration spectra.X-ray diffraction (XRD) was performed using aPW 1390 Philips diffractometer with a CuK a

ARTICLE IN PRESS38C. Frandsen, S. M^rup / Journal of Magnetism and Magnetic Materials 266 (2003) 36–48radiation source. In addition to identifying thestructure of the particles by XRD, the particle sizewas determined from the broadening of the lineprofiles.Transmission electron microscopy (TEM)images were obtained by a Philips EM 430operated at voltages up to 300 kV.3. Results3.1. Relaxation in samples of pure a-Fe 2 O 3nanoparticlesThe M.ossbauer spectra of the a-Fe 2 O 3 ferrofluid(Fig. 1a) show a typical superparamagnetic behaviour.At low temperatures the spectra aredominated by a sextet, but at the highesttemperature (180 K) the spectrum consists of adoublet. At intermediate temperatures the spectracan be described as a superposition of a sextet anda doublet, both with relatively narrow lines,indicating that most of the particles have eithermuch longer or much shorter relaxation times thanthe time scale of M.ossbauer spectroscopy(B5 10 9 s). The superparamagnetic blockingtemperature, defined as the temperature at whichthe sextet and the doublet have identical areas, isabout 70 K.Fig. 1b shows spectra of a-Fe 2 O 3 particles thathave been allowed to aggregate during drying ofan aqueous suspension and thus interact. Comparisonwith the spectra in Fig. 1a clearly shows thatthe magnetic properties have changed dramaticallybecause of the enhanced interaction. The spectraof the interacting particles do not collapse into adoublet even above 250 K, but with increasingtemperature the average hyperfine field decreasesand the lines of the sextet become asymmetricallybroadened. Similar spectra have been observed inseveral other studies of interacting magneticnanoparticles [1–3,8,9] and have been explainedby an ordering of the sublattice magnetisationdirections of the particles induced by inter-particleexchange interactions of varying strengths. This isdiscussed in Section 4.1.3.2. Relaxation in mixtures of differentnanoparticlesFigs. 2a and b show the M.ossbauer spectra ofthe a-Fe 2 O 3 particles mixed with CoO and NiOα-Fe 2 O 3 ferrofluid α-Fe 2 O 3(a)180 K(b)300 K120 K250 KRelative absorption100 K80 K180 K120 K50 K80 K25 K25 K-12 -8 -4 0 4 8 12 -12 -8 -4 0 4 8 12Velocity (mm/s)Fig 1. M.ossbauer spectra obtained at the indicated temperatures of: (a) the a-Fe 2 O 3 ferrofluid and (b) dried a-Fe 2 O 3 nanoparticles.

ARTICLE IN PRESSC. Frandsen, S. M^rup / Journal of Magnetism and Magnetic Materials 266 (2003) 36–48 39α-Fe 2 O 3 + CoOα-Fe 2 O 3 + NiO(a)295 K(b)250 K250 K180 KRelative absorption180 K120 K120 K100 K80 K80 K20 K20 K-12 -8 -4 0 4 8 12 -12 -8 -4 0 4 8 12Velocity (mm/s)Fig. 2. M.ossbauer spectra of a-Fe 2 O 3 nanoparticles mixed with (a) CoO and (b) NiO nanoparticles.nanoparticles, respectively. When the a-Fe 2 O 3particles are mixed with the CoO particles thespectra consist of sextets with relatively sharp linesup to 180 K. At temperatures of 250 K and above,a doublet appears in the spectra. At temperaturesabove 80 K the lines of the sextet are clearlynarrower than those of the sample consistingsolely of interacting a-Fe 2 O 3 nanoparticles(Fig. 1b). In Fig. 1b, there is, however, not aclearly visible doublet even at the highest temperatures.Therefore, it seems that the relaxationbehaviour of the hematite particles mixed withCoO is quite different from that in the sampleconsisting solely of interacting a-Fe 2 O 3 particles.The spectra of the a-Fe 2 O 3 +CoO sample havesimilarities with those of non-interacting a-Fe 2 O 3particles, but the blocking temperature is muchhigher. The same behaviour was seen for a-Fe 2 O 3nanoparticles mixed with CoO particles, whichcontained no metallic Co impurity [5].The evolution with temperature of the spectra ofa-Fe 2 O 3 particles mixed with NiO, shown inFig. 2b, is somehow between those seen inFigs. 1a and b. The sextets are considerablybroadened at the highest temperatures, but at180 K and above, the spectra also contain adoublet with narrow lines. Thus, interaction betweenthe a-Fe 2 O 3 nanoparticles and NiO nanoparticlesaffects the relaxation behaviour of a-Fe 2 O 3 particlesin a way that is different from the interactionbetween a-Fe 2 O 3 and CoO particles.Fig. 3a and b show, respectively, M.ossbauerspectra of a sample of interacting 57 Fe-doped NiOnanoparticles and 57 Fe-doped NiO nanoparticlesfrom the same batch mixed with CoO nanoparticles.In both samples, the spectra consist of asuperposition of a singlet and a sextet in arelatively large temperature range. The blockingtemperature in the sample of interacting NiOparticles is about 140 K, but it increases when theparticles are mixed with CoO particles.3.3. The Morin transition in a-Fe 2 O 3 nanoparticlesIn bulk a-Fe 2 O 3 , the Morin transition takesplace as a first-order transition at T M C263 K [10].At this temperature, the spin structure changesfrom being confined to lie in the rhombohedral(1 1 1) plane above T M to lying alongthe [1 1 1] axis below T M : This magnetic phase

ARTICLE IN PRESS40C. Frandsen, S. M^rup / Journal of Magnetism and Magnetic Materials 266 (2003) 36–4857 Fe-NiO 57 Fe-NiO + CoO(a)300 K(b)295 K250 K250 KRelative absorption180 K120 K180 K120 K80 K80 K20 K20 K-12 -8 -4 0 4 8 12 -12 -8 -4 0 4 8 12Velocity (mm/s)Fig. 3. M.ossbauer spectra of: (a) 57 Fe-doped NiO nanoparticles and (b) 57 Fe-doped NiO nanoparticles mixed with CoO nanoparticles.transition is clearly visible in M.ossbauer spectrabecause the quadrupole shift changes sign andmagnitude (from e ¼ 0:1mms 1 above T M toe ¼þ0:2mms 1 below T M ). In small particles ofa-Fe 2 O 3 , the transition temperature decreases withdecreasing particle size and it has been reportedthat there is no Morin transition above liquidhelium temperature in particles with diametersbelow about 20 nm [11–13].In the spectra of the samples of pure 9 nm a-Fe 2 O 3 nanoparticles (Figs. 1a and b) there is asexpected no indication of a Morin transition.The quadrupole shift is negative in all themagnetically split spectra at low temperatures(eD 0:1mms 1 ) as in bulk a-Fe 2 O 3 above theMorin transition temperature. This is also the casein all spectra of a-Fe 2 O 3 nanoparticles mixed withCoO (Fig. 2a). However, surprisingly, the a-Fe 2 O 3particles mixed with NiO nanoparticles (Fig. 2b)show a Morin transition at low temperature. At20 K the spectrum has a quadrupole shift close to+0.2 mm s 1 . With increasing temperature up toB160 K there is a gradual change of the spectra,indicating a Morin transition. This is most clearlyseen in the broadening of line number 6 comparedto the width of line 1. The presence of a Morintemperature was also observed in several othersamples consisting of mixtures of a-Fe 2 O 3 andNiO nanoparticles with other particle sizes andmorphologies. The low-temperature spectra werefitted with two sextets. One of these corresponds tothe low-temperature state with e ¼þ0:2mms 1 .The other component did not show a quadrupoleshift of about 0.1 mm s 1 as expected for a-Fe 2 O 3particles above the Morin transition, but a valueclose to zero. In some studies of a-Fe 2 O 3nanoparticles and Al-substituted hematite samples,similar values for the quadrupole shift havebeen found [12]. The observations suggest that thesublattice magnetisation in a temperature range isneither fixed in the [1 1 1] direction nor in the (1 1 1)plane.3.4. Influence of added cations and pHWe have made a number of experiments toinvestigate the possible influence of adsorbedCo 2+ or Ni 2+ ions on the magnetic properties ofthe a-Fe 2 O 3 nanoparticles. The samples wereprepared by using suspension media with various

ARTICLE IN PRESSC. Frandsen, S. M^rup / Journal of Magnetism and Magnetic Materials 266 (2003) 36–48 41α-Fe 2 O 3 + Co 2+ (Fe:Co=38)α-Fe 2 O 3 + Co 2+ (Fe:Co=5)(a)295 K(b)295 K250 K250 KRelative absorption180 K120 K180 K120 K80 K80 K20 K17 K-12 -8 -4 0 4 8 12 -12 -8 -4 0 4 8 12Velocity (mm/s)Fig. 4. M.ossbauer spectra of a-Fe 2 O 3 nanoparticles prepared by drying suspensions of the particles in aqueous solutions of Co 2+ ions:(a) cation ratio Fe:Co=38 and (b) cation ratio Fe:Co=5.α-Fe 2 O 3 + Ni 2+ (Fe:Ni=27)α-Fe 2 O 3 + Ni 2+ (Fe:Ni=4)(a)295 K(b)295 K250 K250 KRelative absorption180 K120 K180 K120 K100 K80 K25 K20 K-12 -8 -4 0 4 8 12 -12 -8 -4 0 4 8 12Velocity (mm/s)Fig. 5. M.ossbauer spectra of a-Fe 2 O 3 nanoparticles prepared by drying suspensions of particles in aqueous solutions of Ni 2+ ions:(a) cation ratio Fe:Ni=27 and (b) cation ratio Fe:Ni=4.

ARTICLE IN PRESS42C. Frandsen, S. M^rup / Journal of Magnetism and Magnetic Materials 266 (2003) 36–48concentrations of Co 2+ or Ni 2+ ions. Sometypical temperature series of M.ossbauer spectraare shown in Figs. 4 and 5. By comparing thespectra in Fig. 4a with those in Fig. 1b, it canbe seen that small amounts of Co 2+ (about theamount needed to form a monolayer on thehematite particles) result in narrower lines ofthe sextet at the highest temperatures. The spectrain Fig. 4a do, however, not contain a doublet asthe spectra of a-Fe 2 O 3 particles mixed with CoO.Larger amounts of Co 2+ (Fig. 4b) result in adoublet component at the highest temperaturesindicating the presence of particles with shortrelaxation times. When Ni 2+ ions are added (Figs.5a and b) the spectra obtained at the highesttemperatures contain a doublet, which is especiallydominating in the sample with the highest Ni 2+concentration. It is notable that in contrast to thesample of a-Fe 2 O 3 particles mixed with NiO, thereis no Morin transition in the samples preparedwith Ni 2+ ions.High-resolution TEM studies of agglomerationin samples of TiO 2 nanoparticles [14,15] haveshown that the pH of the suspension medium canhave an important influence on the way particlesaggregate. We therefore tried to change the pH ofthe aqueous solution in which a-Fe 2 O 3 particleswere suspended to see if this had an effect on theproperties of the dried samples. All samples,prepared with pH values ranging from 1 to 8,yielded spectra like those shown in Fig. 1b. Thus,the pH of the suspension medium had no influenceon the relaxation behaviour of the dried samples.4. Discussion4.1. M .ossbauer spectra of non-interacting andinteracting a-Fe 2 O 3 particlesAs illustrated in Fig. 1, the evolution withtemperature of the M.ossbauer spectra of samplesof non-interacting and interacting a-Fe 2 O 3 particlesis quite different. In both cases, the lowtemperaturespectra consist of a sextet withrelatively narrow lines, but at higher temperatures,substantial differences are seen. We will use thesespectra and the theoretical interpretation of themas an introduction to the discussion of the featuresof the nanocomposites.In the spectra of non-interacting particles(Fig. 1a) a doublet appears at relatively lowtemperatures. The relative area of the doubletincreases with temperature at the expense of thesextet. At 180 K the spectrum only contains thedoublet component. (The small asymmetry ofthe doublet is an effect of the relaxation time beingof the order of 10 10 s [16].) Both components haverelatively narrow lines in the whole temperaturerange. Similar spectra have been found in numerousother studies of nanoparticles of various magneticmaterials. It is often assumed that the magneticanisotropy of magnetic nanoparticles is uniaxialwith the anisotropy energy given byEðyÞ ¼KV sin 2 y;ð1Þwhere K is the magnetic anisotropy constant, Vthe particle volume, and y the angle between the(sublattice) magnetisation direction and an easydirection of magnetisation. The expression for themagnetic anisotropy energy of a-Fe 2 O 3 is morecomplex than Eq. (1) [10,16], but for simplicity weuse Eq. (1) in the following discussion. A detaileddiscussion of the magnetic energy of a-Fe 2 O 3nanoparticles is given elsewhere [2,16].The superparamagnetic relaxation time of magneticnanoparticles with magnetic energy given byEq. (1), i.e. the average time between transitionsacross the energy barrier, separating the minima aty ¼ 0 and y ¼ 180 ; is given by the N!eel–Brownexpression [17,18]t ¼ t 0 expðKV=k B TÞ;ð2Þwhere k B is Boltzmann’s constant and T thetemperature. t 0 is typically in the range 10 12 –10 9 s and depends weakly on temperature [18].For 9 nm a-Fe 2 O 3 particles, t 0 E10 11 s [13]. Thetemperature dependence of the relaxation time fornon-interacting a-Fe 2 O 3 particles has previously[13,16] been found to be in accordance withEq. (2). Spectra like those shown in Fig. 1a canbe well fitted with the Blume–Tjon model [19] forM.ossbauer relaxation spectra when taking theparticle size distribution into account [2,13,16].At intermediate temperatures, some of theparticles will have relaxation times of the order

ARTICLE IN PRESSC. Frandsen, S. M^rup / Journal of Magnetism and Magnetic Materials 266 (2003) 36–48 43of 10 9 –10 8 s and these particles will givecontributions with broad lines [19]. However, ift 0 o10 10 s, the exponential dependence of therelaxation time in conjunction with the particlesize distribution results in a very broad distributionof relaxation times such that only a smallfraction of the particles have relaxation times inthis range. The contribution of these particles tothe spectra is therefore almost negligible. This isdiscussed in more detail elsewhere [20].Below the superparamagnetic blocking temperature,the (sublattice) magnetisation vectors fluctuatein directions close to the easy directions ofmagnetisation. These fluctuations (collective magneticexcitations) are usually fast compared to thetime scale of M.ossbauer spectroscopy and result ina reduction in the magnetic splitting of the spectragiven by [21,22]B obs CB 0 f1 k B T=ð2 KVÞg; ð3Þwhere B 0 is the magnetic hyperfine field in theabsence of these fluctuations. The maximumreduction will normally not exceed 10–15%,because further increase of the temperature ordecrease of the particle size results in fast superparamagneticrelaxation [22], i.e. the spectrumcollapses to a doublet. Collective magnetic excitationsin conjunction with the particle size distributionresults in some line broadening, but becausethe reduction of the magnetic splitting is less than10–15%, the lines in the sextet remain relativelynarrow at all temperatures. In the present casewith t 0 E10 11 s, one finds from Eq. (2) thattE5 10 9 s for KV=k B TE6: Therefore, themagnetic splitting collapses when the reductionof the magnetic hyperfine field approaches 8%. Asubstantial line broadening, like that seen in, forexample, the high-temperature spectra in Figs. 1band 4a, cannot be explained by collective magneticexcitations, because these spectra contain sextetswith hyperfine fields, which are reduced by muchmore than 10%.The evolution with temperature of the spectra ofthe interacting particles (Fig. 1b) is completelydifferent from that of the non-interacting particles.The lines of the a-Fe 2 O 3 sextet become increasinglybroadened with increasing temperature, butthere is no clearly visible doublet at least up to250 K. The spectra are dominated by sextets withbroad lines far above the temperature where thespectra of the non-interacting particles havecollapsed to a doublet. The magnetic energy of aparticle, i; with volume V i ; which interacts with itsneighbours, j; may be written [1,2]E i ¼ KV i sin 2 y M i X K ij M j :ð4ÞjHere M i and M j represent the (sublattice)magnetisation of the particles i and j; respectively.K ij represents the effective exchange couplingconstant originating from exchange couplingbetween surface atoms of the particles i and j: Ifthe anisotropy term (the first term) in Eq. (4) ispredominant, superparamagnetic relaxation of themagnetisation may take place between orientationsof the sublattice magnetisation along the easyaxes close to y ¼ 0 and 180 . In this case thedistribution of the values of the energy barriers(KV i ) in a typical sample results in a broaddistribution of relaxation times leading toM.ossbauer spectra like those in Fig. 1a. If theinteraction term (the second term) is large, it may,below a critical temperature, result in formation ofan ordered state of otherwise superparamagneticparticles [1,2,8,9]. If the interaction energy ispredominant compared to the anisotropy energy,there will be only one energy minimum, defined bythe effective interaction field. At finite temperatures,the (sublattice) magnetisation vectors maythen fluctuate in directions close to that correspondingto the energy minimum. The magneticproperties of such samples have been described bya simple mean field model, in which the summationin the last term of Eq. (4) is replaced by theaverage value [1,2]. The degree of ordering can bedescribed by an order parameter, which is unity atT ¼ 0 K and decreases with increasing temperaturesuntil it vanishes at the transition temperatureat which the sample becomes superparamagnetic.The temperature dependence of the order parametercan be calculated by using Boltzmannstatistics [1,2]. Well below the ordering temperaturethere is no energy barrier, which limits thefrequency of the fluctuations of the sublatticemagnetisation directions. Therefore, it is likelythat the fluctuations are fast compared to the time

ARTICLE IN PRESS44C. Frandsen, S. M^rup / Journal of Magnetism and Magnetic Materials 266 (2003) 36–48scale of M.ossbauer spectroscopy. Thus, themagnetic splitting in the M.ossbauer spectra shouldbe proportional to the order parameter. In asample of more or less randomly packed nanoparticlesthere will be a variation of the effectiveexchange coupling constants, K ij ; such that at agiven temperature different parts of the samplewill have different values of the order parameter.This will result in a distribution of magnetichyperfine fields, which can explain the line broadeningof the sextets. Detailed analyses of spectra ofthis type have shown that the model can explainquantitatively the properties of interactinga-Fe 2 O 3 particles [2].Qualitatively, the spectra of interacting andnon-interacting particles of maghemite (g-Fe 2 O 3 )[9], NiO [3] and goethite (a-FeOOH) [23] differ inthe same way as those of a-Fe 2 O 3 particles.Therefore, the difference in the temperaturedependence of the M.ossbauer spectra of interactingand non-interacting magnetic nanoparticles,illustrated in Fig. 1, seems to be a common featureof magnetic nanoparticles. If the interactionenergy gradually increases from a negligible valueto become predominant compared to the anisotropyenergy, one should expect a gradual changeof the spectra from being similar to those of Fig.1a to resemble those in Fig. 1b.If the neighbouring particles are randomlyoriented, one might expect that the contributionsfrom different neighbouring particles in the secondterm of Eq. (4) partially cancel, and therefore thenet interaction field may be small. However, highresolution TEM studies of samples TiO 2 nanoparticles,obtained by drying aqueous suspensions,have shown a large tendency for neighbouringnanoparticles to align with parallel lattice planes[14,15]. If the particles in our samples have asimilar tendency, this might explain the stronginteraction. Indeed, preliminary TEM studies doin fact indicate such a tendency both for a-Fe 2 O 3and NiO nanoparticles. As an example, Fig. 6shows an electron micrograph of NiO nanoparticles.It is seen that several neighbouring NiOnanoparticles have well aligned lattice planes.When analysing the M.ossbauer spectra ofmixtures of different particles in the present work,it should be realised that there may be local10 nmFig. 6. Transmission electron micrograph of NiO nanoparticles.Note the alignment of the lattice planes of neighbouringparticles.regions in the samples, in which the particles thatcontribute to the signals in the M.ossbauer spectra,mainly interact with each other. In other localregions they may interact mainly with the particlesof the other material. Therefore, the spectra mayhave different types of contributions. The detailedatomic arrangement at the interfaces is probablyalso a parameter, which can have an importantinfluence on the exchange coupling betweenparticles, and which can vary considerably in asample. However, in all cases discussed here andreported previously [5], the spectra of mixtures ofdifferent nanoparticles are significantly differentfrom those of the samples with only one type ofparticles. This shows that the mixing with otherparticles has a large influence on the magneticproperties of the composites.4.2. Interaction of a-Fe 2 O 3 nanoparticles with CoOnanoparticles and Co 2+ ionsThe spectra of the a-Fe 2 O 3 particles interactingwith CoO particles (Fig. 2a) consist up to 180 K ofa sextet with lines that are much narrower thanthose of the corresponding spectra of pure interactinghematite particles. This indicates thatinteractions with CoO significantly reduce magneticfluctuations in the a-Fe 2 O 3 particles. At 250and 295 K a coexistence of a sextet and a doublet isseen and there is only a moderate broadening ofthe sextet compared to the spectra in Fig. 1b.Thus, the shape of these spectra is more similar to

ARTICLE IN PRESSC. Frandsen, S. M^rup / Journal of Magnetism and Magnetic Materials 266 (2003) 36–48 45those of non-interacting a-Fe 2 O 3 particles than tothose of strongly interacting particles. The blockingtemperature is, however, much higher thanthat of the a-Fe 2 O 3 ferrofluid. It is possible that astrong exchange interaction between the surfaceatoms of the a-Fe 2 O 3 particles and the CoOparticles results in a strong coupling of thesublattice magnetisation directions of the twodifferent types of particles. The CoO particles arelarger than the hematite particles and the magneticanisotropy constant is also larger. Therefore, it islikely that the anisotropy energy for CoO particlesis large compared to the interaction energy and themagnetic properties may be dominated by superparamagneticrelaxation across the anisotropyenergy barrier rather than by the inter-particleinteraction. A strong coupling of the a-Fe 2 O 3particles to these CoO particles will result in asituation where the relaxation of the a-Fe 2 O 3particles follows the relaxation of the CoOparticles. This may explain why the spectra inFig. 2a are typical for samples for which theanisotropy energy is predominant. The presence ofa doublet at the highest temperatures may not bedue to superparamagnetic relaxation of the CoOparticles to which the a-Fe 2 O 3 particles arecoupled. It could be related to the transition ofCoO from an antiferromagnetic to a paramagneticstate. The N"eel temperature of bulk CoO is 293 K.However, even well above this temperature, thesextets have much sharper lines than in the spectraof pure a-Fe 2 O 3 particles [5]. The CoO particlestherefore seem to have a much larger influence onthe relaxation of some of the a-Fe 2 O 3 particlesthan expected for a paramagnetic phase. Becausethe CoO is in contact with a-Fe 2 O 3 , which has amuch higher magnetic transition temperature, it ispossible that its N"eel temperature is increased as inthe case when CoO interacts with Fe 3 O 4 [4].Further investigations are necessary to clarify themechanisms by which CoO particles influence therelaxation of a-Fe 2 O 3 particles.A possible explanation of the spectra in Fig. 2acould be that small amounts of Co 2+ ions aredissolved during the mixing procedure and subsequentlyadsorbed on the surface of a-Fe 2 O 3particles. Because of the large single-ion anisotropyof Co 2+ this could result in an enhancedanisotropy of the a-Fe 2 O 3 particles, which thenmay become predominant compared to the interactionenergy. This might explain the temperaturedependence of the spectra, which is typical forparticles for which the anisotropy is predominantand it could also explain the high blockingtemperature. The spectra of the sample preparedfrom an aqueous solution of Co 2+ with an Fe:Coratio of 38 consist of sextets at all temperatures upto 295 K (Fig. 4a). The substantial line broadening,seen at the highest temperatures and theabsence of a doublet is typical for a sample inwhich the inter-particle interactions dominate overthe anisotropy energy. The spectra are similar tothose of pure, interacting hematite nanoparticles(Fig. 1b), but significantly different from those ofthe mixture of hematite and CoO nanoparticles. Inthe spectra of a sample with an Fe:Co ratio of 5(Fig. 4b), a doublet appears at TX120 K, indicatingthat some of the hematite nanoparticles exhibitfast relaxation. We suggest that with the relativelylarge amount of Co 2+ ions, a paramagnetic cobaltsalt is formed during the drying of the sample.Such a paramagnetic salt may separate thea-Fe 2 O 3 particles and thereby reduce the interparticleinteraction and lead to fast superparamagneticrelaxation. In both samples it is expectedthat the surface of the a-Fe 2 O 3 particles is coveredby Co 2+ ions, at least to the same extend as in thesample consisting of a mixture of hematite andCoO nanoparticles. Therefore, if the single ionanisotropy of adsorbed Co 2+ ions were responsiblefor the behaviour of the sample of hematitemixed with CoO, one would expect the spectra inFigs. 2a, 4a and b to be similar. This is not the caseand therefore it seems that the relaxation behaviourof hematite in the samples with CoOnanoparticles cannot be explained by adsorbedCo 2+ ions.4.3. Interaction of a-Fe 2 O 3 nanoparticles with NiOnanoparticles and Ni 2+ ionsWhen the a-Fe 2 O 3 particles are mixed with NiOparticles (Fig. 2b), the M.ossbauer spectra obtainedat To180 K consist of sextets and the spectrashow a gradual Morin transition that is not seen inthe spectra of pure, interacting or non-interacting

ARTICLE IN PRESS46C. Frandsen, S. M^rup / Journal of Magnetism and Magnetic Materials 266 (2003) 36–48a-Fe 2 O 3 nanoparticles. At TX180 K the spectracontain both a doublet with narrow lines and asextet with rather broad lines. Thus, these hightemperature spectra have similarities to both thoseof pure non-interacting and interacting a-Fe 2 O 3nanoparticles. The NiO particles are much smallerthan the CoO particles and therefore they areexpected to have a smaller magnetic anisotropyenergy. In fact, the spectra in Fig. 3a show thatthey are superparamagnetic at TX180 K. (Neutrondiffraction studies of a similar sample of NiOnanoparticles [24] have shown that the N!eeltemperature is about 460 K, i.e. a little lower thanthe N!eel temperature of bulk NiO (523 K).) Wepropose that the sextets with broad lines in Fig. 2bat TX180 K are due to hematite particles forwhich the magnetic energy is dominated bymagnetic interaction with other a-Fe 2 O 3 nanoparticles.The doublets in the spectra of Fig. 2b atTX180 K may be due to hematite particles, whichperform fast superparamagnetic relaxation, becausethey mainly are in contact with NiO particleswith a small magnetic anisotropy energy.The spectra of a-Fe 2 O 3 nanoparticles, preparedby drying suspensions in aqueous solutions ofNi 2+ ions (Fig. 5), contain a doublet at the highesttemperatures, indicating the presence of a-Fe 2 O 3particles with fast superparamagnetic relaxation.The spectra at the highest temperatures of thesample with a Fe:Ni ratio of 27 are similar to thoseof a-Fe 2 O 3 nanoparticles mixed with NiO, shownin Fig. 2b. This might suggest that the fastrelaxation in the samples consisting of a-Fe 2 O 3mixed with NiO in fact could be due to adsorbedNi 2+ ions. However, the low-temperature spectrain Fig. 5 show no indication of a Morintemperature in contrast to the sample of a-Fe 2 O 3particles mixed with NiO particles. Therefore,inter-particle interaction effects in the a-Fe 2 O 3 +NiO sample also seem to have an importantinfluence on the magnetic properties of theparticles. The spectra of the sample with an Fe:Niratio of 4 (Fig. 5b) show an evolution withtemperature typical for particles for which theanisotropy energy is predominant. Almost all thea-Fe 2 O 3 particles relax rapidly at the highesttemperatures. This is presumably because a paramagneticnickel salt is formed during the drying,and such a paramagnetic phase in the sample mayseparate the a-Fe 2 O 3 nanoparticles and therebyreduce the inter-particle interactions.4.4. Interactions between 57 Fe-doped NiOnanoparticles and CoO nanoparticlesThe spectra of 57 Fe-doped NiO nanoparticleswith and without CoO nanoparticles (Fig. 3) showa coexistence of a sextet and a doublet in a broadtemperature range. This indicates that the magneticproperties are dominated by relaxationacross an energy barrier, i.e. the inter-particleinteraction energy seems to be small compared tothe anisotropy energy in both samples. Thesuperparamagnetic blocking temperature is highestin the sample with CoO nanoparticles. Wesuggest that the mechanism for the suppression ofthe relaxation may be the same as for the a-Fe 2 O 3nanoparticles, i.e. a strong exchange coupling atthe CoO–NiO interfaces hinders to some extendthe relaxation of the NiO particles.Although the spectra of 57 Fe-doped NiO nanoparticlesqualitatively are similar to those typicalfor non-interacting particles one cannot concludethat the inter-particle interaction is weak. Theshape of M.ossbauer spectra of interacting nanoparticlesdoes not give direct information aboutthe absolute value of the strength of inter-particleinteractions, but it depends on the ratio betweenthe anisotropy and the interaction energies.a-Fe 2 O 3 nanoparticles have unusually small magneticanisotropy constants (t10 4 Jm 3 [13]).Typical values for nanoparticles of other materialsare in the range 10 4 –10 6 Jm 3 . Therefore, themagnetic energy of a-Fe 2 O 3 nanoparticles mayeasily be dominated by inter-particle interactions,leading to M.ossbauer spectra like those shown inFig. 1b. The coexistence of sextets and singlets ordoublets (e.g. Figs. 3a and b) does not show thatthe inter-particle interactions are small, but onlythat the anisotropy energy is predominant.5. ConclusionsWe have studied the effects of inter-particleinteractions in mixtures of antiferromagnetic

ARTICLE IN PRESSC. Frandsen, S. M^rup / Journal of Magnetism and Magnetic Materials 266 (2003) 36–48 47nanoparticles prepared by drying aqueous suspensions.The M.ossbauer spectra of non-interacting9nm a-Fe 2 O 3 particles exhibit a typical superparamagneticbehaviour with a blocking temperatureof about 70 K. The distribution in energybarriers results in a broad distribution of relaxationtimes and therefore the spectra essentially canbe described as superpositions of sextets anddoublets. If the a-Fe 2 O 3 particles are allowed tointeract, the superparamagnetic relaxation issuppressed and the M.ossbauer spectra are inaccordance with the existence of an ordered statein which the interaction energy is predominantcompared to the anisotropy energy. The linebroadening of the sextets in these spectra can beexplained by a variation of the inter-particleinteraction strength in the sample.When the a-Fe 2 O 3 particles are mixed with CoOparticles, the M.ossbauer spectra are typical forparticles for which superparamagnetic relaxationacross an energy barrier is predominant, but theblocking temperature is much higher than for thenon-interacting particles. We suggest that a strongexchange coupling between the a-Fe 2 O 3 particlesand the CoO particles, which have larger magneticanisotropy energy, can explain the results. In thesample of a-Fe 2 O 3 particles mixed with NiOparticles, some of the particles exhibit fast superparamagneticrelaxation above the blocking temperatureof the NiO particles. This can beexplained by a-Fe 2 O 3 particles surrounded byNiO nanoparticles with small anisotropy energy.Other particles in the sample seem to be moreinfluenced by interactions between a-Fe 2 O 3 particles.At lower temperatures, the a-Fe 2 O 3 particlesmixed with NiO particles show a partial Morintransition, which usually is absent in hematitenanoparticles.Studies of a-Fe 2 O 3 particles, prepared by dryingsuspensions in aqueous solutions of Co 2+ andNi 2+ , showed that adsorbed cobalt and nickel ionscan significantly affect the magnetic properties ofthe a-Fe 2 O 3 particles, but in ways that are differentfrom CoO and NiO particles.Spectra of 57 Fe-doped NiO nanoparticles, withand without admixed CoO nanoparticles, showeda temperature dependence typical for superparamagneticparticles, i.e. the anisotropy energyseems to be predominant compared to the interactionenergy. The blocking temperature is increasedwhen the particles interact with CoO,presumably because the 57 Fe-doped NiO nanoparticlesare exchange coupled to the CoOparticles with large anisotropy energy.The present studies of composites of magneticnanoparticles show that inter-particle interactionsbetween particles of different materials can have asubstantial influence on the magnetic properties.The results suggest that exchange coupling betweensurface atoms of nanoparticles of differentmaterials play an important role in these materials.If such interaction effects are prevalent we suggestthat they can be used to tailor magnetic materialswith new properties from mixtures of nanoparticles.AcknowledgementsThis work was supported by the DanishTechnical Research Council and the DanishResearch Council for Natural Sciences. Lis Lilleballeand Franz B^dker are thanked for their helpwith sample preparation, Helge K. Rasmussen forhelp with the M.ossbauer spectroscopy measurements,Flemming Grumsen for help with the TEMstudies and Leif Gerward for help with the XRDmeasurements.References[1] S. M^rup, M.B. Madsen, J. Franck, J. Villadsen, C.J.W.Koch, J. Magn. Magn. Mater. 40 (1983) 163.[2] M.F. Hansen, C. Bender Koch, S. M^rup, Phys. Rev. B 62(2000) 1124.[3] F. B^dker, M.F. Hansen, C. Bender Koch, S. M^rup, J.Magn. Magn. Mater. 221 (2000) 32.[4] P.J. van der Zaag, Y. Ijiri, J.A. Borchers, L.F. Feiner,R.M. Wolf, J.M. Gaines, R.W. Erwin, M.A. Verheijen,Phys. Rev. Lett. 84 (2000) 6102.[5] C.W. Ostenfeld, S. M^rup, Hyperfine Interact. C5 (2002)83.[6] T. Sugimoto, Y. Wang, H. Itoh, A. Muramatsu, Colloid.Surf. A 134 (1998) 265.[7] S.A. Mahlouf, F.T. Parker, F.E. Spada, A.E. Berkowitz, J.Appl. Phys. 81 (1997) 5561.[8] S. M^rup, Hyperfine Interact. 90 (1994) 171.

ARTICLE IN PRESS48C. Frandsen, S. M^rup / Journal of Magnetism and Magnetic Materials 266 (2003) 36–48[9] S. M^rup, F. B^dker, P.V. Hendriksen, S. Linderoth,Phys. Rev. B 52 (1995) 287.[10] A.H. Morrish, Canted Antiferromagnetism: Hematite,World Scientific, Singapore, 1994.[11] W. K.undig, H. B.ommel, G. Constabaris, R.H. Lindquist,Phys. Rev. 142 (1966) 327.[12] R.E. Vandenberghe, E. Van San, E. De Grave, G.M. DaCosta, Czech. J. Phys. 51 (2001) 663.[13] F. B^dker, S. M^rup, Europhys. Lett. 52 (2000) 217.[14] R.L. Penn, J.F. Banfield, Geochim. Cosmochim. Acta 63(1999) 1549.[15] F. Banfield, S.A. Welch, H. Zhang, T.T. Ebert, R.L. Penn,Science 289 (2000) 751.[16] F. B^dker, M.F. Hansen, C. Bender Koch, K. Lefmann, S.M^rup, Phys. Rev. B 61 (2000) 6826.[17] L. N!eel, Ann. Geophys. 5 (1949) 99.[18] W.F. Brown Jr, Phys. Rev. 130 (1963) 167.[19] M. Blume, J.A. Tjon, Phys. Rev. 165 (1968) 446.[20] S. M^rup, C. Frandsen, F. B^dker, S.N. Klausen,K. Lefmann, P.-A. Lindg(ard, M.F. Hansen, HyperfineInteract, in press.[21] S. M^rup, H. Tops^e, Appl. Phys. 11 (1976) 63.[22] S. M^rup, J. Magn. Magn. Mater. 37 (1983) 39.[23] S. M^rup, Hyperfine Interact. 60 (1990) 959.[24] S.N. Klausen, P.-A. Lindg(ard, K. Lefmann, F. B^dker, S.M^rup, Phys. Stat. Sol. A 189 (2002) 1039.

Paper V

PROOF COPY [BQ9013] 036437PRBPHYSICAL REVIEW B 70, 1(2004)Interparticle interactions in composites of nanoparticles of ferrimagnetic „-Fe 2 O 3 …and antiferromagnetic „CoO,NiO… materialsC. Frandsen, 1 C. W. Ostenfeld, 1 M. Xu, 1, * C. S. Jacobsen, 1 L. Keller, 2 K. Lefmann, 3 and S. Mørup 11 Department of Physics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark2 Laboratory for Neutron Scattering, ETHZ & PSI, CH-5232 Villigen PSI, Switzerland3 Materials Research Department, Risø National Laboratory, DK-4000 Roskilde, Denmark(Received 8 March 2004; revised manuscript received 1 July 2004)PROOF COPY [BQ9013] 036437PRBThe magnetic properties of mixtures of ferrimagnetic -Fe 2 O 3 (maghemite) and antiferromagnetic NiO orCoO nanoparticles have been studied by use of 57 Fe Mössbauer spectroscopy, neutron powder diffraction andmagnetization measurements. The studies showed that the interaction with antiferromagnetic particles has asignificant influence on the magnetic properties of the -Fe 2 O 3 nanoparticles. It was found that mixing the-Fe 2 O 3 nanoparticles with NiO nanoparticles resulted in a faster superparamagnetic relaxation and a reducedcoercivity compared to a sample consisting solely of -Fe 2 O 3 nanoparticles. On the contrary, mixing of -Fe 2 O 3 nanoparticles with CoO nanoparticles resulted in a suppression of the relaxation and an increase incoercivity. These results suggest that the properties of the ferrimagnetic -Fe 2 O 3 nanoparticles are influencedby the anisotropy of their neighboring antiferromagnetic particles. The dominating type of magnetic interactionbetween the particles in the composites seems to be exchange interaction between surface atoms of neighboringparticles.DOI: XXXXPACS number(s): 75.50.Tt, 75.75.a, 76.80.y, 75.60.EjI. INTRODUCTIONInterparticle interactions between magnetic nanoparticlescan have strong influence on the magnetic properties; in particular,the superparamagnetic relaxation of the particles canbe significantly affected by interactions. 1–18 The influence ofdipolar interactions between ferromagnetic or ferrimagneticnanoparticles has been studied in, for example, frozen ferrofluidswith different interparticle distances. Weak dipole interactionscan lead to faster relaxation, 12 whereas strong interactionsmay result in slowing down of the relaxation andeventually to a divergence of the superparamagnetic relaxationtime at a critical temperature, which increases withincreasing strength of the interaction. 1,2,13–16 Below this criticaltemperature the samples have many similarities withspin-glasses. 2–5Dipolar interactions between antiferromagnetic nanoparticlesare typically too weak to have any significant influenceon the relaxation behaviour, even if the particles are in closecontact. 6,7 Still, Mössbauer spectroscopy studies have shownthat antiferromagnetic nanoparticles in close proximity oftenhave their superparamagnetic relaxation suppressed comparedto noninteracting particles. 7,9–11 This suggests that exchangeinteractions between surface atoms of neighboringparticles can be significant.Exchange interaction across interfaces between ferro- orferrimagnetic materials and antiferromagnetic materials hasgreat technological importance because it can lead to enhancedcoercivity and shifted hysteresis loops, known as“exchange bias,” due to the pinning of the magnetization ofthe ferromagnet by the antiferromagnet. 19,20 Studies of thinfilms of Fe 3 O 4 interlayered with either CoO or NiO haverevealed another interesting phenomenon, namely that theinteractions between the two materials can result in a substantialincrease of the Néel temperature of CoO andNiO. 21,22 Most of the studies of exchange interaction acrossinterfaces have been focused on thin film structures, becauseof their use in spin valves, which play an important role in,for example, read heads in present day computers. It hasrecently been shown that the exchange coupling of ferromagneticnanoparticles to an antiferromagnetic environmentcan lead to a greatly enhanced anisotropy and this maybe utilized to increase the information density in magneticrecording media. 23 Studies of annealed self-assemblednanoparticles have revealed strong exchange coupling, whichcan be used for creating permanent magnets. 24 In other studies,nanoparticles of ferro- or ferrimagnetic materials havebeen mixed with antiferromagnetic nanoparticles byball-milling. 25–27 When using this preparation technique,nanoparticles of the different materials may be welded togetherand therefore come in close contact such that exchangecoupling between the particles can be significant. Inthese studies, it was found that interaction with the antiferromagneticparticles can result in both an enhanced coercivityand a nonzero exchange bias.We have earlier investigated the influence of interparticleinteractions between antiferromagnetic nanoparticles of differentmaterials, prepared by drying aqueous suspensions ofthe particles. 9,10 With this preparation technique one mightexpect the interparticle interactions to be weak. However,Mössbauer studies of pure -Fe 2 O 3 (Refs. 7 and 10) or57 Fe-doped NiO (Ref. 11) nanoparticles have shown that thesuperparamagnetic relaxation is significantly suppressed insamples prepared by drying aqueous suspensions. The studiesof samples of nanoparticles of different materials alsogave some unexpected results. 9,10 For example, mixing of-Fe 2 O 3 nanoparticles with CoO nanoparticles resulted in astrong suppression of the superparamagnetic relaxation,whereas mixing -Fe 2 O 3 nanoparticles with NiO nanoparticleshad the opposite effect. Furthermore, surprisingly it1098-0121/2004/70(13)/1(0)/$22.50 70 1-1©2004 The American Physical SocietyPROOF COPY [BQ9013] 036437PRB

PROOF COPY [BQ9013] 036437PRBFRANDSEN et al. PHYSICAL REVIEW B 70, 1(2004)was found that mixing with NiO particles resulted in a MorinE = K sin 2 − M · B int , 3replaced by 7,8,10 particle interactions.transition in 9 nm -Fe 2 O 3 nanoparticles, although this magneticphase transition normally is absent in -Fe 2 O 3 particles where B int is an effective interaction field, which may havewith diameters below 20 nm. In this paper, we present the its main contributions from exchange interactions withresults of studies of mixtures of 7 nm ferrimagnetic - neighboring magnetic particles, and M is the (sublattice)Fe 2 O 3 nanoparticles with antiferromagnetic NiO or CoO magnetization. If the second term in Eq. (3) is predominant,nanoparticles. By use of Mössbauer spectroscopy, we have there will be only one energy minimum of the magnetic energy,and the magnetization vector may then fluctuate aroundstudied the influence of interactions on the relaxation of the-Fe 2 O 3 nanoparticles. The results are qualitatively similar the direction of the effective interaction field. In this case theto those obtained in our previous studies of mixtures with average of the magnetic hyperfine field has a finite value, and-Fe 2 O 3 nanoparticles. 9,10 Magnetization measurements on the Mössbauer spectra will therefore be magnetically split.the composites show that interparticle interactions affect also However, even for very fast fluctuations, the spectra willthe coercivity of the -Fe 2 O 3 nanoparticles. This result supportsthat there is a strong exchange interaction between the teraction fields in samples of interacting nanoparticles. 7,8,10have broad lines because of the distribution of effective in-particles in the samples.Only at high temperatures, where the thermal energy becomescomparable to or larger than the interparticle interactionenergy, there will be a doublet or singlet component inII. MÖSSBAUER SPECTRA OF NONINTERACTINGAND INTERACTING MAGNETIC NANOPARTICLESthe spectra.The magnetic anisotropy of an isolated magnetic nanoparticleis often assumed uniaxial with a magnetic anisotropyenergy density given byIII. EXPERIMENTAL DETAILS-Fe 2 O 3 nanoparticles were prepared by oxidation at ambientconditions of Fe 3 O 4 nanoparticles, which were made byE = K sin 2 ,1co-precipitation of FeII and FeIII from an aqueous solutionof 2.0 M FeNO 3 3 and 1.0 M FeSO 4 by adding a 1.0 Maqueous solution of NaOH. The particles were washedwhere K is the magnetic anisotropy energy constant, and isthe angle between the (sublattice) magnetization directionand an easy direction of magnetization. Very small particlesmay perform superparamagnetic relaxation [i.e., thermalfluctuations of the (sublattice) magnetization between thetwo minima at =0° and =180°] with a relaxation time, ,given by the Néel-Brown expression 28,29through several steps with H 2 O and acetone. After washing,the particles in a part of the sample were coated with oleicacid and suspended in heptane in order to minimize interparticleinteractions. The particles in the remaining part of thesample were left uncoated and freeze-dried.NiO nanoparticles were prepared by thermal decompositionof NiOH 2 at 325°C in air for 3 h, similar to the preparation = 0 expKV/k B T,2 described in Ref. 11.CoO nanoparticles were prepared by two different methods.A sample, called CoO-ann, was prepared by heatingwhere V is the particle volume, k B is Boltzmann’s constant, cobalt acetate in an argon atmosphere at 300°C for 4 h. Thisand T is the temperature. 0 is typically in the range sample contained a minor impurity of metallic Co. Another10 −11 –10 −9 s. In nanoparticles, for which 0 is small sample of CoO particles, CoO-bm, was prepared by highenergy10 −11 s compared to the time scale of Mössbauer spectroscopy, M 5·10 −9 s, a typical (i.e., not truly monodisperse)particle size distribution will result in a very widerange of relaxation times at temperatures where the averagerelaxation time is close to M . This is due to the exponentialdependence of on V. Therefore, close to the blocking temperature,only a tiny fraction of the particles will have relaxationtimes close to M , which would give rise to broad componentsin the spectra. 10,30 Instead, the spectra will mainlyconsist of a superposition of a sextet with narrow lines, representingthose particles, which are below their blockingtemperature M , and a sharp central doublet or singlet,representing those particles which exhibit fast superparamagneticrelaxation M . However, if 0 is of the order of10 −10 –10 −9 s, a large fraction of the particles in a sample hasrelaxation times comparable to the time scale of Mössbauerspectroscopy in a temperature range where KV/k B T is small.This will result in spectra with broadened lines around theblocking temperature.If the particles are in close proximity, Eq. (1) may beball-milling of a 1:1 molar ratio mixture of Co 3 O 4and Co in argon for 115 h. This preparation method seems tobe a convenient way to produce pure and fairly small CoOparticles.Mixtures of nanoparticles of -Fe 2 O 3 with NiO or CoO(1:1 by weight, unless otherwise indicated) were preparedby suspending the particles in distilled water, and subsequentlyexposing them to intense ultrasound with the aim tobreak apart agglomerates and to obtain a homogeneous mixture.The mixed samples were left to dry in open petri dishesin air at room temperature for about 2 days or at 200 °C for2 h. The dried powders were collected from the petri disheswith a plastic spatula and packed into sample containers. ForMössbauer spectroscopy and magnetization measurements,the powders were tightly packed. In particular for magnetizationmeasurements, where magnetic fields of up to 1 Twere applied, the powders were densely compacted to a coherentsolid, with the aim to avoid rotation of the particlesduring measurements. No binding materials such as epoxywere added to the powders in order not to affect the inter-PROOF COPY [BQ9013] 036437PRBPROOF COPY [BQ9013] 036437PRB1-2

PROOF COPY [BQ9013] 036437PRBINTERPARTICLE INTERACTIONS IN COMPOSITES OF… PHYSICAL REVIEW B 70, 1(2004)FIG. 1.57 Fe-Mössbauer spectraobtained at the indicated temperaturesof samples of pure 7 nm-Fe 2 O 3 particles. (a) Coated witholeic acid and suspended in heptane(b) uncoated, freeze-dried, (c)uncoated, dried at roomtemperature.PROOF COPY [BQ9013] 036437PRBX-ray diffraction (XRD) was performed using a PW 1390Philips diffractometer with a Cu K radiation source.Transmission electron microscopy (TEM) images wereobtained by a Philips EM 430 operated at voltages up to300 kV.Mössbauer spectra were obtained using conventional constantacceleration spectrometers with sources of 57 Co inrhodium. The instruments were calibrated by use of a12.5 m foil of -Fe. Velocities and isomer shifts are givenrelative to the centroid of the calibration spectrum.Neutron powder diffraction measurements were performedon the DMC diffractometer at the Swiss SpallationNeutron Source, Paul Scherrer Institute, Villigen, Switzerland.The diffractometer uses a multi-detector, which spans atwo-theta angle of 80° with a detector separation of 0.2°. Weused a wavelength of 4.2 Å for the measurements. By usinga two-theta starting angle of 33°, we were able to record, forCoO, the antiferromagnetic ½½½ reflection at 1.28 Å −1 ,the magnetic ½½3/2 reflection at 2.45 Å −1 , and the structural111 reflection at 2.56 Å −1 .Magnetic hysteresis loops were measured by use of a vibratingsample magnetometer with a superconducting coilmagnet. The samples were enclosed in copper cylinders withtypical sample masses of 125 mg. The instrument was calibratedusing the known magnetic saturation moment of acobalt sample. Measurements were performed at temperaturesbetween 5 K and 310 K in applied fields up to 1 T.Field cooled hysteresis curves were obtained by cooling in afield of 1 T over less than 30 min and then recording theloop starting from 1 T.IV. RESULTSA. X-ray and neutron powder diffractionThe average particle diameter was estimated for allsamples from the XRD data by use of the Scherrer formula.In the analysis we neglected the possible influence of strainon the line broadening. This may result in an underestimateof the particle size, especially for the ball-milled sample. Theanalysis showed that the -Fe 2 O 3 particles had an averagediameter of about 7 nm. The particles of the CoO-annsample had an average diameter of 16 nm, whereas the particlesof the CoO-bm sample had a diameter of about 10 nm.The mean diameter of the NiO particles was found to beabout 5 nm. The results of the XRD analysis were confirmedby electron microscopy studies. TEM studies further showedthat the -Fe 2 O 3 and CoO particles are pseudo-spherical inshape, while the NiO particles were plate-shaped with a diameterof about 17 nm and a thickness of about 3 nm.Neutron powder diffraction data of the two CoO samples,CoO-ann and CoO-bm showed that the Néel temperaturesof the nanoparticles are very close to the bulk value 293 K.This was found from following the decrease in integratedintensity of the antiferromagnetic ½½½ reflection. Previousneutron powder diffraction studies of NiOnanoparticles, 31 which are similar to the NiO particles studiedhere, have shown that the Néel temperature of theseplate-shaped nanoparticles is about 60 K lower than the bulkvalue 523 K.By use of neutron diffraction, we have not been able toresolve a possible increase in the Néel temperature of theCoO nanoparticles above the bulk value, when in compositeswith iron oxides with higher ordering temperatures, such asreported for CoO/Fe 3 O 4 multilayer structures. 22 For both-Fe 2 O 3 +CoO and -Fe 2 O 3 +NiO composites, overlappingreflection lines made it impossible to determine the criticaltemperatures of CoO or NiO. Complementary, we havelooked at samples of -Fe 2 O 3 +CoO, composites in whichsignificant interparticle interactions have previously been observedby Mössbauer spectroscopy. 9,10 In such composites,the diffraction lines of the two components can clearly beresolved and it was seen that the antiferromagnetic reflectionof CoO vanished at a temperature close to 300 K. Thus theNéel temperature of CoO nanoparticles does not seem toincrease due to the interparticle interactions.B. Mössbauer spectroscopyFigure 1 shows Mössbauer spectra of samples consistingsolely of 7 nm -Fe 2 O 3 nanoparticles. The spectra shown inFig. 1(a) were obtained from a sample of particles coatedwith oleic acid. These spectra show an evolution with tem-1-3PROOF COPY [BQ9013] 036437PRB

PROOF COPY [BQ9013] 036437PRBFRANDSEN et al. PHYSICAL REVIEW B 70, 1(2004)FIG. 2.57 Fe-Mössbauer spectraobtained at the indicated temperaturesof 7 nm -Fe 2 O 3 particles(a) mixed with NiOnanoparticles and dried at roomtemperature, (b) mixed with NiOnanoparticles and dried at 200°C,and (c) pure -Fe 2 O 3 particlesdried at 200°C.PROOF COPY [BQ9013] 036437PRBperature, which is typical for noninteracting or weakly interactingsuperparamagnetic particles, i.e., a coexistence of adoublet and a sextet, with the relative area of the doubletincreasing with increasing temperature at the expense of thesextet. In the spectra, where both a doublet and a sextet arepresent (e.g., at 150 K), neither of them have narrow lines. Inspectra of noninteracting nanoparticles of -Fe 2 O 3 the linesof both the sextet and the doublet are considerablynarrower. 32,33 The difference between the two iron oxidescan be explained by the different values of the parameter 0in the two materials as discussed in Sec. II. A small value of 0 results in a very wide distribution of relaxation times inthe temperature range where the Mössbauer spectrum graduallytransforms from a sextet to a doublet such that most ofthe particles have relaxation times that are either muchlonger or much shorter than M . This is the case for -Fe 2 O 3 nanoparticles where 0 10 −11 s. 32–34 In 7 nm -Fe 2 O 3 particles the value of 0 is of the order of 5·10 −10 s. 35This means that for small values of the parameter KV/k B Tthe particles will have relaxation times of the order of10 −9 –10 −8 s. This results in broad lines in the Mössbauerspectra. 10,30The spectra in Fig. 1(b) were obtained from a sample ofuncoated particles, which were freeze-dried. These spectraare quite similar to those shown in Fig. 1(a), indicating thatthe interparticle interactions only play a minor role in thissample.Figure 1(c) shows spectra of a sample of uncoated particles,which was prepared by suspending the freeze-driedparticles in water by exposing them to ultrasound and thenallowing them to dry at room temperature. In these spectrathe superparamagnetic relaxation is to a large extent suppressedat intermediate temperatures. For example, at 150 Konly a sextet with broad lines is visible in contrast to Figs.1(a) and 1(b) in which an intense doublet is also visible atthis temperature. Such a suppression of the superparamagneticrelaxation is a typical feature of nanoparticles with asignificant interparticle magnetic interaction. 7–11,17 A comparisonof the spectra in Figs. 1(b) and 1(c) shows that theway in which the samples are prepared plays a crucial rolefor the magnetic properties of nanopowders.Mössbauer spectra of a sample consisting of a mixture of-Fe 2 O 3 and NiO nanoparticles, prepared by exposing anaqueous suspension of the particles to ultrasound followedby drying at room temperature, are shown in Fig. 2(a). Comparedto the spectra of the pure -Fe 2 O 3 particles, preparedin the same way [Fig. 1(c)], the spectra of the mixture indicatea faster relaxation of the -Fe 2 O 3 particles. This is inparticular evident when comparing the spectra obtained at150 and 200 K of the two samples. Spectra of mixtures of-Fe 2 O 3 and NiO nanoparticles, dried at 200°C [Fig. 2(b)],show less influence of relaxation, presumably because of astronger interparticle interaction induced by the heating. Forcomparison, Fig. 2(c) shows spectra of the pure -Fe 2 O 3nanoparticles, dried at the same temperature. These spectraalso suggest an enhanced interaction compared to the sampledried at room temperature, but the spectra of samples containingNiO are much more influenced by relaxation than thesamples of pure -Fe 2 O 3 nanoparticles.Figure 3 shows spectra of a mixture of -Fe 2 O 3 and CoO(CoO-ann) nanoparticles, prepared by exposing an aqueousFIG. 3.57 Fe-Mössbauer spectra obtained at the indicated temperaturesof 7 nm -Fe 2 O 3 particles mixed with CoO-ace nanoparticlesat room temperature.1-4PROOF COPY [BQ9013] 036437PRB

PROOF COPY [BQ9013] 036437PRBINTERPARTICLE INTERACTIONS IN COMPOSITES OF… PHYSICAL REVIEW B 70, 1(2004)PROOF COPY [BQ9013] 036437PRBFIG. 4. Hysteresis loops of -Fe 2 O 3 , -Fe 2 O 3 +CoO-bm and-Fe 2 O 3 +NiO at 5 K. The magnetization is given per mass unit of-Fe 2 O 3 in the samples.suspension to ultrasound with subsequent drying at roomtemperature. A comparison with the spectra in Figs. 1(c) and2(a) shows that CoO has the opposite effect of NiO, i.e., itleads to suppression of the superparamagnetic relaxation inthe -Fe 2 O 3 particles. This is most clearly seen in the spectraobtained at 150 K.In order to study the influence of the method for preparationof CoO and the mixing ratio in samples with -Fe 2 O 3and CoO nanoparticles, we prepared samples with differentratios of the two oxides. In this series we used the CoO thatwas prepared by ball milling (CoO-bm) and we preparedsamples with 75%, 50%, 25%, and 10% -Fe 2 O 3 . The spectraof all these samples did not differ much and they werevery similar to those in Fig. 3. Thus, a relatively smallamount of CoO nanoparticles is sufficient to produce theinteraction effect. Moreover, the different preparation techniquesand the different average particle size of the two CoOsamples have little influence on the interaction effects.Drying mixtures of -Fe 2 O 3 and CoO nanoparticles withdifferent mixing ratios at 200°C did not result in systematicvariations of the relaxation behavior, but XRD studies of thesamples showed that part of the CoO had oxidized to Co 3 O 4 ,which is paramagnetic at temperatures above 80 K. Therefore,the samples containing CoO dried at room temperatureand at 200°C cannot be compared directly.C. Magnetization measurementsFigure 4 shows hysteresis loops of the pure -Fe 2 O 3nanoparticles and of the composites of -Fe 2 O 3 +NiO and-Fe 2 O 3 +CoO-bm nanoparticles at 5 K after cooling inzero-field. All three samples are those prepared by ultrasoundtreatment of aqueous suspensions followed by drying. Themagnetization at 1 T of the sample of pure -Fe 2 O 3 nanoparticlesis about 57 A m 2 /kg. For each sample, the magnetizationis shown per unit mass -Fe 2 O 3 . It can be seen thatthe NiO particles have a nonzero moment (of about25 A m 2 /kg, presumably due to uncompensated spins of theplaty NiO particles), whereas a magnetic moment from CoOparticles could not be resolved at the maximum applied fieldof 1 T. Rather, the magnetization of the -Fe 2 O 3 +CoO-bmcomposite is less than that of the pure -Fe 2 O 3 nanoparticles.An explanation for the latter could be that the sample ofFIG. 5. The coercivity of pure -Fe 2 O 3 and -Fe 2 O 3 +CoO-bmnanoparticles plotted as a function of temperature. The solid linesare guides to the eye.-Fe 2 O 3 nanoparticles interacting with CoO is not as close tosaturation at 1 T as the pure sample of -Fe 2 O 3 . This issupported by the different slopes of the magnetization curvesof -Fe 2 O 3 and -Fe 2 O 3 +CoO-bm when approaching 1 T.All three loops are smooth and thus show no sign of havingmore than one type of contribution, i.e., the composites seemto behave magnetically as single-phase materials indicatingthat there is a strong exchange interaction between theparticles. 24 From the loops, we find that the 7 nm -Fe 2 O 3particles have a coercivity, 0 H C =55±2 mT, while thecomposite of -Fe 2 O 3 +NiO has a slightly lower value, about43±3 mT. Quite contrary, for the -Fe 2 O 3 +CoO-bm composite,we find that 0 H C =185±10 mT, which is more thanthree times as large as it is for the sample consisting purelyof -Fe 2 O 3 nanoparticles from the same batch. Thus, theinfluence of the interparticle interactions on the coercivitycan be quite significant.In Fig. 5, it is shown how the coercivity of the samples of-Fe 2 O 3 and -Fe 2 O 3 +CoO-bm changes with temperature.The difference between the two samples observed at lowtemperatures diminishes with increasing temperature and atT100 K, the coercivity is similar and almost negligible forthe two samples. The fact that the coercivity does not becomezero seems to be an effect of the magnetometer.In order to see if the interaction with the antiferromagneticparticles could be observed directly as a shifted hysteresisloop, i.e., as exchange bias, of the ferrimagnetic -Fe 2 O 3 nanoparticles, we recorded the loops of the pure -Fe 2 O 3 and the composites of -Fe 2 O 3 +NiO and -Fe 2 O 3+CoO-bm at 5 K after cooling in a field of 1 T from 310 K(i.e., from a temperature above the Néel temperature of CoOand above the blocking temperature of the NiO nanoparticlesas determined by Mössbauer spectroscopy studies of similar57 Fe-doped NiO nanoparticles 10,11 ). For both the pure -Fe 2 O 3 sample and the composites we observed small loopshifts, which (in relative values) were nearly identical for thethree samples. Therefore, it seems that the loop shifts are notrelated to exchange coupling at the interface between ferrimagneticand antiferromagnetic particles, but it is rather anintrinsic property of the -Fe 2 O 3 nanoparticles. Such a behaviorof pure -Fe 2 O 3 nanoparticles has been reported byMartínez et al. 361-5PROOF COPY [BQ9013] 036437PRB

PROOF COPY [BQ9013] 036437PRBFRANDSEN et al. PHYSICAL REVIEW B 70, 1(2004)V. DISCUSSIONOur studies of differently prepared samples of -Fe 2 O 3nanoparticles show that the preparation conditions have agreat influence on the magnetic properties. Mössbauer studiesof an uncoated freeze-dried sample of -Fe 2 O 3 nanoparticlesand an uncoated sample dried at room temperatureshowed significantly different relaxation behavior. Mixing-Fe 2 O 3 nanoparticles with NiO nanoparticles results infaster relaxation of -Fe 2 O 3 particles. However, mixing -Fe 2 O 3 nanoparticles with CoO nanoparticles had the oppositeeffect.It could be argued that the change of relaxation behaviorin the composites might be due to a change in the magneticanisotropy of the maghemite nanoparticles induced bychemisorbed Co 2+ or Ni 2+ ions. During the ultrasonic treatmentin water, such ions may be dissolved from the CoO orNiO particles. In fact, because Co 2+ ions have large singleionanisotropy, chemisorbed Co 2+ ions might result in anenhanced anisotropy, which could explain the suppression ofthe relaxation. However, we have prepared samples by drying-Fe 2 O 3 particles from aqueous solutions of Co 2+ , andwe have found no effect on the relaxation. Moreover, inagreement with this, previous studies of -Fe 2 O 3 nanoparticleswith chemisorbed Ni 2+ or Co 2+ ions have also shownthat these ions cannot account for the measured effects innanocomposites. 10Dipolar interactions in the nanopowders might play a rolefor the magnetic properties of the samples, especially sinceboth the -Fe 2 O 3 and NiO nanoparticles have been found tohave significant magnetic moments. The energy of the dipoleinteraction between two adjacent spherical -Fe 2 O 3 particles,which are 7 nm in diameter and have a magnetization of57 A m 2 /kg, is about 100 K, and for two spherical 5 nmNiO particles with a magnetization of 25 A m 2 /kg, the dipoleinteraction energy is about 10 K. These interaction energiesmight account for some of the observed effects. Forinstance, the increased relaxation of -Fe 2 O 3 nanoparticlesin the composite of -Fe 2 O 3 +NiO, compared to the pure-Fe 2 O 3 nanoparticles, could be explained by the reducedinteraction energy, when interaction with NiO instead of-Fe 2 O 3 particles. On the other hand, we have seen how CoOnanoparticles, which have insignificant external magneticmoments, had the most profound influence on the propertiesof -Fe 2 O 3 nanoparticles. Therefore, exchange interactionsbetween the particles must be prevalent in the samples. Thisis also in accordance with the results obtained on antiferromagneticcomposites. 10It is remarkable that exchange interactions across the interfacesof nanoparticles in close proximity in a powder arestrong enough to result in a significant change in the relaxationand coercivity. If the particles were separated by layersof, for example, adsorbed water or if there are mismatchesbetween the directions of sublattice magnetizations, onewould expect the interparticle exchange interaction to besmall (in insulators, one would not expect exchange couplingif the magnetic materials are separated by a nonmagneticspacer, but this can be the case in metallic systems 37 ). Further,if a particle interacts with several neighbors, one mightalso expect that the interaction fields would partly compensate.However, since the drying method influences thestrength of interparticle interaction [Figs. 1(b) and 1(c)], theresults suggest that during drying of aqueous suspensions theparticles are brought in close proximity in such a way thatthe magnetic interaction strength is large. Here, van derWaals or magnetic forces may play a role.It is interesting that mixing -Fe 2 O 3 particles with NiOand CoO nanoparticles have the opposite effects on the relaxationof -Fe 2 O 3 particles. Similar results were found formixtures of -Fe 2 O 3 nanoparticles with NiO and CoOnanoparticles. 9,10 We believe that the observed different influencesof NiO and CoO nanoparticles are mainly a consequenceof their different anisotropy energies. The NiO particleshave very small volumes and the magnetic anisotropyconstant of NiO is not very large. Therefore, the NiO particlesare expected to have small magnetic anisotropy energy.It is possible that the effective anisotropy of the NiO particlesis too small compared to that of the -Fe 2 O 3 particlesto induce exchange coupling effects. 38 Mössbauer studies ofa similarly prepared sample of NiO, which was doped with57 Fe, showed that the NiO particles are superparamagneticwith a blocking temperature of about 120 K. 11 When the -Fe 2 O 3 particles are separated by NiO particles, their magneticcoupling to other -Fe 2 O 3 particles may therefore beweakened. The CoO particles are larger than the NiO particlesand they have larger magnetic anisotropy energy constant.Therefore, a -Fe 2 O 3 particle, which is coupled to aCoO particle, cannot relax in the same way as it could whenit was isolated or only in contact with other -Fe 2 O 3 particles.It may, to a certain extent, have to follow the fluctuationsof the magnetization direction of the CoO particles,which have slow relaxation because of the large anisotropyenergy. The different morphologies of the NiO and CoO particlesalso may lead to differences in the physical contactwith the -Fe 2 O 3 particles, and this can also play a role forthe exact strength of interparticle coupling.The magnetization measurements indicate, in agreementwith Mössbauer spectroscopy studies, that exchange anisotropyinfluences the properties of the -Fe 2 O 3 nanoparticles.The coercivity of the -Fe 2 O 3 nanoparticles was tripled atlow temperatures when interacting with CoO nanoparticles,while it was slightly reduced when interacting with NiOnanoparticles. This can be explained by the differentanisotropies of the CoO and NiO particles, which the -Fe 2 O 3 particles apparently couple to. At increasing temperatureswe have seen how the coercivity of -Fe 2 O 3 +CoO decreases.This is presumably because the coupled CoO and-Fe 2 O 3 particles perform superparamagnetic relaxation. Thetemperature range where it happens in the magnetizationmeasurements is somewhat lower than the temperaturerange, where the Mössbauer spectra change from a sextet toa doublet, as expected due to the different time scales of thetwo techniques. Although exchange coupling seems prevalentbetween the particles, we were not able to observe exchangebias in the composite systems. In studies of thin filmsit has also been found that exchange coupling can lead to anenhanced coercivity which is not related to the size of exchangebias. 39 In the present case, the absence of exchangebias is probably due to rather small anisotropies of the nano-PROOF COPY [BQ9013] 036437PRBPROOF COPY [BQ9013] 036437PRB1-6

PROOF COPY [BQ9013] 036437PRBINTERPARTICLE INTERACTIONS IN COMPOSITES OF… PHYSICAL REVIEW B 70, 1(2004)particles on an absolute scale. This implies that the -Fe 2 O 3 particles can drag the sublattice magnetization of theantiferromagnets around due to the coupling between theparticles. This is seen as an effect to the coercivity of theferrimagnetic particles, but the anisotropy of the antiferromagneticparticles is too small to result in shifted hysteresisloops.VI. CONCLUSIONSThe present studies have shown that during drying bothsuspensions of nanoparticles of the same material and nanoparticlesof different materials, a strong magnetic interparticleinteraction can be established. Such interactions play animportant role for the coercivity and the superparamagneticrelaxation of the nanoparticles. The results also show that theway in which the nanopowders are dried can have a decisiveinfluence on the magnetic properties. The effects can be explainedby exchange coupling of neighboring particles inclose contact. We suggest that the different influence of theNiO and CoO nanoparticles on the relaxation of iron oxidenanoparticles is related to a difference in magnetic anisotropyof the NiO and CoO particles.ACKNOWLEDGMENTSWe thank L. Lilleballe for sample preparations, H. K.Rasmussen for help with Mössbauer measurements, and F.Grumsen for TEM micrographs. The Danish Technical ResearchCouncil (“Nanomagnetism” framework programme)and the Danish Natural Sciences Research Council (frameworkprogramme 51-00-0363 and DANSCATT) have financiallysupported the work. The neutron diffraction measurementswere performed at the Swiss Spallation NeutronSource, Paul Scherrer Institute, Villigen, Switzerland.PROOF COPY [BQ9013] 036437PRB*Present address: School of Materials and Metallurgy, NortheasternUniversity, Shenyang 110004, China.1 W. Luo, S. R. Nagel, T. F. Rosenbaum, and R. E. Rosensweig,Phys. Rev. Lett. 67, 2721 (1991).2 C. Djurberg, P. Svedlindh, P. Nordblad, M. F. Hansen, F. Bødker,and S. Mørup, Phys. Rev. Lett. 79, 5154 (1997).3 H. Mamiya, I. Nakatani, and T. Furubayashi, Phys. Rev. Lett. 80,177 (1998).4 T. Jonsson, P. Svedlindh, and M. F. Hansen, Phys. Rev. Lett. 81,3976 (1998).5 Y. Sun, M. B. Salamon, K. Garnier, and R. S. Averback, Phys.Rev. Lett. 91, 167206 (2003).6 C. J. W. Koch, M. B. Madsen, S. Mørup, G. Christiansen, and L.Gerward, Clay Miner. 34, 17(1986) .7 M. F. Hansen, C. B. Koch, and S. Mørup, Phys. Rev. B 62, 1124(2000).8 S. Mørup, M. B. Madsen, J. Franck, J. Villadsen, and C. J. W.Koch, J. Magn. Magn. Mater. 40, 163 (1983).9 C. W. Ostenfeld and S. Mørup, Hyperfine Interact. 5, 83(2002).10 C. Frandsen and S. Mørup, J. Magn. Magn. Mater. 266, 36(2003).11 F. Bødker, M. F. Hansen, C. B. Koch, and S. Mørup, J. Magn.Magn. Mater. 221, 32(2000).12 S. Mørup and E. Tronc, Phys. Rev. Lett. 72, 3278 (1994).13 S. Mørup, Europhys. Lett. 28, 3278 (1994).14 M. F. Hansen and S. Mørup, J. Magn. Magn. Mater. 184, 262(1998).15 F. Luis, F. Petroff, J. M. Torres, L. M. García, J. Bartolomé, J.Carrey, and A. Vaurès, Phys. Rev. Lett. 88, 217205 (2002).16 M. F. Hansen and S. Mørup, Phys. Rev. Lett. 90, 059705 (2003).17 S. Mørup, F. Bødker, P. V. Hendriksen, and S. Linderoth, Phys.Rev. B 52, 287 (1995).18 D. Fiorani, J. L. Dormann, R. Cherkaoui, E. Tronc, F. Lucari, F.D’Orazio, L. Spinu, M. Nogues, A. Garcia, and A. M. Testa, J.Magn. Magn. Mater. 196-197, 143 (1999).19 J. Nogués and I. K. Schuller, J. Magn. Magn. Mater. 192, 203(1999).20 A. E. Berkowitz and K. Takano, J. Magn. Magn. Mater. 200, 552(1999).21 J. A. Borchers, R. W. Erwin, S. D. Berry, D. M. Lind, J. F.Ankner, E. Lochner, K. A. Shaw, and D. Hilton, Phys. Rev. B51, 8276 (1995).22 P. J. van der Zaag, Y. Ijiri, J. A. Borchers, L. F. Feiner, R. M.Wolf, J. M. Gaines, R. W. Erwin, and M. A. Verheijen, Phys.Rev. Lett. 84, 6102 (2000).23 V. Skumryev, S. Stoyanov, Y. Zhang, G. Hadjipanayis, D. Givord,and J. Nogués, Nature (London) 423, 850 (2003).24 H. Zeng, J. Li, J. P. Liu, Z. L. Wang, and S. Sun, Nature (London)420, 395 (2002).25 J. Sort, J. Nogués, X. Amils, S. Surinach, J. S. Munoz, and M. D.Baro, Appl. Phys. Lett. 75, 3177 (1999).26 J. Sort, J. Nogués, X. Amils, S. Surinach, J. S. Munoz, and M. D.Baro, J. Magn. Magn. Mater. 219, 53(2000).27 T. A. Anhøj, C. S. Jacobsen, and S. Mørup, J. Appl. Phys.1 95,3649 (2004).28 L. Néel, Ann. Geophys. (C.N.R.S.) 5, 99(1949).29 W. F. Brown, Jr., Phys. Rev. 130, 1677 (1963).30 S. Mørup, C. Frandsen, F. Bødker, S. N. Klausen, K. Lefmann,P.-A. Lindgård, and M. F. Hansen, Hyperfine Interact. 144/145,347 (2002).31 S. N. Klausen, P.-A. Lindgård, K. Lefmann, F. Bødker, and S.Mørup, Phys. Status Solidi A 189, 1039 (2002).32 F. Bødker and S. Mørup, Europhys. Lett. 52, 217 (2000).33 F. Bødker, M. F. Hansen, C. B. Koch, K. Lefmann, and S. Mørup,Phys. Rev. B 61, 6826 (2000).34 M. F. Hansen, F. Bødker, S. Mørup, K. Lefmann, K. N. Clausen,and P.-A. Lindgård, Phys. Rev. Lett. 79, 4910 (1997).35 T. Jonsson, J. Mattsson, P. Nordblad, and P. Svedlindh, J. Magn.Magn. Mater. 168, 269 (1997).36 B. Martínez, X. Obradors, Ll. Balcells, A. Rouanet, and C.Monty, Phys. Rev. Lett. 80, 181 (1998).37 N. J. Gökemeijer, T. Ambrose, and C. L. Chien, Phys. Rev. Lett.79, 4270 (1997).38 M. S. Lund, W. A. A. Macedo, Kai Liu, J. Nogués, Ivan K.Schuller, and C. Leighton, Phys. Rev. B 66, 054422 (2002).39 N. J. Gökemeijer, J. W. Cai, and C. L. Chien, Phys. Rev. B 60,3033 (1999).1-7PROOF COPY [BQ9013] 036437PRB

Paper VI

INSTITUTE OF PHYSICS PUBLISHINGJOURNAL OF PHYSICS: CONDENSED MATTERJ. Phys.: Condens. Matter 16 (2004) 6977–6981 PII: S0953-8984(04)83564-1AMössbauer study of the magnetization of γ-Fe 2 O 3nanoparticles in applied fields: the influence ofinteraction with CoOCathrine Frandsen, Helge K Rasmussen and Steen MørupDepartment of Physics, Building 307, Technical University of Denmark, DK-2800 KongensLyngby, DenmarkReceived 13 July 2004, in final form 19 August 2004Published 17 September 2004Online at stacks.iop.org/JPhysCM/16/6977doi:10.1088/0953-8984/16/39/030AbstractBy use of Mössbauer spectroscopy we have followed the gradual alignmentof the magnetization of γ -Fe 2 O 3 nanoparticles as a function of the appliedfield. At moderate fields, the magnetization was less aligned with the fieldif the particles were mixed with CoO nanoparticles. This indicates a strongexchange interaction between the γ -Fe 2 O 3 and the CoO nanoparticles. Theeffect manifests itself in a way which can be difficult to distinguish fromlocalized spin canting.1. IntroductionMagnetic nanoparticles are interesting because their properties in several ways deviate fromthose of the corresponding bulk materials. One example is superparamagnetic relaxation,which can be described in terms of fluctuations of the (sublattice) magnetization directionsamong the easy directions of magnetization. Interactions between magnetic nanoparticles canhave a significant influence on their magnetic behaviour. Dipole interaction between ferroorferrimagnetic particles can have a large influence on the superparamagnetic relaxation,and can lead to a transition to a spin-glass-like state at low temperatures [1–5]. Interactionsbetween antiferromagnetic particles of α-Fe 2 O 3 [6–8] or NiO [9] can also have a stronginfluence on the relaxation. In this case dipole interactions are insufficient to produce theeffect, and it has been concluded that it is due to exchange interaction between surfaceatoms of neighbouring particles. Recently we have used Mössbauer spectroscopy to studynanocomposites of magnetic materials with two different types of nanoparticles, and foundsome unexpected results. When nanoparticles of α-Fe 2 O 3 [7, 8] or γ -Fe 2 O 3 [10] were mixedwith NiO nanoparticles it resulted in a faster superparamagnetic relaxation compared tosamples of the pure iron oxide nanoparticles. However, when the iron oxide nanoparticleswere mixed with CoO nanoparticles the relaxation was to a large extent suppressed. The0953-8984/04/396977+05$30.00 © 2004 IOP Publishing Ltd Printed in the UK 6977

6978 C Frandsen et aldifference between nanocomposites with NiO and CoO was explained by the different magneticanisotropy energies of these particles.In 57 Fe Mössbauer spectra of magnetic materials, the relative areas of the six lines dependon the angle, θ, between the magnetic field at the nucleus and the gamma ray direction and aregivenby3:x:1:1:x:3 with x = 4sin 2 θ/(1+cos 2 θ). Thus the area ratio can give informationon, for example, the degree of alignment of the magnetization in a ferro- or ferrimagneticsample exposed to a magnetic field. This has been utilized in numerous studies of spin cantingboth in nanoparticles and in bulk materials; see, for example [11–15].In this paper we report on results of Mössbauer studies of the magnetic structure of bothpure γ -Fe 2 O 3 nanoparticles and γ -Fe 2 O 3 nanoparticles mixed with CoO nanoparticles. Weshow that in applied fields of the order of 1 T the degree of alignment of the magnetizationdiffer for the two samples. Thus the interaction with CoO has a significant influence on themagnetization of the γ -Fe 2 O 3 nanoparticles in moderate applied fields.2. Experimental detailsSamples of γ -Fe 2 O 3 nanoparticles were prepared by oxidation of Fe 3 O 4 nanoparticles, whichwere made by co-precipitation of Fe 2+ and Fe 3+ in an aqueous solution by adding a solutionof NaOH [10]. CoO nanoparticles were prepared by high-energy ball milling of a 1:1 molarratio mixture of Co 3 O 4 and Co in argon for 115 h.The samples of pure γ -Fe 2 O 3 nanoparticles and mixtures of nanoparticles of γ -Fe 2 O 3 andCoO (1:1 by weight) were prepared by suspending the particles in distilled water, and exposingthem to intense ultrasound to obtain a homogeneous mixture. The samples were left to dry inopen Petri dishes in air at room temperature for about two days. Mössbauer absorbers of thetwo samples were prepared with a thickness of 20 mg γ -Fe 2 O 3 cm −2 .Mössbauer spectra were obtained with a conventional constant acceleration Mössbauerspectrometer with a 100 mCi source of 57 Co in rhodium. The measurements were obtained at6 K in a liquid helium cryostat equipped with a superconducting coil. In-field measurementswere made with the magnetic field applied parallel to the gamma ray direction. Thespectrometer was calibrated with a 12.5 µm foil of metallic iron at room temperature.3. Results and discussionThe average diameter of the γ -Fe 2 O 3 particles, estimated from XRD data, was about 7 nm,whereas the CoO particles were found to have an average diameter of about 10 nm [10].The results of the XRD analysis were confirmed by transmission electron microscopy studies,which also showed that the γ -Fe 2 O 3 and CoO particles were pseudo-spherical in shape [10].Mössbauer spectra of the two samples, obtained at different fields, are shown in figure 1.In zero field the area ratio of the six lines is close to 3:2:1:1:2:3, as expected for a sample withrandom orientation of the magnetization directions. With increasing field the relative areasof lines 2 and 5 gradually decrease, indicating an increasing alignment of the magnetizationdirections. The sample containing CoO nanoparticles shows a slower decrease in the relativeintensity of lines 2 and 5 than the sample of the pure γ -Fe 2 O 3 nanoparticles. This is inparticular visible in the spectra obtained with applied magnetic fields in the range 0.5–1.25 T.For smaller and larger applied fields, the spectra of the two samples have almost identical arearatios. Each of the spectra was fitted with a sextet in which the lines pairwise were constrainedto have identical areas with the relative areas given by y:x:1:1:x:y. The field dependence ofthe relative areas of lines 2 and 5, x, for the two samples, is shown in figure 2. The value

γ -Fe 2 O 3 nanoparticles interacting with CoO 6979γ-Fe 2O 3γ-Fe 2O 3/CoO0.0 T0.0 TRelative absorption0.5 T0.5 T1.5 T1.5 T-12 -8 -4 0 4 8 12Velocity (mm/s)-12 -8 -4 0 4 8 12Velocity (mm/s)Figure 1. Mössbauer spectra of pure γ -Fe 2 O 3 nanoparticles and γ -Fe 2 O 3 nanoparticles mixedwith CoO nanoparticles. The spectra were obtained at 6 K with the indicated magnetic fieldsapplied parallel to the gamma ray direction.Figure 2. The relative area, x, of line 2 and 5 in the Mössbauer spectra obtained at 6 K as a functionof the applied magnetic field.of y is constant (≈2.72) in all spectra with a scatter of the values of about ±0.01, indicatingthat we can measure the relative areas with this accuracy. The deviation from y = 3.0 can beexplained by the influence of absorber thickness.

6980 C Frandsen et alFor applied fields in the range 0.5–1.25 T the relative areas of lines 2 and 5 for the twosamples are clearly different, and it appears that the magnetization in the sample containingCoO is consistently less aligned with the applied field than the magnetization in the samplewithout CoO at the same applied fields. In the sample without CoO the magnetization directionis mainly determined by a competition between the applied field and the magnetic anisotropy.The smaller degree of alignment in the sample with CoO indicates that in this sample the appliedfield also has to overcome an interaction field due to interactions between γ -Fe 2 O 3 and CoOnanoparticles. As we have shown earlier [10], the interaction between CoO and γ -Fe 2 O 3nanoparticles can lead to a significant suppression of the superparamagnetic relaxation of theγ -Fe 2 O 3 nanoparticles and to an enhanced coercivity. Similar observations have been madefor α-Fe 2 O 3 nanoparticles mixed with CoO nanoparticles [8]. The effect was explained by astrong exchange interaction between the nanoparticles of iron oxide and cobalt oxide, whichhave a relatively large anisotropy. The present measurements support this interpretation.In several previous Mössbauer studies of incomplete spin alignment in nanoparticlesin external magnetic fields, the data were interpreted in terms of localized spin canting ofsurface spins due to the different magnetic environment of surface ions compared to the bulkenvironments; see, for example, [11, 13, 16]. Magnetization data for magnetic nanoparticleshave been explained by a similar model [17, 18]. Another source of localized spin canting canbe defects in the interior of the particles [16, 19]. This mechanism can also be important inbulk materials, such as, for example, diamagnetically substituted ferrites [14–16]. The presentstudy shows that still another mechanism, namely exchange coupling between nanoparticles,can give rise to a smaller degree of spin alignment in an external magnetic field, even insamples prepared just by drying aqueous suspensions of nanoparticles of γ -Fe 2 O 3 and CoOat room temperature. The interface regions of neighbouring γ -Fe 2 O 3 and CoO nanoparticlespresumably involve only a small fraction of the atoms because of the rounded shape of theparticles. Therefore, it is unlikely that the data can be explained by a localized spin canting inthe interface regions. The results rather indicate that rotation of the magnetization directionof each γ -Fe 2 O 3 particle as a whole gives the main contribution to the effect. It is likelythat the effect can be larger in nanocomposites prepared in other ways such that the exchangeinteraction is larger. The mechanism may also be effective in samples consisting solely of onetype of nanoparticles, e.g. γ -Fe 2 O 3 , but in this case it will presumably be smaller, becausethe exchange coupling between γ -Fe 2 O 3 particles is much smaller than that between γ -Fe 2 O 3and CoO nanoparticles [10].4. SummaryBy use of Mössbauer spectroscopy at low temperatures and with applied magnetic fields wehave studied the magnetic properties of samples of nanoparticles of pure γ -Fe 2 O 3 and γ -Fe 2 O 3nanoparticles mixed with CoO nanoparticles. Both samples were prepared by drying aqueoussuspensions at room temperature. The studies show that the alignment of the magnetization ofγ -Fe 2 O 3 nanoparticles in applied magnetic fields of the order of 1 T is reduced if the particles aremixed with CoO nanoparticles. This indicates that there is a significant exchange interactionbetween γ -Fe 2 O 3 and CoO nanoparticles in samples. The results are in accordance withprevious studies of superparamagnetic relaxation in similar samples at higher temperatures.AcknowledgmentsWe thank Lis Lilleballe for help with sample preparations. The work was supported by theDanish Technical Research Council.

γ -Fe 2 O 3 nanoparticles interacting with CoO 6981References[1] Luo W, Nagel S R, Rosenbaum T F and Rosensweig R E 1991 Phys. Rev. Lett. 67 2721[2] Djurberg C, Svedlindh P, Nordblad P, Hansen M F, Bødker F and Mørup S 1997 Phys. Rev. Lett. 79 5154[3] Mamiya H, Nakatani I and Furubayashi T 1998 Phys. Rev. Lett. 80 177[4] Jonsson T, Svedlindh P and Hansen M F 1998 Phys. Rev. Lett. 81 3976[5] Sun Y, Salamon M B, Garnier K and Averback R S 2003 Phys. Rev. Lett. 91 167206[6] Hansen M F, Koch C B and Mørup S 2000 Phys. Rev. B 62 1124[7] Ostenfeld C W and Mørup S 2002 Hyperfine Interact. C 5 83[8] Frandsen C and Mørup S 2003 J. Magn. Magn. Mater. 266 36[9] Bødker F, Hansen M F, Koch C B and Mørup S 2000 J. Magn. Magn. Mater. 221 32[10] Frandsen C, Ostenfeld C W, Xu M, Jacobsen C S, Keller L, Lefmann K and Mørup S 2004 Phys. Rev. Batpress[11] Coey J M D 1971 Phys.Rev.Lett.27 1140[12] Coey J M D 1987 Can. J. Phys. 65 1210[13] Morrish A H and Haneda K 1983 J. Magn. Magn. Mater. 35 105[14] Dormann J L and Nogues M 1990 J. Phys.: Condens. Matter 2 1223[15] Anhøj T A, Bilenberg B, Thomsen B, Damsgaard C D, Rasmussen H K, Jacobsen C S, Mygind J andMørup S 2003 J. Magn. Magn. Mater. 260 115[16] Mørup S 2003 J. Magn. Magn. Mater. 266 110[17] Kodama R H, Berkowitz A E, McNiff E J Jr and Foner S 1996 Phys.Rev.Lett.77 394[18] Martínez B, Obradors X, Balcells L, Rouanet A and Monty C 1998 Phys. Rev. Lett. 80 181[19] Morales M P, Serna C J, Bødker F and Mørup S 1997 J. Phys.: Condens. Matter 9 5461

Paper VII

Submitted July 17, 2004.Self-assembly and exchange coupling of antiferromagnetic nanoparticlesC. Frandsen, 1 C.R.H. Bahl, 2 B. Lebech, 2 K. Lefmann, 2 L. Theil Kuhn 2 , L. Keller 3 , N.Hessel Andersen, 2 M. v. Zimmermann, 4 E. Johnson, 2,5 S.N. Klausen, 2 and S. Mørup. 11 Department of Physics, Technical University of Denmark, DK-2800 Kgs. Lyngby,Denmark2 Materials Research Department, Risø National Laboratory, DK-4000 Roskilde, Denmark3 Laboratory for Neutron Scattering, ETHZ & PSI, CH-5232 Villigen PSI, Switzerland4 Hamburger Synchrotronstrahlungslabor HASYLAB at Deutsches Elektronen-SynchrotronDESY, D-22603 Hamburg, Germany5 Nano Science Center, NBIfAPG, University of Copenhagen, DK-2100 Copenhagen Ø,DenmarkPACS: 75.50.Tt, 61.46.+w, 75.25.+z, 68.35.CtAbstract. We show that nanoparticles of α-Fe 2 O 3 (hematite) under wet conditions canassemble into chains along a common [001] axis. X-ray and neutron diffraction studiesshow that both structural and magnetic correlations are continued across the interfacesalong this direction. The exchange coupling between the particles suppresses thesuperparamagnetic relaxation, and may play a role for the assembly along preferreddirections. The inter-particle interactions are found to be very sensitive to sampletreatments such as gentle grinding, exposure to ultrasound, and the drying conditions.There is currently considerable interest in understanding and controlling assembly ofnanoparticles, because it is of importance for a number of interesting phenomena, e.g.revealing the mechanisms behind crystal growth [1-4], affecting the magnetic properties ofnanoparticles [5], and developing new technologies for building up nanostructured devices[6].In order to control positioning of magnetic nanoparticles, their magnetic dipole momenthas been utilized to guide them in applied fields or in stray fields from neighboringparticles [7-9], and many studies have revealed that dipole interactions betweennanoparticles strongly influence their magnetic properties [10,11]. Another method ofcontrolling the position and properties of magnetic nanoparticles is to utilize exchangeinteraction between particles. Although this kind of interaction is rather unexplored, itholds interesting prospects. Exchange coupling between particles can be orders of1

magnitude larger than the dipole coupling, if the particles are in close proximity. However,it is considered a major challenge to establish strong exchange coupling betweennanoparticles [5].To examine the exchange coupling between particles, it is fruitful to study particles ofantiferromagnetic materials, which have insignificant magnetic dipole interactions. Themost abundant antiferromagnetic material is probably α-Fe 2 O 3 (hematite) [12,13]. It has apseudo-hexagonal unit cell consisting of six puckered Fe-layers perpendicular to the [001]direction and the spins of adjacent Fe-layers are coupled antiparallel [12,14]. In α-Fe 2 O 3nanoparticles the spins are confined to lie in the (001) plane [12]. Within this plane thesublattice magnetization directions can easily rotate while rotation out of the planerequires much more energy. Therefore, superparamagnetic relaxation, for which the totalspin structure rotates coherently because of thermal excitation, mainly takes place withinthe (001) plane. Recent studies by Mössbauer spectroscopy have shown that thesuperparamagnetic relaxation can be suppressed in samples in which α-Fe 2 O 3nanoparticles have agglomerated, suggesting that strong exchange interaction existsbetween the particles [15,16], but no direct observation of the coupling has been reportedso far. In this letter, we present studies of nanoparticles of α-Fe 2 O 3 using high-resolutionelectron microscopy (HREM), high-energy synchrotron x-ray diffraction (HES-XRD),neutron powder diffraction (NPD), and Mössbauer spectroscopy (MS). We find that α-Fe 2 O 3 nanoparticles assemble into chains along a common [001] axis, and by NPD wedirectly observe that the magnetic order continues across the interfaces. Moreover, weshow that it is possible to control the local coupling by macroscopic treatments.HREM images were obtained using a Jeol 3000F FEG TEM using lacey carbon on 200mesh Cu grids as sample supports. Cryo-TEM imaging was made with a Philips CM200FEG TEM using an Oxford Instruments CT3500 cryoholder at liquid nitrogentemperature. HES-XRD measurements were performed at the BW5 beam-line atHASYLAB at DESY using 100 keV photons (wavelength equal to 0.12536 Å). TheFWHM instrumental resolution at 2.75 Å -1 is 0.0095 Å -1 and at 3.1 Å -1 it is 0.0125 Å -1 .NPD measurements were performed at the DMC diffractometer, Swiss Spallation NeutronSource, Paul Scherrer Institute. A wavelength of 4.2 Å was used. The instrumentalresolution at 1.37 Å -1 is 0.018 Å -1 . 57 Fe Mössbauer spectra were obtained as described in[16].We prepared α-Fe 2 O 3 nanoparticles by a gel-sol method similar to that described bySugimoto et al. [17]. After formation of the particles in an aqueous solution, excess ionswere washed out, and the particles were dried. HREM micrographs of agglomerates of theparticles, dried on a grid, are shown in Figs. 1a and 1b. The individual particles aretypically 5-10 nm in diameter and have round shapes without pronounced facets.Noticeably, the micrographs show that the particles have a tendency to align along acommon [001] axis (since no (00k) planes are seen due to extinction, the orientation of the[001] axis of the particles can only be established from other planes, identified from theirplanar spacings and mutual angles). Typically, chains of 2-4 particles are observed. Insome cases the assembly appears epitaxial (Fig. 1a); in other cases it does not (Fig. 1b),but in both cases the particles share a common [001] axis. Electron micrographs of afrozen aqueous suspension (cryo-TEM) show that the assembly is not induced by thesubstrate since the chain formation also appears prevalent in suspension (Fig. 1c).2

(112)(102)[001](a)(213)(113)48°[001](b)52°52°(102)(c)(112)(d)FIG. 1. Transmission electron microscopy images of α-Fe 2 O 3 nanoparticles. (a-b) HREMimages showing that the particles are attached to one another along their common [001] axis. Thearrows and angles indicate the direction of the [001] axis of the particles relative to the plane of thepaper. (c) Cryo-TEM image of a frozen aqueous suspension of the particles. (d) Electronmicrograph of the separated α-Fe 2 O 3 particles (dark spots) after grinding with amorphous SiO 2particles (the gray matrix of the composite).A quantitative measure of the correlation lengths associated with the assembled particlescan be obtained from diffraction measurements (Fig. 2) because the correlation lengths areinversely proportional to the broadening of the diffraction lines. Fig. 2a shows HES-XRDmeasurements. All diffraction lines, apart from an impurity line, correspond to thoseexpected for α-Fe 2 O 3 . The data were fitted with Gaussian shaped lines and a polynomialbackground. The crystalline correlation length, estimated from the FWHM of the Fe 2 O 3reflections, except (006), was found to be 8-9 nm. This is similar to the average particlesize found by HREM. The weak (006) reflection (Fig. 2a inset) has a width correspondingto an average correlation length along [001] of about 13 nm, indicating that the crystallinecorrelation exceeds the particle size in that direction.While XRD provides information solely about the crystalline structure, NPD can alsoreveal magnetic correlations. NPD measurements (Fig. 2b) show that the alignment along[001] is accompanied by magnetic correlation in that direction, since the antiferromagnetic(003) reflection is clearly narrower than the other reflections, which have widths inaccordance with the average particle size. The strong (003) reflection, which allows for amore detailed analysis than the weak (006) reflection, is most adequately described by twocontributions (see fit to data in Fig. 2b). One of these has a width corresponding to theaverage particle size, while the other, which covers ~ 36 % of the total (003) reflectionarea, has a width corresponding to 22 nm. This suggests that on average about one third ofthe particles have magnetic correlations extending over about three particle diametersalong the [001] direction.3

The observation that correlation exceeds the particle size in the [001] direction indicatesthat the distance between the (001) layers is the same across the interface as inside theparticles. For the other crystal planes, there can be a mismatch at the interface. Suchmismatch can be incorporated during the assembly of the particles if the order of the sixFe-layers in the unit cell is not continued across the grain boundaries (this is equivalent toformation of stacking faults or twinning of (001) planes at the interfaces). The constantseparation of the (001) layers across the interface indicates that the surface layer of wateror hydroxyl groups, which typically is adsorbed to nanoparticles, is expelled from theinterface. The assembly of particles with interfaces with more or less the same structureand chemical bonds as inside the crystals is expected to result in relatively strongmechanical coupling between the particles.(104)(006)(213)(202)2.7 2.8 2.9 3.0(102)(a)(210)(006)(213)(202)impurity(204)1.0 1.5 2.0 2.5 3.0 3.5(003)(101)(102)(b)(104)(210)1.0 1.5 2.0 2.5[001](c)(d)1.0 1.5 2.0 2.5Scattering vector (Å -1 )FIG. 2. (color online) Diffraction data of α-Fe 2 O 3 particles obtained at room temperature.The solid lines represent the fits to the data (green denotes individual Bragg peaks, red the sum ofBragg peaks). (a) HES-XRD data of the as-prepared nanoparticles. The region around (213) isshown on expanded scales in the inset. The horizontal (blue) bars on the inset indicate the widthsof (006), (213), and (202). The lower bar at (213) is a repeat of the (006) width. (b) NPD data ofthe same sample as in a. The (003) and (101) reflections at 1.37 and 1.51 Å -1 are purely magnetic,the (213) reflection is mixed magnetic and structural and the remaining reflections are structural.(c) NPD data of the α-Fe 2 O 3 sample after grinding. (d) Schematic illustration of theantiferromagnetic correlation across the particle interfaces in the as-prepared sample.The magnetic correlation along [001] shows that the alternating magnetization directionsof the (001) layers of the particles are continued across the particle interfaces asschematically illustrated in Fig. 2d. Regardless of the relative crystalline orientations ofparallel (001) planes of neighboring particles, the sublattice magnetization directions arearranged within the (001) planes such that the antiferromagnetic order is continued acrossthe interface. The correlation implies that the exchange coupling exists across theinterfaces and is similar to the exchange coupling between the Fe-layers within theparticles. This is a direct indication of strong exchange coupling between agglomeratedparticles, which leads to freezing of the otherwise rapidly fluctuating spin structure of thenanoparticles [15,16]. Weaker interactions between non-aligned particles may alsocontribute to the suppression of the relaxation [15].4

By use of MS we have studied the influence of drying on interactions via studies of thesuperparamagnetic relaxation of the particles. The Mössbauer spectrum of the as-preparedsample, obtained at 180 K (Fig. 3a) consists of a sextet with broadened lines, typical forsamples of interacting nanoparticles [15,16]. The absence of a doublet indicates that thereis no fast superparamagnetic relaxation in this sample. We prepared an aqueoussuspension of the particles and exposed it to intense ultrasonic treatment for six hours.Immediately hereafter, part of the sample was frozen in a sample holder for MS byimmersion in liquid nitrogen, and the spectrum, shown in Fig. 3b, was obtained at 180 K.This spectrum only contains a doublet, indicating that all the particles now have fastsuperparamagnetic relaxation at this temperature. Thus the inter-particle interaction hasbeen substantially diminished by the treatment. Another part of the ultrasonically treatedsample was dried and a Mössbauer spectrum was obtained at 180 K (Fig. 3c). Thisspectrum is qualitatively similar to that of the as-prepared sample (Fig. 3a), but the linesare slightly broader, indicating that the interactions to a large extent have beenreestablished. These results show that during the drying procedure the particlesagglomerate in a way, which leads to a strong inter-particle exchange coupling. Studies ofdrying the particles with increasing duration indicate that this can lead to even strongerinter-particle interactions. We suggest that Brownian motion brings separated particlestogether in the suspension [3] whereupon strong short-range forces cause the attachment.Relative absorption(a)(b)(c)(d)(e)(f)-12 -8 -4 0 4 8 12 -12 -8 -4 0 4 8 12Velocity (mm/s)FIG. 3. Mössbauer spectra of α-Fe 2 O 3 nanoparticles. (a) The as-prepared sample at 180 K.(b) The wet sample at 180 K after intense ultrasonic treatment of an aquous suspension. (c) Thesample at 180 K after drying the ultrasonically treated suspension. (d) The as-prepared samplemeasured at room temperature (RT). (e) The sample at RT after grinding. (f) Spectrum of thegrinded sample obtained at 80 K.Until recently, the general understanding was that crystals grow by addition of atoms, butstudies of TiO 2 and iron oxyhydroxides have lately revealed that crystals can also grow byoriented attachment of nanoparticles [1-4]. It has been suggested that reduction of surfaceenergy of nanoparticles is the driving mechanism for this type of crystal growth [1-4]. Thepreferred attachment of the 8 nm α-Fe 2 O 3 particles is surprising because the particles arenominally equidimensional [18] and the (001) planes of α-Fe 2 O 3 are generally consideredto be the planes of low surface energy, although hydration as well as oxygen vs. iron5

termination of the planes can alter the surface energies [19,20]. The (001) surface energyof α-Fe 2 O 3 has been calculated to have values between 0.75 and 1.65 J/m 2 depending onthe environment [Refs. 19 and 20 and references therein].Since α-Fe 2 O 3 is magnetic and since we observe exchange coupling betweenagglomerated particles, it is worth considering if exchange interaction between particlescan affect the assembly. Magnetic coupling mechanisms make it favorable for the particlesto assemble along [001]: The superexchange coupling across the oxygen-layers isdominant compared to in-plane exchange interaction [12], and the (001) plane is the planewhere all spins are parallel so that coupling of two (001) planes will lead to least spinfrustration. We find the exchange interaction between (001) planes to be 0.2 J/m 2 by usingthat that the density of Fe-atoms in the (001) plane is one Fe per 11 · 10 -20 m 2 and that theexchange energy density is 2 · 10 -20 J/Fe-atom (the energy density is calculated from theexperimentally found exchange coupling constants, J 3 and J 4 , of Ref. 21; an overview ofthe different types of exchange couplings within hematite is found in Ref. 12). Since theexchange energy is comparable in size, although smaller, to the surface energy, thecontribution from the exchange energy may thus be considered an extra driving force forthe oriented assembly. Exchange interactions between particles with non-parallel (001)planes may lead to magnetic frustration, resulting in repulsive forces.We also studied how the interactions may be diminished due to mechanical treatments.The agglomerated α-Fe 2 O 3 particles were ground together with non-magneticnanoparticles of amorphous SiO 2 (wt. ratio 1:3) in air in an agate ball mill. The millrotated gently, 40 times per minute for 2 days. The weight ratio between balls and samplewas 15:1. Mössbauer spectroscopy and XRD showed that no chemical reaction (less than5 wt%, if any) took place during grinding. NPD data, displayed in Fig. 2c (aftersubtracting the contribution of grinded SiO 2 particles), show that after grinding, almost allof the (003) reflection as well as the other reflections have a width corresponding to theparticle size, i.e. the grinding has to a large extent destroyed the magnetic correlation ofneighboring particles without reducing the particle size. The small narrow contribution tothe (003) reflection after grinding indicates remains of small agglomerates of locallyaligned particles. HREM (Fig. 1d) shows accordingly that after the grinding the α-Fe 2 O 3particles are rather well separated. The effect on relaxation, due to separating the particles,is also clear from MS. Figures 3d and 3e show room temperature Mössbauer spectra of thesample before and after grinding. Whereas the sample before grinding shows no centraldoublet, the spectrum of the grinded sample at room temperature consists of a doublet.The doublet dominates down to at least 80 K (Fig. 3f). This shows that the grinding hasled to a significant reduction of the interactions such that the grinded particles exhibit fastsuperparamagnetic relaxation.The present study shows that nanoparticles prepared from aqueous suspensions mayassemble at ambient temperature and pressure in such a way that the crystallographic andthe magnetic correlations continue across the interfaces. We have found that the interparticleinteractions, as revealed from Mössbauer spectra, to a large extent can be reducedby exposure of an aqueous suspension to ultrasound and can be reestablished by drying thesuspensions at room temperature. We have also found that it is possible to control theinter-particle interactions by gentle grinding of the dried samples. Thus, simplemacroscopic treatments, which more or less unintentionally may take place both inlaboratories and in nature, can significantly affect the local inter-particle interactions. Our6

findings are important for the understanding of the magnetic and the mechanical propertiesof, for example, sediments formed under different conditions in nature. Furthermore, selfassembledchains of magnetic nanoparticles, like those reported here, may have interestingapplications in nanotechnology.Acknowledgments We thank Haldor Topsøe A/S, Kgs. Lyngby, Denmark for use of theircryo-TEM equipment. We acknowledge beam time allocation at Swiss Spallation NeutronSource, Paul Scherrer Institute, Villigen, Switzerland and at HamburgerSynchrotronstrahlungslabor HASYLAB at Deutsches Elektronen-Synchrotron DESY, D-22603 Hamburg, Germany. The work was supported by the Danish Technical ResearchCouncil and the Danish Natural Science Research Council.References[1] R. Lee Penn and J.F. Banfield, Science 281, 969 (1998).[2] R. Lee Penn and J.F. Banfield, Geochim. Cosmochim. Acta 63, 1549 (1999).[3] J.F. Banfield et al., Science 289, 751 (2000).[4] M. Nesterova, J. Moreau and J.F. Banfield, Geochim. Cosmochim. Acta 67, 1177(2003).[5] H. Zeng et al., Nature 420, 395 (2002).[6] P.M. Mendes et al., J. Phys.: Cond. Matt. 25, S3047 (2003).[7] K. Butter et al., Nat. Mater. 2, 88 (2003).[8] Y. Lalatonne, J. Richardi, and M.P. Pileni, Nat. Mater. 3, 121 (2004).[9] A. Ghazali and J-C. Lévy, Phys. Rev. B 67, 064409 (2003).[10] T. Jonsson, P. Svedlindh, and M.F. Hansen, Phys. Rev. Lett. 81, 3976 (1998).[11] V.F. Puntes et al., Nat. Mater. 3, 263 (2004).[12] A thorough review on the properties of hematite is found in: A.H. Morrish, CantedAntiferromagnetism: Hematite. World Scientific, Singapore (1994).[13] Hematite is the most stable form of iron oxide. It is commonly found in rocks andsediments on Earth and recently also on Mars: P.R. Christensen et al., J. Geophys. Res.-Planets 105, 9623 (2000), Webster, G. & Brown, D. Mineral in Mars 'Berries' Adds toWater Story. http://www.jpl.nasa.gov/releases/2004/88.cfm (March 18, 2004).[14] C.G. Shull, W.A. Stauser and E.O. Wollan, Phys. Rev. 83 333 (1951).[15] M.F. Hansen, C.B. Koch, and S. Mørup, Phys. Rev. B 62, 1124 (2000).[16] C. Frandsen, and S. Mørup, J. Magn. Magn. Mater. 266, 36 (2003).[17] T. Sugimoto et al., Colloid. Surf. A. 134, 265 (1998).[18] R. Lee Penn et al., J. Phys. Chem. B 105, 2177 (2001).7

[19] F. Jones et al. Phys. Chem. Chem. Phys. 2, 3209 (2000).[20] X.-G. Wang et al., Phys. Rev. Lett. 81, 1038 (1998).[21] E.J. Samuelsen and G. Shirane, Phys. Stat. Sol. 42, 241 (1970).8

Paper VIII

Submitted July 14, 2004 – RevisedSpin rotation in α-Fe 2 O 3 nanoparticles by interparticle interactionsCathrine Frandsen and Steen MørupDepartment of Physics, Bldg. 307, Technical University of Denmark, DK-2800 Kgs.Lyngby, DenmarkNanoparticles of α-Fe 2 O 3 (hematite) typically have the sublattice magnetization directionsin the hexagonal (001) plane below the Néel temperature. By use of Mössbauerspectroscopy we have found that for agglomerated particles the sublattice magnetizationmay be rotated of the order of 15° out of plane, depending on the particle size. The spinrotation can be explained by exchange interaction between neighboring particles withnon-parallel (001) planes. The results imply that interparticle interactions can lead to spindirections deviating from the easy axis defined by the magnetic anisotropy.PACS.: 75.25.+z; 75.50.Tt, 75.75.+aIt is well established that the properties of magnetic nanoparticles differ significantly fromthe bulk properties [1]. It is particularly interesting that basic properties of magneticmaterials, such as the magnetic structure can be different for nanoparticles and bulkmaterials. For example, due to surface effects, nanoparticles of antiferromagnetic NiOmay have a complicated 8-sublattice magnetic structure [2]. In α-Fe 2 O 3 nanoparticles, themagnetic phase transition, the Morin transition is suppressed [3,4], and the spin-flop-fielddecreases with decreasing particle size [5]. In ferrimagnetic nanoparticles the lowersymmetry of surface atoms and defects in the interior can lead to spin canting [6-8].Recent studies have shown that the magnetic properties of nanoparticles, besides theydiffer from bulk magnetic properties, are extremely sensitive to interparticle interactions[9-20]. Strong magnetic dipole interactions between nanoparticles of ferro- orferrimagnetic materials have been found to suppress the superparamagnetic relaxation[9,10] and may result in spin-glass-like ordered states of the particles at low temperatures[11-14]. It has also been shown that exchange coupling between nanoparticles cansignificantly affect the superparamagnetic relaxation [15-17] and the coercivity [18-20] aswell as it can induce exchange bias [19]. In nanocrystalline materials, it has been foundthat interactions between ferro- or ferrimagnetic grains can influence the magnetizationdirection within soft magnetic grains [21,22]. However, up to now it has not beengenerally considered that the sublattice magnetization direction in antiferromagneticnanoparticles could be influenced by interactions. We have addressed the question of apossible influence of interparticle interactions on magnetic structures by studyinginteracting nanoparticles of α-Fe 2 O 3 by Mössbauer spectroscopy.The crystal structure of α-Fe 2 O 3 can be described in terms of alternating iron and oxygenlayers stacked along the [001] axis of the hexagonal unit cell [23]. The Fe-layers orderantiferromagnetically below the Néel temperature (955 K in bulk), such that the1

magnetization directions of neighboring Fe-layers are antiparallel [23]. Between the Néeltemperature and the Morin temperature, T M ≈ 263 K in bulk, the sublattice magnetizationdirections in α-Fe 2 O 3 are confined by magnetic anisotropy to lie in the (001) plane. Belowthe Morin transition temperature the sublattice magnetization directions are parallel to the[001] axis. For particles of α-Fe 2 O 3 with diameters less than ~ 20 nm, the Morin transitionis reported absent [3,4,23].The angle θ between the sublattice magnetization directions and the [001] axis of α-Fe 2 O 3can be deduced from the quadrupole shift, ε, of the magnetically split Mössbauer spectra.In α-Fe 2 O 3 the electric field gradient is parallel to the [001] axis and the quadrupole shiftis given byε = ε 0 (3cos 2 θ -1)/2, (1)where ε 0 = 0.200 mm/s [23]. Thus, when the sublattice magnetization of α-Fe 2 O 3nanoparticles is in the (001) plane, ε = -0.100 mm/s. Here we report that agglomeratednanoparticles of α-Fe 2 O 3 can have quadrupole shifts deviating distinctly from -0.100 mm/sindicating an out-of-plane sublattice magnetization due to interparticle exchangeinteractions.Powder samples of 6 nm α-Fe 2 O 3 particles were prepared by thermal decomposition ofFe(NO 3 ) 3·9H 2 O [4], 8, 9, 11, 12, and 13.5 nm particles by means of gel-sol methodssimilar to those described by Sugimoto et al. [4,16,24], and 20 nm particles by forcedhydrolysis [15]. After preparation, the particles were dried from aqueous suspensions. Inorder to prepare reference samples, in which the particles were not in contact with oneanother, particles in part of the samples were coated with phosphate (the 8 nm particles) orwith oleic acid before drying. Uncoated, dried 9 nm particles were separated by lowenergyballing with particles of SiO 2 [25,26]. The samples were characterized by XRD andTEM, which revealed crystalline, pseudo-spherical particles with some size distribution[4,15,16,25] and with lattice constants close to the bulk value for α-Fe 2 O 3 .The samples of coated particles show typical superparamagnetic relaxation behaviour,while in the samples of uncoated particles, the relaxation is largely suppressed due toexchange interaction between the particles [15,16]. For α-Fe 2 O 3 nanoparticles, dipoleinteractions are too small to explain the effects on relaxation [15,16]. For illustration of theinfluence of interaction on relaxation, Fig. 1 shows Mössbauer spectra of coated anduncoated 8 nm α-Fe 2 O 3 particles. The coated particles show superparamagnetic relaxationwith a blocking temperature of about 40 K, (i.e. 50 % of the sextet has collapsed to acentral doublet at this temperature), while for the agglomerated uncoated particles, thesuperparamagnetic relaxation is suppressed (i.e. only the sextet exists at least up to roomtemperature, but it broadens and the average hyperfine field diminishes in a way typicalfor interacting magnetic nanoparticles [10,15,16]). At low temperatures, the hyperfinefield for the non-interacting particles decreases faster with temperature than the hyperfinefield of interacting particles (Fig.2) in accordance with the expected influence ofinteractions on collective magnetic excitations [15,27].2

(a)200 K(b)295 KRelative absorption50 K200 K18 K18 K-12 -8 -4 0 4 8 12 -12 -8 -4 0 4 8 12Velocity (mm/s)FIG. 1. Mössbauer spectra obtained at the indicated temperatures of (a) coated and (b)uncoated 8 nm α-Fe 2 O 3 particles.Magnetic hyperfine field (T)53.553.052.552.051.50 5 10 15 20Temperature (K)FIG. 2. The magnetic hyperfine field, B hf , of coated (open circles) and uncoated (closedcircles) 8 nm α-Fe 2 O 3 particles found from Mössbauer spectra obtained at low temperatures. Thelines are linear fits to the data extrapolated down to 0 K.The quadrupole shift of the sextet in the Mössbauer spectra of non-interacting particles,obtained at low temperature, is close to the bulk value above the Morin transitiontemperature, ε ≈ -0.100 mm/s. However, the absolute value of ε was smaller for theinteracting samples. For example, for the 8 nm and 9 nm particles, ε = -0.075 mm/s and ε= -0.087 mm/s, respectively. The uncertainty of the values of ε is ±0.0035 mm/s. Thus, thevalues of ε for the interacting nanoparticles are, beyond uncertainty, different from thevalues for non-interacting particles. This is illustrated in Fig. 3a, which shows thequadrupole shifts for interacting and non-interacting 8 nm particles at temperaturesbetween 6 and 25 K. Figure 3a also shows that at low temperatures, where essentially allparticles are below the blocking temperature, the quadrupole shift is, within experimentaluncertainty, independent of temperature for both interacting and non-interacting particles.This was seen also at higher temperatures for samples where all particles were below theirblocking temperature.Figure 3b shows the quadrupole shift at 20 K for a number of different samples ofinteracting particles as a function of particle size. These data show that there is an overalltendency that the smaller the interacting particles are, the more ε deviates from the bulkvalue of -0.100 mm/s. Variations in ε, beyond the general trend, could be caused by3

different strengths of interactions between the particles, which can depend on e.g. samplepreparation and the duration of the drying process [26].Quadrupole shift, ε (mm/s)-0.07-0.08-0.09-0.10-0.11(a)-0.07-0.08-0.09-0.10(b)0 10 20Temperature (K)5 10 15 20Particle size (nm)FIG. 3. (a) The quadrupole shift, ε, of coated (open circles) and uncoated (closed circles) 8nm α-Fe 2 O 3 particles found from Mössbauer spectra obtained at low temperatures. (b) Thequadrupole shifts, ε, found for uncoated samples of α-Fe 2 O 3 nanoparticles of different particlesizes. The dashed line is a guide to the eye.The interparticle interaction between the α-Fe 2 O 3 particles can be reduced by gently ballmillingthe samples with non-magnetic nanoparticles [25], leading to a faster relaxation.Accordingly, we have found that grinding of the interacting 9 nm α-Fe 2 O 3 particleschanged the quadrupole shift of the sample from -0.087 mm/s to -0.094 mm/s (determinedat 20 K). The Mössbauer spectra of the grinded sample show a sextet relaxing to a doubletwith a blocking temperature of about 60 K. In a temperature range close to the blockingtemperature, the six-line component coexists with a central doublet. We have measuredthe quadrupole shifts of the sextet as a function of temperature in this range. The results,which are shown in Fig. 4, indicate that the quadrupole shift of the remaining sextetincreases with temperature. This suggests that the more weakly interacting particles in thesample relax faster while the particles with stronger interparticle interactions have aslower relaxation.Qudrupole shift, ε (mm/s)-0.08-0.09-0.1020 40 60 80Temperature (K)FIG. 4. The quadrupole shifts, ε, of 9 nm α-Fe 2 O 3 particles after grinding with SiO 2nanoparticles, found from Mössbauer spectra obtained at temperatures between 20 K and 70 K.The solid line is a linear fit to the data.4

Deviations from the ε-value of -0.100 mm/s, as found for the samples of the interactingparticles, suggest an out-of-plane sublattice magnetization. The values of θ, estimatedfrom Eq. (1) for the interacting 8 and 9 nm particles, are 72° and 77°, respectively, and forthe grinded 9 nm particles it is 82°. Since spin rotation is only observed in the samples ofinteracting particles, and since it can be diminished by reducing the interparticleinteractions, its origin seems to be interparticle exchange interactions in these samples. Ithas recently been found that α-Fe 2 O 3 nanoparticles often are in direct contact and mayassemble preferably with common [001] axes [26]. An out-of-plane rotation of spins is,however, only expected to be prevalent when [001] axes of neighboring particles are nonparallel.Localized spin-canting at the surface of the particles [6-8] may also contribute tothe size and direction of the effective interaction field. The strong suppression of thesuperparamagnetic relaxation in the samples of agglomerated particles is presumably dueto exchange interactions between a large network of particles with both parallel and nonparallel[001] directions.The sublattice magnetization directions, derived from the quadrupole shifts, are averagesfor the ensembles of particles. In a sample, where the particles are randomlyagglomerated, some particles may show larger out-of-plane rotations, some smaller ones.Since the particles are too small to form magnetic domains, it is expected that the out-ofplanerotations occurs more or less coherently within each particle. In principle, adistribution in angles will give rise to a broadening of the Mössbauer lines. However, wehave estimated that a distribution in the range 0°-30° gives a negligible broadening.A Morin transition in some of the interacting particles, cannot explain the deviation in εfrom -0.100 mm/s, since a Morin transition in part of a sample would give rise to anasymmetry in the spectra such that, for example, line no. 6 is broader and less intense thanline no. 1 [16], but this was not observed here. Moreover, if a Morin transition werepresent, one might expect it to be most pronounced in the samples with the largestparticles. Instead the smallest particles show the largest out-of-plane rotation of theirsublattice magnetization, suggesting that the smallest particles, which have the smallestanisotropy energy, most easily have their sublattice magnetization rotated out of the plane.Neglecting the small in-plane anisotropy, the magnetic energy of an α-Fe 2 O 3 nanoparticlein close contact with its neighbours may be writtenE = K 1 Vsin 2 θ - E int cos(θ - θ 0 ) (2)where K 1 (< 0) is the out-of-plane magnetic anisotropy energy constant, V is the volume,E int is the net interaction energy due to exchange coupling between particles, and θ - θ 0represents the angle between the sublattice magnetization direction and the interactionfield. We consider for simplicity the case where θ 0 = 0 o and find for small E int that thesublattice magnetization direction is given bycosθ = - E int /(2K 1 V). (3)This seems to be qualitatively in accordance with the size dependence of the quadrupoleshift, shown in Fig. 3b, but since the magnetic anisotropy constants of nanoparticles mayincrease with decreasing particle size [28,29] the size dependence of ε may be smaller thanEq. (3) might suggest. The value of K 1 in α-Fe 2 O 3 nanoparticles is of the order of -10 4 – -5

10 5 J/m 3 [4]. Assuming that K 1 = -5⋅10 4 J/m 3 for 9 nm particles, for which ε ≈ - 0.085mm/s, we find that E int ≈ 8·10 -21 J, corresponding to a temperature of about 600 K. Asdiscussed elsewhere [15,27], the value of E int can be estimated from the temperaturedependence of the hyperfine fields of interacting and non-interacting particles. Using thedata of Fig. 2, we find that E int /k B ≈ 1300 K, which is in reasonably agreement with theestimate made above. This strongly supports our conclusion that the rotation of thesublattice magnetization is due to interparticle interactions.The magnetic hyperfine field, B hf , at an iron nucleus has a contribution from the magneticdipole fields from the surrounding magnetic ions. When the sublattice magnetization of α-Fe 2 O 3 rotates out of the (001) plane, the dipole field changes. Tobler et al. [30] calculatedthe magnetic dipole field as a function of the angle between the sublattice magnetizationdirection and the [001] direction and found that this could explain the change in B hf of 0.8T observed at the Morin transition. According to the calculations the dipole field is givenbyB dip = (1 – 3cos 2 θ) ⋅ 0.325 T. (4)From this expression we find that an 18° rotation out of the plane, as we have found forthe 8 nm particles, should result in an increase in B hf of 0.11 T. By extrapolation of thedata of Fig. 2 to 0 K, we find that B hf at 0 K for the interacting particles is 0.09 (± 0.06) Tlarger than the value for the non-interacting particles in reasonably agreement with thecalculated value. This supports our conclusion that the sublattice magnetization is orientedout-of-plane in the samples of interacting particles.The present study shows that interparticle exchange interaction between magneticnanoparticles is a mechanism, which can lead to rotation of the sublattice magnetizationaway from the direction defined by the magnetic anisotropy. This result stresses that themagnetic properties of nanoparticles cannot solely be described by considering individualparticles, but they have to be understood in terms of interactions, too. An influence ofexchange interaction, as deduced from a suppression of superparamagnetic relaxation byMössbauer spectroscopy, has been found also in other types of agglomerated nanoparticlessuch as NiO [17] and γ-Fe 2 O 3 [10,20] as well as in composites containing nanoparticles ofdifferent materials [16,20]. It is therefore likely that the rotation of sublatticemagnetization is prevalent also in other systems of magnetic nanoparticles.Acknowledgments. We thank F. Bødker, M.F. Hansen, C.B. Koch, and L. Lilleballe forsample preparations and H.K. Rasmussen for assistance with the Mössbauermeasurements. The Danish Technical Research Council and The Danish Natural ScienceResearch Council have supported the work.References1. J.L. Dormann, D. Fiorani and E. Tronc, Adv. Chem. Phys. 98, 283 (1997).2. R.H. Kodama, S.A. Makhlouf, and A. E. Berkowitz, Phys. Rev. Lett. 79, 1393(1997).3. W. Kündig, K.J. Ando, G. Constabaris and R.H. Lindquist, Phys. Rev. 142, 327(1966).4. F. Bødker and S. Mørup, Europhys. Lett. 52, 217 (2000).5. R.D. Zysler et al., Phys. Rev. B. 68, 212408 (2003).6

6. J.M.D. Coey, Phys. Rev. Lett. 27, 1140 (1971).7. A.H. Morrish and K. Haneda, J. Magn. Magn. Mater. 35, 105 (1983).8. S. Mørup, J. Magn. Magn. Mater. 266, 110 (2003).9. W. Luo, S.R. Nagel, T.F. Rosenbaum, and R.E. Rosensweig, Phys. Rev. Lett. 67,2721 (1991).10. S. Mørup, F. Bødker, P.V. Hendriksen and S. Linderoth, Phys. Rev. B 52, 287(1995).11. C. Djurberg et al., Phys. Rev. Lett. 79, 5154 (1997).12. H. Mamiya, I. Nakatani and T. Furubayashi, Phys. Rev. Lett. 80, 177 (1998).13. T. Jonsson, P. Svedlindh and M.F. Hansen, Phys. Rev. Lett. 81, 3976 (1998).14. Y. Sun, M.B. Salamon, K. Garnier and R.S. Averback, Phys. Rev. Lett. 91, 167206(2003).15. M.F. Hansen, C. B. Koch and S. Mørup, Phys. Rev. B, 62, 1124 (2000).16. C. Frandsen and S. Mørup, J. Magn. Magn. Mater. 266, 36 (2003).17. F. Bødker, M.F. Hansen, C.B. Koch and S. Mørup, J. Magn. Magn. Mater. 221, 32(2000).18. H. Zeng et al., Nature 420, 395 (2002).19. J. Sort et al., Appl. Phys. Lett. 75 (1999) 3177; J. Sort et al., J. Magn. Magn.Mater. 219, 53 (2000).20. C. Frandsen et al. Phys. Rev. B (in press).21. G. Herzer, Scripta Metallurgica et Materialia 33, 1741 (1995); J. Magn. Magn.Mater. 157, 133 (1996).22. H. Kronmüller, NanoStructured Materials 6, 157 (1995).23. A.H. Morrish, Canted Antiferromagnetism: Hematite (World Scientific, Singapore,1994).24. T. Sugimoto, Y. Wang, H. Itoh, A. Muramatsu, Colloid. Surf. A: Physiochem.Eng. Aspects 134, 265 (1998).25. M. Xu, C.R.H. Bahl, C. Frandsen, and S. Mørup. J. Colloid Interface Sci. 279, 132(2004).26. C. Frandsen et al. (submitted).27. S. Mørup, J. Magn. Magn. Mater. 37, 39 (1983).28. F. Bødker, S. Mørup and S. Linderoth, Phys. Rev. Lett. 72, 282 (1994).29. E. Tronc, Il Nuovo Cimento 18D, 163 (1996).30. L. Tobler, W. Kündig and I. Savic, Hyperfine Interact. 10, 1017 (1981).7

Paper IX

Journal of Colloid and Interface Science 279 (2004) 132–136www.elsevier.com/locate/jcisInterparticle interactions in agglomerates of α-Fe 2 O 3 nanoparticles:influence of grindingMin Xu a,1 , Christian R.H. Bahl a,b , Cathrine Frandsen a , Steen Mørup a,∗a Department of Physics, Bldg. 307, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmarkb Department of Materials Research, Risø National Laboratory, DK-4000 Roskilde, DenmarkReceived 5 November 2003; accepted 16 June 2004Available online 3 August 2004AbstractWe have chemically prepared a sample of antiferromagnetic α-Fe 2 O 3 nanoparticles by a gel–sol technique. Mössbauer spectra of theas-prepared sample showed that superparamagnetic relaxation was suppressed due to strong magnetic interparticle interactions even at roomtemperature. However, subsequent grinding of the sample by hand in a mortar for some minutes resulted in fast superparamagnetic relaxationof some of the particles. The effect was even more dramatic if the α-Fe 2 O 3 powder was ground for a longer time or together with nonmagneticη-Al 2 O 3 nanoparticles. Similar effects were found after low-energy ball milling. Thus it is found that the agglomeration of the nanoparticlesduring preparation under wet conditions results in strong magnetic interparticle interaction, but a relatively gentle mechanical treatment issufficient to break up the agglomerates, resulting in much weaker interactions. We show that these effects can also be seen when a soil samplecontaining magnetic nanoparticles is ground.© 2004 Elsevier Inc. All rights reserved.Keywords: Nanoparticles; Hematite; Mössbauer spectroscopy; Grinding; Agglomeration; Superparamagnetism; Soil1. IntroductionMany studies have shown that interparticle interactionsbetween magnetic nanoparticles can significantly influencethe magnetic properties, in particular the superparamagneticrelaxation, of the particles [1–15]. In samples of ferro- or ferrimagneticparticles, long-range dipole interactions can havea significant effect, even if the particles are coated with nonmagneticmolecules so that they are well separated [1–6].For antiferromagnetic nanoparticles the magnetic dipole interactionsare negligible, but it has been reported [7–15] thatthe superparamagnetic relaxation can be suppressed by interactionsto a large extent if the particles are allowed toagglomerate. This can be explained by the exchange cou-* Corresponding author. Fax: +45-45-93-23-99.E-mail address: morup@fysik.dtu.dk (S. Mørup).1 Present address: School of Materials and Metallurgy, NortheasternUniversity, Shenyang 110004, China.pling between surface atoms of particles in close proximity[8,10,12].The influence of interactions between iron-containingnanoparticles on the superparamagnetic relaxation can convenientlybe studied by Mössbauer spectroscopy. This hasbeen discussed in detail in earlier publications [10,12]. Typically,the spectrum of noninteracting magnetic nanoparticlesis a six-line spectrum (a sextet) at low temperatures,while at higher temperatures a one- or two-line component(a singlet or a doublet) is formed at the expense of the sextetbecause of fast superparamagnetic relaxation. In spectraof samples of interacting nanoparticles, the sextet does notreadily collapse with increasing temperature, but the linesbecome asymmetrically broadened and the average hyperfinesplitting decreases. Usually, the spectral change from asextet into a doublet or a sextet with asymmetrically broadenedlines takes place over a temperature range, typically ofsome tens to hundreds of Kelvin, due to a distribution of particlesize and interaction strength.0021-9797/$ – see front matter © 2004 Elsevier Inc. All rights reserved.doi:10.1016/j.jcis.2004.06.039

M. Xu et al. / Journal of Colloid and Interface Science 279 (2004) 132–136 133During studies of interaction effects in samples containingantiferromagnetic α-Fe 2 O 3 nanoparticles, we found accidentallythat grinding the samples by hand in a smallmortar apparently reduced the interparticle interactions. Wehave therefore carried out a systematic study of the effectsof grinding a sample of 11-nm α-Fe 2 O 3 particles. We havefound that grinding the sample even for a short time can drasticallyincrease the relaxation because the strength of theinterparticle interaction is decreased. Similar effects werefound in samples exposed to low-energy ball milling.Mössbauer spectroscopy has been extensively used forstudies of soils, which often contain magnetic nanoparticles.Commonly, the samples are ground in a mortar beforethe Mössbauer absorber is prepared. In this connection, it isimportant to know if the grinding of such soil samples canhave an effect on the magnetic properties. We have tested thegrinding effect on a natural soil sample, too, and the resultof this study shows consistency with the effect of grindingthe synthetic samples.2. Materials and methodsα-Fe 2 O 3 (hematite) nanoparticles were prepared bymeans of a gel–sol method similar to that developed by Sugimotoet al. [16]. The sample studied here was prepared byfreeze-drying particles precipitated during centrifugation ofan aqueous suspension of the so-called D-preparation [16].η-Al 2 O 3 nanoparticles with an average diameter of 4 nmwere obtained by calcining commercially obtained pseudoboehmitepowder at 500 ◦ C.Grinding was carried out by hand in an agate mortar witha diameter of 60 mm, moving the pestle in a circular motion,applying a pressure of about 2 kg to it. Two series of sampleswere prepared. In the first, 50 mg of α-Fe 2 O 3 nanoparticleswere ground for various periods of time (0, 5, 20, and60 min). In the second, mixtures of 50 mg of α-Fe 2 O 3 and250 mg of η-Al 2 O 3 nanoparticles were ground for differentperiods of time (0, 2, 5, 10, 20, and 60 min).A mixture of 200 mg of α-Fe 2 O 3 and1gofη-Al 2 O 3was ball-milled for different periods of time (0, 5, 20, and60 min). Ball milling was performed using a Retsch reversiblemill with agate vial and balls. A ball-to-powderweight ratio of about 30:1 was used. The dry milling wasperformed at low energy with a rotation speed of 80 rpm.Both grinding and ball milling were performed in air.A magnetic soil sample from a site called the Salten Forestin Jutland, Denmark was also studied in this investigation.A sample of 100 mg of this soil was ground by handfor 60 min by the same method as used for the α-Fe 2 O 3nanoparticles.All three samples, α-Fe 2 O 3 , η-Al 2 O 3 , and Salten Forest,were loose, dry powders with little visible indication of agglomeration.The structure and the particle size of pure α-Fe 2 O 3 samples,both before and after grinding for 60 min, were examinedby X-ray diffractometry (XRD). The XRD spectrawere recorded using CuKα radiation in a Philips PW 1820diffractometer.The samples containing mixtures of α-Fe 2 O 3 and η-Al 2 O 3 were studied by high-resolution transmission electronmicroscopy (HRTEM) and dark-field TEM (DF-TEM) in aJEOL 3000F electron microscope operated at 300 keV. Thesamples were prepared by dipping grids in the dry mixturesof α-Fe 2 O 3 and η-Al 2 O 3 particles.The samples were studied at room temperature and at80 K by 57 Fe Mössbauer spectroscopy using constant-accelerationspectrometers with sources of 57 Co in rhodium. Thespectra were obtained using a temperature-controlled liquidnitrogen cryostat. The spectrometers were calibrated with a12.5-µm-thick α-Fe foil at room temperature.3. Results and discussionThe XRD spectra of the as-prepared α-Fe 2 O 3 sample(Fig. 1a) showed only the presence of diffraction lines characteristicof hematite. From the linewidth of the diffractionpeaks we estimated an average crystallite size of 11 nm. Inα-Fe 2 O 3 nanoparticles, prepared by the gel–sol techniqueused here, the line broadening due to lattice strain is negligible[17].The HRTEM images of α-Fe 2 O 3 mixed with η-Al 2 O 3nanoparticles showed well-crystallized hematite particleswith sizes in accordance with the XRD data, both before andafter grinding for 60 min. In both samples, the α-Fe 2 O 3 andη-Al 2 O 3 nanoparticle mixture was found to consist of ∼0.1–1 µm sized agglomerates. No lattice planes of the η-Al 2 O 3were observed. This is probably due to the small crystallitesize of the η-Al 2 O 3 or possibly a destruction of the crystalstructure of this phase by the electron beam. Using DF-TEMit can be seen that the α-Fe 2 O 3 particles, seen as brightspots, stick together in agglomerates in the as-prepared sample(Fig. 2a); i.e., the α-Fe 2 O 3 particles are in close contact.Fig. 1. XRD spectra of α-Fe 2 O 3 samples, as prepared and ground for60mininamortar.

134 M. Xu et al. / Journal of Colloid and Interface Science 279 (2004) 132–136Fig. 2. Dark-field TEM images of the mixed α-Fe 2 O 3 /η-Al 2 O 3 sample.The bright spots are the α-Fe 2 O 3 nanoparticles. (a) Image obtained fromthe sample before grinding. (b) Image obtained after grinding for 60 min.The image obtained after grinding (Fig. 2b) shows that theparticles are distributed more evenly.Fig. 3 shows room-temperature and 80-K Mössbauerspectra of the pure α-Fe 2 O 3 nanoparticles after grinding inthe mortar for up to 60 min. The room-temperature spectrashow a clear evolution with grinding time. The spectrumof the as-prepared sample has the typical features ofnanoparticles with strong interparticle interactions [10,12,14], i.e., a sextet with very broad and asymmetric lines,but no doublet component due to particles with fast superparamagneticrelaxation. However, after 5 min of grinding,there is already an indication of a doublet with a relative intensitythat increases with further increased grinding time.After 60 min the doublet is predominant in the spectrum.These results show that an increasing fraction of the particlesperform superparamagnetic relaxation when the samplehas been ground because the interparticle interactions are reduced.All the spectra obtained at 80 K consist of sextets,but the linewidth and the line asymmetry also increase withgrinding time. This is also in accordance with weakened interparticleinteraction [10,14].It might be argued that the evolution of the Mössbauerspectra with grinding time could be explained by a decreaseof the particle size during grinding, and this would resultin faster superparamagnetic relaxation. To check this possibilitywe have obtained XRD spectra of the samples aftergrinding for 60 min (Fig. 1b). A decrease of the size of theindividual crystallites should result in a broadening of thediffraction lines. However, the data in Fig. 1 show the oppositeeffect, namely a slight line narrowing indicating an∼10% growth of the crystallites during grinding. This isclearly visible by considering, for example, the peaks between60 ◦ and 65 ◦ . The increase of the crystallite size may atfirst glance seem surprising. However, it has previously beenshown that mechanical treatment of nanoparticles by ballmilling can result in an increase of the crystallite size [18].It is likely that a similar process takes place during grindingin a mortar. One might expect increased lattice strain aftergrinding. This should result in line broadening, but this wasnot observed. The XRD data show clearly that the changein relaxation behavior upon grinding is not due to a reduc-Fig. 3. Mössbauer spectra of α-Fe 2 O 3 nanoparticles ground in a mortarfor the indicated periods of time. (a) Spectra obtained at room temperature.(b) Spectra obtained at 80 K.tion of the crystallite size. This supports our interpretation interms of diminished magnetic interaction between the particlesafter grinding.In order to further study the influence of grinding, we repeatedthe grinding experiments with a mixture of α-Fe 2 O 3and η-Al 2 O 3 nanoparticles. The Mössbauer data are shownin Fig. 4. In this case, the evolution of the spectra is muchfaster than that seen in the sample of pure α-Fe 2 O 3 nanoparticles.In the room-temperature spectra there is a clearly visibledoublet already after 2 min and after only 10 min thespectrum consists of an intense doublet and a sextet withalmost negligible intensity. After longer grinding times the

M. Xu et al. / Journal of Colloid and Interface Science 279 (2004) 132–136 135Fig. 5. Mössbauer spectra of a soil sample from the Salten Forest in Denmark.The spectra are from an untreated sample and one that has beenground for 60 min.Fig. 4. Mössbauer spectra of α-Fe 2 O 3 nanoparticles ground in a mortarwith η-Al 2 O 3 nanoparticles for the indicated periods of time. (a) Spectraobtained at room temperature. (b) Spectra obtained at 80 K.spectra essentially consist of a doublet. In the spectra obtainedat 80 K, a doublet gradually appears and grows to asignificant intensity after 60 min. These spectra consist ofsuperpositions of doublets and sextets with relatively narrowlines. This is characteristic for particles for which therelaxation is governed by the anisotropy energy barrier ofthe individual particles rather than by interparticle interactions[10,12,14]. In fact, the spectrum obtained at 80 K aftergrinding for 60 min is similar to those of coated (noninteracting)α-Fe 2 O 3 particles with similar size obtained at thesame temperature [12,17].Some of the grinding experiments were repeated in orderto check the reproducibility. It was found that the spectrawere qualitatively similar to those of the first series althoughthere were small differences in the relative areas of the sextetsand the doublets. We also found that if the amount ofpowder in the mortar was increased, the evolution of thespectra with grinding time was correspondingly slower.The evolution of the Mössbauer spectra of the ball-milledsample of a mixture of α-Fe 2 O 3 and η-Al 2 O 3 nanoparticlesas a function of milling time is similar to the evolution of thespectra of the corresponding hand-ground samples (Fig. 4).However, the transformation to a doublet took longer in theball-milling experiment. This can be explained by the significantlyincreased amount of sample and the low energy ofthe ball mill.The results of these experiments show that the aspreparedα-Fe 2 O 3 nanoparticles are attached to each otherin a way which gives rise to a strong magnetic interparticleinteraction. During grinding, these agglomerates are brokenup so that the magnetic interaction between the particles isconsiderably reduced. Although new agglomerates may beformed during grinding under dry conditions, the interparticleinteractions in these agglomerates are much weaker. Ifthe α-Fe 2 O 3 nanoparticles are mixed with an excess of nonmagneticη-Al 2 O 3 nanoparticles, the grinding results in analmost negligible magnetic interparticle interaction.In order to investigate if similar phenomena can be encounteredin natural samples, we have studied a magneticsoil sample from the location Salten Forest in Jutland, Denmark.Soils from this location, which have a saturation magnetization,σ s > 1Am 2 /kg, have recently been characterizedby Mössbauer spectroscopy [19]. Room-temperatureMössbauer spectra of a sample from Salten Forest before and

136 M. Xu et al. / Journal of Colloid and Interface Science 279 (2004) 132–136after grinding in a mortar for 60 min are shown in Fig. 5.Asin the synthetic samples, there is a clear effect of the grinding:the relative area of the doublet increases at the expenseof the sextet. Thus, it is found that the spectrum of a naturalsample can change considerably if the material is ground.Although it is unlikely that one would normally grind anatural sample for 60 min before making an absorber forMössbauer spectroscopy, changes may also take place aftershorter grinding times. In fact, it has been reported that evena gentle smearing of a soil sample that had been heated at225 ◦ C can have a significant effect on the Mössbauer spectra[19], which is similar to our results for synthetic samplesthat have been ground for several minutes.4. SummaryThe present study has shown that the magnetic propertiesof the α-Fe 2 O 3 nanoparticles formed by the gel–soltechnique are strongly influenced by interparticle interactions.However, grinding by hand in a mortar or ball millingat very low energy can result in a dramatic reduction ofthe strength of these magnetic interactions. Thus a relativelygentle macroscopic mechanical treatment affects theagglomeration on the nanometer scale. Especially when themagnetic nanoparticles are ground together with an excessof nonmagnetic alumina nanoparticles, there is a very significanteffect of grinding. It is also shown that the magneticproperties of natural soil samples can be strongly changedby a gentle mechanical treatment. Thus the results showthat the as-prepared sample consists of agglomerates with astrong magnetic interparticle interaction, but after mechanicaltreatment under dry conditions, the contact between thenanoparticles is reduced so that the magnetic interaction ismuch weaker.AcknowledgmentsThis work was supported by the Danish Technical ResearchCouncil and the Danish Natural Science ResearchCouncil. We thank Franz Bødker and Lis Lilleballe forpreparation of the synthetic α-Fe 2 O 3 samples and H.P. Gunnlaugssonfor providing the Salten Forest sample.References[1] W. Luo, S.R. Nagel, T.F. Rosenbaum, R.E. Rosensweig, Phys. Rev.Lett. 67 (1991) 2721.[2] S. Mørup, E. Tronc, Phys. Rev. Lett. 72 (1994) 3278.[3] C. Djurberg, P. Svedlindh, P. Nordblad, M.F. Hansen, F. Bødker,S. Mørup, Phys. Rev. Lett. 79 (1997) 5154.[4] H. Mamiya, I. Nakatani, T. Furubayashi, Phys. Rev. Lett. 80 (1998)177.[5] T. Jonsson, P. Svedlindh, M.F. Hansen, Phys. Rev. Lett. 81 (1998)3976.[6] D. Fiorani, J.L. Dormann, R. Cherkaoui, E. Tronc, F. Lucari, F. D’-Orazio, L. Spinu, M. Nogués, A. Garcia, A.M. Testa, J. Magn. Magn.Mater. 196–197 (1999) 143.[7] S. Mørup, M.B. Madsen, J. Franck, J. Villadsen, C.J.W. Koch, J. Magn.Magn. Mater. 40 (1983) 163.[8] C.J.W. Koch, M.B. Madsen, S. Mørup, G. Christiansen, L. Gerward,Clays Clay Miner. 34 (1986) 17.[9] R.A. Borzi, S.J. Stewart, G. Punte, R.C. Mercader, M. Vasquez-Mansilla,R.D. Zysler, E.D. Cabanillas, J. Magn. Magn. Mater. 205 (1999)234.[10] M.F. Hansen, C.B. Koch, S. Mørup, Phys. Rev. B 62 (2000) 1124.[11] C.W. Ostenfeld, S. Mørup, Hyperfine Interact. C 5 (2002) 83.[12] C. Frandsen, S. Mørup, J. Magn. Magn. Mater. 266 (2003) 36.[13] F. Bødker, M.F. Hansen, C.B. Koch, S. Mørup, J. Magn. Magn.Mater. 221 (2000) 32.[14] S. Mørup, C. Frandsen, F. Bødker, S.N. Klausen, K. Lefmann,P.-A. Lindgård, M.F. Hansen, Hyperfine Interact. 144–145 (2002)347.[15] M.A. Polykarpov, I.V. Trushin, S.S. Yakimov, J. Magn. Magn.Mater. 116 (1992) 372.[16] T. Sugimoto, Y. Wang, H. Itoh, A. Muramatsu, Colloids Surf. A 134(1998) 265.[17] F. Bødker, S. Mørup, Europhys. Lett. 52 (2000) 217.[18] S. Mørup, J.Z. Jiang, F. Bødker, A. Horsewell, Europhys. Lett. 56(2001) 441.[19] H.P. Gunnlaugsson, J.P. Merrison, L.A. Mossin, P. Nørnberg,J. Sanden, E. Uggerhøj, G. Weyer, Hyperfine Interact. 144–145(2002) 365.

Paper X

PHYSICAL REVIEW B 67, 184425 2003Metastable states in magnetic nanoringsF. J. Castaño and C. A. RossDepartment of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139C. FrandsenDepartment of Physics, Technical University of Denmark, DK-2800 Kgs.Lyngby, DenmarkA. Eilez, D. Gil, and Henry I. SmithDepartment of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139M. Redjdal and F. B. HumphreyDepartment of Electrical and Computer Engineering, Boston University, Boston, Massachusetts 02215Received 13 February 2003; published 30 May 2003Magnetization states and hysteresis behavior of small ferromagnetic rings, of diameters 180–520 nm, havebeen investigated using magnetic force microscopy. In addition to the expected bi-domain ‘‘onion’’ andflux-closed ‘‘vortex’’ magnetization states, a metastable state has been found. This ‘‘twisted’’ state contains a360° domain wall which can exist over a wide range of applied fields. Four possible configurations of thetwisted state are possible. Micromagnetic modeling shows that the twisted state is stabilised in small diameter,narrow rings. Additionally, more complex configurations such as double twisted states with two 360° wallshave been observed.DOI: 10.1103/PhysRevB.67.184425PACS numbers: 75.75.a, 75.60.d, 85.75.dINTRODUCTIONThere is increasing interest in the magnetic properties ofsmall magnetic solids nanomagnets, with thicknesses of afew nanometers and deep-submicron lateral dimensions. 1,2These structures can be engineered to display different stablemagnetized states depending on their shape, dimensions, andcomposition. An understanding of the stability of differentstates, and the ability to control the switching field, enablesnanomagnets to find application in high-density magneticrandom access memories, 2 magnetic logic, 3 or other magnetoelectronicdevices. The majority of work has been carriedout on magnetic discs, wires, or bars, but ring-shaped magnetshave recently been the subject of several theoretical 4 andexperimental 5–8 studies. The ring shape is particularly interestingbecause of the existence of flux-closed magnetic configurations‘‘vortex’’ states, in which the magnetizationruns circumferentially around the ring, either clockwise orcounterclockwise, which may make rings ideal candidatesfor high-density storage devices. 4 The transitions betweenthe magnetic states in rings can give information about thenucleation, movement and annihilation of domain walls inwell-controlled structures.To date, micron-size rings 5,6 and 300–800 nm wide octagonalring structures 7,8 have been produced. The experimentalresults support the existence of just two differentmagnetic states: one being the flux-closure or ‘‘vortex’’ stateand the other a state with two domain walls, known as an‘‘onion’’ state. However, the behavior of submicron circularrings has not been investigated, and fundamental questionsremain, in particular which magnetic states are stable, andthe mechanism by which the ring switches from one state toanother. We have fabricated circular rings with diameters of180 nm and above, and widths of 30 nm and above, and havecharacterized and modeled their magnetic behavior. Inthe present paper we present clear experimental evidencefor the existence of additional magnetic states in submicronring-shaped ferromagnets, and discuss the evolution ofthe magnetic state of small rings as a function of appliedfield.EXPERIMENTAL METHODSNanorings were fabricated by a liftoff process from ringshapedpatterns written into a resist layer by electron-beamlithography. To create shapes as close as possible to a perfectring, the electron beam was deflected in a circular trajectorywith a precision of 2 nm. Circles were made using singlepixellines spaced 18 nm. By varying the number of singlepixellines and the e-beam dose, rings with submicron dimensionswere produced. The nanorings had outerdiameters of 180–520 nm and widths of 30–200 nm. Magneticfilms of Co or permalloy (Ni 80 Fe 20 ) with thicknesses of10 nm were deposited onto the resist patterns. To preventoxidation, magnetic films were coated with 3 nm of Cuor Au. The films were made either by electron-beam evaporationin a chamber with a base pressure of 10 6 Torr, orby ion-beam sputtering at 0.1 mTorr in a chamber witha base pressure of 10 9 Torr. In each case the films werepolycrystalline with grain size of approximately 10 nm,and substrates were oxidized silicon. As an example, Fig. 1shows arrays of nanorings with varying dimensions.The magnetic states of the nanorings were imaged bymagnetic force microscopy MFM, using a Digital InstrumentsNanoscope with a low-moment commercial tip. Thetip height during scanning was typically 35 nm. The nanoringswere saturated in an in-plane magnetic field of 1 T, thenthe field was removed and the rings were imaged at rema-0163-1829/2003/6718/1844255/$20.0067 184425-1©2003 The American Physical Society

F. J. CASTAÑO et al. PHYSICAL REVIEW B 67, 184425 2003FIG. 1. Plan-view and tilted scanning electron micrographs offour arrays of Co rings with diameters and widths of a 520 and120 nm, b 360 and 160 nm, c 190 and 30 nm, and d 180 and 50nm.nence. Further images were recorded after applying then removingreverse fields of various amplitudes, using permanentmagnets attached to an adjustable fixture.RESULTS AND DISCUSSIONFigures 2a–2f show the evolution of the magneticstates of one 520-nm diameter Co ring as a function of reversefield. After saturation, the ring is present in an onionstate shown schematically in the top panel of Fig. 2, whichis characterized by dark and light contrast at opposite sidesof the ring originating from the two domain walls. At a certainreverse field, in this case 299 Oe, the ring ‘‘disappears’’from the image as a vortex state forms, Fig. 2e. The vortexhas zero external field so it does not produce any MFM contrast.Both the onion and vortex states have been identifiedpreviously in rings. 5,7 However, over a range of fieldssmaller than that needed to produce the vortex state, a state isvisible which we call a twisted state. This state, which can beseen in Figs. 2c and 2d, is characterized by adjacent lightand dark contrast at one side of the ring. There are fourpossible variants of the twisted state, depending whether thedark-light contrast is on the left or right of the ring, andwhether the dark spot is above or below the light spot. All ofthese variants have been observed in our arrays. This behaviorcontrasts with that seen in larger rings where a directtransition from an onion to a vortex was reported. 5 AlthoughFig. 2 shows a 520 nm diameter ring, similar magnetizationstates can be seen in 180 and 360 nm rings, though the imageshave less contrast due to the lower moment of the rings.From the MFM, it appears that the twisted state is formedfrom the onion state by the movement of one wall around thering until it reaches the other wall. Significantly, the resultingconfiguration can have an extensive range of stability withrespect to applied field. Although common, the twisted stateis not seen in all rings in an array. For instance, out of 64rings similar to that of Fig. 2a, 15 showed twisted states.Figure 2g shows the stability ranges for the twisted statesseen in these 15 rings: in one ring the twisted state existedfor applied fields between 60 and 460 Oe. The twisted statesFIG. 2. At the top, a schematic of the onion, twisted and vortexstates in a ring. Below, data from a 520 nm diameter ring: a anatomic force micrograph. b–f a sequence of MFM images measuredat remanence after first saturating the sample at 10 000 Oe,then applying and removing a reverse field of b 28 Oe, c 162 Oe,d 267 Oe, e 299 Oe, and f 496 Oe. g a plot showing the rangeof stability of the twisted state for 15 rings out of a 64-ring array,for rings of diameter 520 nm and width 175 nm. Each of the horizontalbars represents the field range over which the twisted statewas seen in an individual ring; there is a wide range of behavior. hRemanent hysteresis loop of the 64-ring array. The low-field step,corresponding to the formation of twisted or vortex states, issmoothed out by the variability in switching field between individualrings.do not represent a configuration where two domain walls arecoincidentally pinned next to one another by an irregularityin the ring. If that were the case, we might expect to seeother examples where walls are pinned at different positionsaround the rings. All of our twisted states have the sameMFM contrast, so appear to represent a distinct magneticstate containing two interacting walls that do not annihilateeach other. At sufficiently high fields, the twisted states turninto vortex states and eventually into onion states of oppositeorientation to the starting state, as shown in Fig. 2f.Within the arrays, there is a range of behavior, evidentfrom Fig. 2g. The transitions between onion, twisted, andvortex states occur at different fields for individual rings.Some rings do not show twisted states, indicating a directtransition from the onion to the vortex state or even from theonion to the reverse onion state; 5 another possibility is thatthe stability range of the twisted state in these rings issmaller than the field intervals used for imaging. Trends inbehavior can be followed by plotting collective hysteresisloops for arrays of 64 rings, based on the MFM images. Ifthe original saturating field is applied in the x in-planedirection, then a moment of 1 is assigned to rings showingan onion state oriented along x, and 0 for a vortex ortwisted state. Figures 2h and 3 show hysteresis loops forarrays of rings, 520 nm diameter and 360 nm diameter, re-184425-2

METASTABLE STATES IN MAGNETIC NANORINGSPHYSICAL REVIEW B 67, 184425 2003FIG. 3. Remanent hysteresis loops calculated from MFM datafor two arrays with ring diameters of 360 nm and widths of 110 and160 nm, similar to Fig. 1b. The steps showing the destruction ofthe initial onion state and the formation of the reverse onion stateat higher field are clear.spectively. Two steps can be seen in the loops, as reported forlarger rings: 5,7,9 a low-field step corresponding to the destructionof the positive onion state, and a high-field step correspondingto the creation of the reverse onion state. Betweenthese steps is a plateau region corresponding to the existenceof vortex or twisted states. The steps occur at higher fieldsfor rings with narrower widths.The differences in response of individual rings are attributedto edge roughness or microstructural variation, whichcan locally alter the nucleation or pinning fields of domainwalls. 5,10,11 For instance, notches are known to pin walls inrings. 12 An edge roughness of a few nm is inevitable duringlithographic processing, and the random orientation of grainswithin the films also causes local variations in magnetocrystallineanisotropy. These small-scale fluctuations make itlikely that one wall will begin to move at a lower appliedfield than the other, leading to the formation of a twisted orvortex state, instead of a direct transition from one onionstate to the other by the simultaneous movement of the twowalls. 5 It is worth pointing out that since the twisted stateshave almost zero remanence, magnetometry methods wouldbe incapable of distinguishing between vortex and twistedstates. In contrast to Co rings, NiFe showed much smallerswitching fields, and the magnetic states were strongly perturbedby the low-moment tip, preventing quantitative measurementsof switching fields.To characterize the twisted state it is necessary to considerthe nature of the domain walls in narrow thin-film structures.In the onion state, two head-on domain walls are present ineach nanoring. Such head-on walls can have different magneticconfigurations depending on the width and thickness ofthe magnetic strip. For narrow, thin rectangular strips, thewall has a transverse Néel character in which all momentslie in plane, while head-on walls in wider strips have a fluxclosurestructure containing an out-of-plane vortex. 13 Weused a 3D micromagnetic model 14 to calculate equilibriummagnetization states in magnetic rings, neglecting magnetocrystallineanisotropy. Rings are discretized into cubic cellstypically 2 nm across, and the Landau-Lifschitz-Gilbertequation is solved for the magnetization in each cell usingFIG. 4. Micromagnetic simulations of magnetization patterns in150 nm diameter, 30 nm wide, and 10 nm thick rings. a Onionstate obtained by saturating the magnetization in plane, then relaxingat zero field. b A state containing two 360° walls, at remanence.c Greyscale image of the z component of the field abovethe configuration in b, at a height of 35 nm. The maximum field is600 Oe.the saturation moment for Co, an exchange constant of10 6 erg cm 1 , a gyromagnetic ratio of 0.0179 Oe s 1 and adamping constant of 1 to obtain rapid convergence. For narrowCo rings we found that the head-on walls have a transversecharacter, in agreement with other results onrings 6,7,15,16 and rectangular strips. 13 As an example, Fig. 4ashows a remanent onion-state obtained by equilibration afterin-plane saturation.The transition from the onion state to the vortex state hasbeen studied previously using micromagnetics. If one wall ispinned by a notch or other asymmetry in the ring then avortex state forms by the movement of the unpinned walluntil it annihilates the pinned wall. 5,15–17 However, our modelingshowed that instead of the walls annihilating, it is alsopossible for a stable configuration to form which is analogousto a 360° head-on wall which has been described innarrow thin-film strips. 14,18,19 In this structure, the magnetizationrotates through 360° about an axis perpendicular tothe film plane. We were able to model this structure by artificiallyplacing four transverse domain walls in a ring andallowing the structure to equilibrate. This leads to a configurationwhich contains two pairs of walls, as shown in Fig.4b. Each pair forms a complete 360° wall with in-planemoments. Of course, the 360° walls are metastable states,having a higher energy both exchange and magnetostaticthan a vortex state, but the 360° wall in the model representsa local energy minimum and cannot relax into a vortex stateunless it is perturbed. Such structures have been modeled 18and observed by electron microscopy 19 in rectangular thinfilm strips, but not previously in rings. Notably, our modelingshowed that the walls in wider rings have a flux-closurestructure, and annihilate more easily to produce a vortexstate in the ring. Larger rings are therefore less likely tosupport twisted states.184425-3

F. J. CASTAÑO et al. PHYSICAL REVIEW B 67, 184425 2003The stability of the 360° wall in a ring may be understoodfrom the micromagnetic simulation. Each transverse wallcauses surface charge at the inner and outer edges of the ring.There is an attraction between the two transverse walls becausethey have opposite senses of rotation. The tendency ofthe walls to attract is balanced by the exchange energy in theregion between the two walls, leading to an equilibriumspacing between the walls. It is interesting to compare themagnetization of a ring to the magnetization of a domainwall surrounding a cylindrical bubble in a perpendicularlymagnetized film. 19,20–22 Although the magnetic structure isvery different, there is a topological analogy between transversewalls in small rings and Bloch lines in bubble walls.Bubble walls, similar to rings, can also support a variety ofmagnetization states.To illustrate the correspondence between the 360° walland the twisted state, the out-of-plane component of the fieldabove the ring can be compared to the MFM image. 23 Individualtransverse walls have stray-fields resembling an asymmetrical,radially oriented in-plane dipole, but at a height ofa few times the film thickness, the details of the field distributionbecome blurred and the wall is imaged as a singlebright or dark spot displaced towards the outer edge of thering. 6 The vertical component of the external field of the360° wall of Fig. 4b was calculated at a height of 35 nmabove the ring, and is shown in Fig. 4c, in which it appearsas adjacent light and dark contrast. There is a good correspondencebetween the calculated field distribution of one ofthese 360° walls and the MFM images of the twisted statesshown in Figs. 2c and 2d.More complex wall configurations such as a doubletwisted state Fig. 5 have also been observed in nanorings.Figure 5a shows a 520 nm diameter ring that was originallysaturated to form an onion state. On application of a reversefield, an additional pair of walls nucleates within the top halfof the ring, reversing the magnetization of the top half tocreate a vortex state containing two 360° walls, shown inFigs. 5b, 5c. At a higher field, Fig. 5d, the 360° wall onthe right side of the ring separates into two transverse walls,and one of the transverse walls moves around the lower partof the ring to reverse the magnetization direction of that halfof the ring. Finally, the complex 540° wall on the left collapsesinto a single transverse wall, producing the reverseonion state, Fig. 5e. The same behavior was seen in repeatedapplied field scans. Figures 5b and c have a strongresemblance to the field distributions shown in Fig. 4c for aring containing a pair of 360° walls.The existence of a twisted state in nanorings has interestingconsequences for the design of magnetoelectronic devices.It increases the possible number of observable states ina single-layer nanoring from the four already identified twoopposite onion states and two opposite vortex states to atleast eight including four variants of the twisted state. Formultilayer nanorings such as spin valves or tunnel junctions,there is clearly an even larger number of possible magneticstates, with as-yet unexplored electronic or magnetotransportproperties. The properties of such rings are likely to be veryinteresting, for example, quantum interference effects havebeen reported in 500 nm diameter rings, 24 and head-on wallsFIG. 5. Complex twisted states formed in a 520 nm diameterring, imaged at remanence. a Onion state, following saturationthen application of a reverse field of 299 Oe. b After applying areverse field of b 338 Oe and c 433 Oe, a vortex state with two360° walls is observed. d After applying a reverse field of 442 Oe,the right-hand 360° wall separates and one transverse wall movesaround the lower half of the ring. e The left-hand wall collapses toform a reverse onion state at 473 Oe.in micron-size rings show measurable anisotropicmagnetoresistance. 12 The 360° walls in twisted states may beexpected to have larger magnetoresistance than a head-onwall, and could be useful in a data storage or magnetic logicdevice. As mentioned above, the twisted state is a higherenergy configuration than a vortex state, so it represents ametastable configuration. However, we have shown that thestability range of twisted states can be several hundred Oe,exceeding the stability range over which vortex states exist,so it should be possible to create and manipulate twistedstates in narrow rings or other useful geometries. The intriguingquestion is whether the twisted states can be sufficientlycontrollable to enable them to be used in data storage orlogic applications, which will depend on control of the pinningand annihilation of domain walls in nanorings.ACKNOWLEDGMENTSThe authors acknowledge the financial support of theCambridge-MIT Institute and the Danish Technical ResearchCouncil, and Xiaobin Zhu for helpful discussion.184425-4

METASTABLE STATES IN MAGNETIC NANORINGS1 C. Stamm, F. Marty, A. Vaterlaus, V. Weich, S. Egger, U. Maier,U. Ramsperger, H. Fuhrmann, and D. Pescia, Science 282, 4491998.2 S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S.von Molnár, M. L. Roukes, A. Y. Chtchelkanova, and D. M.Treger, Science 294, 1488 2001.3 R. P. Cowburn and M. E. Welland, Science 287, 1466 2000.4 J. G. Zhu, Y. Zheng, and G. A. Prinz, J. Appl. Phys. 87, 66682000.5 J. Rothman, M. Klaui, L. Lopez-Diaz, C. A. F. Vaz, A. Bleloch, J.A. C. Bland, Z. Cui, and R. Speaks, Phys. Rev. Lett. 86, 10982001.6 X. Zhu, Ph.D. thesis, McGill University, Canada, 2002.7 S. P. Li, D. Peyrade, M. Natali, A. Lebib, Y. Chen, U. Ebels, L. D.Buda, and K. Ounadjela, Phys. Rev. Lett. 86, 1102 2001.8 Y. Chen, A. Lebib, S. P. Li, M. Natali, D. Peyrande, and E. Cambril,Microelectron. Eng. 57, 405 2001.9 M. Klaui, J. Rothman, L. Lopez-Diaz, C. A. F. Vaz, and J. A. C.Bland, Appl. Phys. Lett. 78, 3268 2001.10 C. A. Ross, M. Hwang, M. Shima, J. Y. Cheng, M. Farhoud, T. A.Savas, Henry I. Smith, W. Schwarzacher, F. M. Ross, F. B. Humphrey,and M. Redjdal, Phys. Rev. B 65, 144417 2002.11 J. Yu, U. Rudiger, L. Thomas, S. S. P. Parkin, and A. D. Kent, J.Appl. Phys. 85, 5501 1999.PHYSICAL REVIEW B 67, 184425 200312 M. Klaui, C. A. F. Vaz, J. A. C. Bland, W. Wernsdorfer, G. Faini,and E. Cambril, Appl. Phys. Lett. 81, 108 2002.13 R. D. McMichael and M. J. Donahue, IEEE Trans. Magn. 33,4167 1997.14 M. Redjdal, P. W. Gross, A. Kazmi, and F. B. Humphrey, J. Appl.Phys. 85, 6193 1999.15 L. Lopez-Diaz, J. Rothman, M. Klaui, and J. A. C. Bland, IEEETrans. Magn. 36, 3155 2001.16 L. Lopez-Diaz, J. Rothman, M. Klaui, and J. A. C. Bland, J. Appl.Phys. 89, 7579 2001.17 L. Lopez-Diaz, M. Klaui, J. Rothman, and J. A. C. Bland, PhysicaB 306, 2112001.18 Y. Zheng and J.-G. Zhu, IEEE Trans. Magn. 33, 3286 1997.19 X. Portier and A. Petford-Long, Appl. Phys. Lett. 76, 754 2000.20 A. Hubert and R. Schaefer, Magnetic Domains Springer-Verlag,Berlin, 1998.21 F. B. Humphrey and J. C. Wu, IEEE Trans. Magn. 21, 17621985.22 A. H. Eschenfelder, Magnetic Bubble Technology Springer, Berlin,1981.23 R. Wiesendanger, Scanning Probe Microscopy and SpectroscopyCambridge University Press, Cambridge, UK, 1994.24 S. Kasai, T. Niiyama, E. Saitoh, and M. Miyajima, J. Appl. Phys.91, 6938 2002.184425-5

Paper XI

PHYSICAL REVIEW B 69, 144421 2004Magnetic configurations in 160–520-nm-diameter ferromagnetic ringsF. J. Castaño, C. A. Ross,* A. Eilez, † W. Jung, and C. Frandsen ‡Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USAReceived 29 August 2003; revised manuscript received 24 November 2003; published 21 April 2004The remanent states and hysteretic behavior of thin-film magnetic rings has been investigated experimentallyand by micromagnetic modeling. Rings of diameters 160–520 nm, made from Co using lift-off processing,show three distinct remanent states: a vortex state, an ‘‘onion’’ state with two head-on walls, and a ‘‘twisted’’state containing a 360° wall. The range of stability of these states varies with ring geometry, with smaller widthrings showing higher switching fields and greater variability.DOI: 10.1103/PhysRevB.69.144421PACS numbers: 75.75.a, 75.60.d, 85.75.dI. INTRODUCTIONMagnetic ring-shaped structures have been studied formany years, and macroscopic ferrite rings were used in corememory, an early magnetic data storage device, over fiftyyears ago. 1 More recently, there has been an upsurge in interestin small thin-film ring-shaped structures for a reviewsee Ref. 2, motivated in part by their proposed use in magneticrandom access memories. 3,4 One appealing feature ofthin-film rings is the existence of well-defined remanentstates, which could be used to store one or more data bits ineach ring. Previous work in micron- and submicron-diameterrings 5–14 has confirmed the existence of distinct ‘‘vortex’’states, where the magnetization runs clockwise or counterclockwisearound the ring, and ‘‘onion’’ or bidomain stateswhich contain two head-on (180°) walls at opposite ends ofa diameter. Lately a third state, called a ‘‘twisted’’ state, wasidentified in submicron rings: 15 this consists of a vortex statecontaining a 360° wall. Although metastable with respect tothe vortex state, the twisted state can exist over a range offields and at remanence. The twisted state has also recentlybeen proposed for use in magnetic random access memories 4in which the ring is switched between two twisted states by asmall circumferential field.The behavior of thin-film rings has been explored by severalgroups as a function of the geometry of the ring. Thering can be parametrized by its outer diameter d, its width wi.e., the inner diameter is given by d-2w), and its thicknesst. The majority of experimental work has been carried out onrings with outer diameters from about 500 nm up to severalmicrons, 5–14 but rings with d90 nm and above, 2 d180– 520 nm, 15 and octagonal ring shapes with d300– 800 nm Ref. 16 have also been investigated. All therings exhibit vortex and onion states, and transitions betweenthe states occur by the movement, formation or combinationof domain walls. For instance, a vortex state is formed froman onion state by the unpinning of one wall and its movementaround the ring until it combines with the other wall. Incontrast, twisted states have only been observed in thesmaller rings, with diameters of about 500 nm and below. 15This may be a result of the transverse Néel micromagneticstructure of the head-on walls in the onion state in smallerrings, which makes the formation of a metastable 360° wallmore likely.Deep-submicron diameter rings are interesting because ofpotential applications in high-density devices, and it is thereforeimportant to explore the effect of diameter, width andthickness on ring behavior, in particular the formation andstability of the twisted state. Previous work has shown thatthe switching field for the onion-vortex transition increaseswith increasing diameter and film thickness and decreaseswith increasing width, 12 and that the vortex state is lesslikely to occur in rings made from thinner films. 2 However,there has not been any detailed investigation of the formationand stability of the twisted state. In this paper, the behaviorof Co rings with diameters of 160–520 nm has been investigatedas a function of diameter and width. Results are comparedwith the predictions of a micromagnetic model, whichreproduces the existence of vortex, onion, and twisted states.II. EXPERIMENTAL METHODSCircular Co rings were fabricated using a Raith-150electron-beam lithography system 17 and liftoff processing.To avoid edge roughness due to pixellation, the rings werewritten by scanning the electron-beam along parallel singlepixelcircular trajectories. Typically 10 fields with an area of100100 m 2 were written with increasing electron-beamdose. Each of these fields contained nine 88 arrays of ringsof various dimensions written in a 120 nm thick polymethylmethacrylatelayer, spun onto 3 diameter Si100 wafers.The resist was developed in a 2:1 solution of isopropyl alcoholand methylisobutylketone at a temperature of 21 °C for90 sec. After development of the resist, Co 12nm/ Au3nm bilayers were deposited onto the patterns by electronbeamevaporation and a final lift-off step inn-methylpyrrolidone at 120 °C was performed. The rings hada width variation of less than 10 nm. Figure 1 shows a schematicrepresentation of the lithography processing, as well ascorresponding scanning electron micrographs SEM’s afterthe metal evaporation onto the resist and after the lift-offstep. The films were polycrystalline with grain size of order10 nm. In the present work we investigate circular Co ringswith thickness of 12 nm, outer diameters ranging from 160 to520 nm, and widths of 30 nm and above.A Zeiss LEO 982 scanning electron microscope withGemini column was used to image the structures. Magneticstates were determined using a Digital Instruments Nanoscopemagnetic force microscope MFM with a lowmomenttip, typically at 35 nm lift height. MFM tips can0163-1829/2004/6914/1444217/$22.5069 144421-1©2004 The American Physical Society

CASTAÑO, ROSS, EILEZ, JUNG, AND FRANDSENPHYSICAL REVIEW B 69, 144421 2004FIG. 1. Schematic representation of the lithographic processing,a after the e-beam exposure and resist development, b after themetal evaporation, and c after the lift-off step. Part d shows aSEM corresponding to step b, while e corresponds to step c, inan array of rings with outer diameter of 160 nm and width of 30nm.produce significant fringing fields, 18 with components bothparallel and perpendicular to the sample surface, but unlikesimilarly sized NiFe rings we found no evidence of tipinducedperturbation of the magnetic states of the Co ringsduring repeated scans in different directions. This is attributedto the high switching fields of the Co rings. To image,the rings were first saturated in an in-plane field of 10 kOe inan electromagnet, then imaged at remanence. Reverse inplanefields of different magnitudes and opposite direction tothat of the saturating field were then applied and removed,and the rings again imaged at remanence. Remanence imageswere taken every 70–100 Oe. The reverse in-plane fieldswere applied in situ in the MFM using permanent magnetson an adjustable holder, which were calibrated prior to theexperiments. The maximum field that could be applied at thesample was 2500 Oe.Micromagnetic simulations were performed using twodimensionalOOMMF software, available from NIST NationalInstitute of Standards and Technology. Circular ringshapes with equivalent dimensions to those of the experimentalstructures were discretized into 5 nm5 nm squareelements. Simulations were also made with 2 nm square elementswhich gave similar results for switching fields. Themodel used parameters appropriate for hcp Co exchangeconstant A310 6 erg/cm, saturation moment M s1422 emu/cm 3 , and anisotropy K 1 5.210 6 erg/cm 3 ),with a damping coefficient of 1. The direction of the uniaxialanisotropy within each square element was varied randomlyin three dimensions to simulate a polycrystalline film. Theremanent loops were calculated by equilibrating the magneticstructure at an applied field, then setting the field tozero, equilibrating the magnetization again and then recalculatingthe remanent magnetization.III. RESULTSA. Hysteresis of rings as a function of width and diameterIn all the arrays investigated, MFM indicates that theonion state is present at remanence after saturating the ringsFIG. 2. Top row: SEM images of rings with outer diameters of500 left, 360 middle, and 180 nm right column. The larger ringis shown in plan view while the other rings are shown tilted. Middlerow: MFM remanent images after saturating the sample in a horizontalfield of 10 kOe, showing onion states. Bottom row: MFMscans after applying reversing fields of 216, 1000, and 1700 Oe,respectively. The images show twisted states, except for two of thesmallest rings which are in the vortex state and therefore show nocontrast.at a high field. As the reverse field is increased, the ringstypically switch into a twisted state and then into a vortexstate, and eventually into a reverse onion state. By appropriatefield cycling, all of these states can be imaged at remanence.Figure 2 shows remanent MFM images of onion,twisted and vortex states in rings of different dimensions.Onion states are characterized by dark and light contrast atopposite sides of the ring, the 360° wall in the twisted stateshows as a dark-light pair, and the vortex state shows nocontrast.Based on the MFM data, a qualitative remanence loop foran individual ring can be constructed by assigning a remanenceof zero for the twisted or vortex state and 1 for theonion state. An example is shown in Fig. 3 for a 520 nmdiameter ring. The zero-moment plateau corresponds to thetwisted and vortex states. Two switching fields H C1 andH C2 , corresponding to the destruction of the onion state andthe creation of the reverse onion state, respectively, 2,5–16 canbe measured from the remanence loops.Individual rings show a range of switching fields, so toobtain average values, the collective remanence loop of anarray of typically 64 rings was constructed from MFM data.Figure 4 shows how the remanence loops of ring arrays varywith ring diameter and ring width. The fields H C1 and H C2both increase with decreasing ring width, as shown in TableI. The dependence of switching fields on diameter is weaker;from the table H C1 changes little or increases with increasingdiameter, while H C2 decreases. This corresponds to a widerzero-remanence plateau for smaller-diameter rings. Additionally,the switching field distribution is greater for narrowerrings.144421-2

MAGNETIC CONFIGURATIONS IN 160–520-NM- ...FIG. 3. MFM images of a 520-nm-diameter Co ring showing theevolution of remanent magnetic states in the ring as a function ofreverse field, at 0, 108, 179, and 460 Oe. The arrows on the schematicrepresentation of the states indicate the magnetization directionsin the ring. a Onion state, b twisted state, c vortex state,d reverse onion state. At the center, a remanence loop of the ringhas been constructed from these and other MFM images.Figure 4b also shows a minor loop for an array of ringswith diameter 360 nm and width 110 nm. After positive saturation,a reverse field of 1370 Oe was applied briefly, whichput all of the rings into the vortex state. An increasing positivefield was then applied. At a field of H C2 , the forwardFIG. 4. a Remanence loops deduced from MFM data for ringswith outer diameter of 520 nm and widths of 110, 135, and 170 nm.The solid lines are provided for clarity and one of the data sets ismirrored to illustrate the entire remanent loop. b Remanent hysteresisloops for arrays of rings with outer diameter of 360 nm andwidths 110 or 160 nm, and for rings with diameter 180 nm andwidth 40 nm. Note that the field scale is different from that in a.Aminor remanent loop for the 360 nm diameter, 110 nm wide rings isalso shown in which a reverse field of 1370 Oe was applied togenerate vortex states, then the field was increased back to positivesaturation.PHYSICAL REVIEW B 69, 144421 2004onion state formed, shown in the minor remanence loop.However, in a separate experiment to those undertaken todeduce the minor loop, rings were initially magnetized intotwisted states by a smaller reverse field, then an increasingpositive field was applied. Average positive fields of 100 and200 Oe were required to switch twisted states into forwardsonion states in nanorings with outer diameter of 520 nm andwidths of 170 and 110 nm, respectively. This indicates thatonly a relatively small field is needed to separate the 360°wall into its two component head-on walls.Although individual rings behave reproducibly on repeatedscans, there is a wide range of behavior betweennominally identical rings. An indication of the variation inbehavior can be obtained by plotting the range of fields overwhich a twisted state is observed in the rings of an array. Thefield ranges for the existence of twisted states of several 520-nm-diameter Co rings are shown in Fig. 5. The twisted statein some rings is found over field ranges of several hundredOe, while in other rings the state is short lived. The narrowestrings show the most variation in the stability of thetwisted states.B. Morphology of the twisted stateThere are four variants of the twisted state depending onwhich of the two domain walls in the initial onion statemoved around the ring and which direction it moved. Fourvariants observed in a 520-nm diameter ring array are shownin Fig. 6, two with clockwise and two with counterclockwisemagnetization directions. The variants occurred with equalfrequency in each array. Although it cannot be imaged directlyby MFM, once a vortex state forms from a twistedstate, the vortex necessarily maintains the magnetization directionof the twisted state that precedes it.All the twisted states in an array of rings of the samegeometry have similar appearance in the MFM images. Thearc angle between the domain walls was estimated by measuringthe angle between the lines joining the center of thering to the centers of the dark and light MFM contrast, asindicated in Fig. 6b. For rings with diameters below 200nm, quantitative measurement was not possible because it isdifficult to resolve the positions of the walls with respect tothe center of the ring. Results for 360–520 nm diameter ringsare shown in Table I, along with the corresponding lengthsalong the circumference of the ring. The uniformity of thisangle for a given ring width and diameter makes it unlikelythat creation of the twisted state is controlled by randompinning of the walls. Pinning of walls is seen occasionally,but this gives a different MFM contrast, as exemplified inFigs. 6e, 6f. Figure 7 shows the wall angles measured forthe twisted, pinned and onion states seen in an array of 520-nm-diameter 170-nm wide rings.As the ring becomes wider, the angle between the twocomponent head-on walls, and the overall length of the 360°wall in the twisted state decreases. For a constant ring width,the arc length is constant within the error of the measurement.In rare cases, other, more complex states were observed,for instance, a double twisted state consisting of two360° walls, as well as a triple twisted state containing a 540°wall were reported in 520 nm diameter rings. 15144421-3

CASTAÑO, ROSS, EILEZ, JUNG, AND FRANDSENPHYSICAL REVIEW B 69, 144421 2004TABLE I. Data for the switching fields, the arc angle between the positions of maximum contrast in theMFM images of twisted states, and the corresponding length of the feature in the MFM images, for rings ofdifferent geometries. Data for the arc angles was based on measuring 5–15 rings of each size.Ringdiameter,nmRingwidth,nmH C1 ,OeH C2 ,OeAngle betweenwalls in thetwisted state,deg.Circumferentiallength of twistedstate, nm520 170 170 410 338 15036520 135 330 690 246 10927520 110 470 850 202 919360 160 150 850 3911 12335360 110 240 1900 328 10025C. Modeling resultsBoth remanence loops and conventional hysteresis loopswere simulated for single rings with dimensions matchingthose fabricated. Figure 8 shows calculated hysteresis loopsfor a 360 nm diameter, 110 or 160 nm wide ring. The modelreproduces the decrease in switching field with increasingring width observed experimentally. There is a reasonablequantitative agreement between calculated switching fieldsand the measured average switching fields, except that themodel underestimates H C2 for the narrower ring.Figure 9 shows the calculated remanence loop for the ringof 520 nm diameter and 110 nm width, along with images ofthe magnetization state of the ring at different stages in themagnetization reversal. Remanence loops display sharpertransitions and a lower saturation magnetization than hysteresisloops because the moments relax along the edges of therings at remanence. The model reproduces the states observedin the MFM images in Fig. 3. In particular, the anglebetween the midpoints of the head-on domain walls in thetwisted state is 25°, which compares well with the measuredvalue of 20 (2)° from the MFM measurements.IV. DISCUSSIONThe rings in this study are sufficiently narrow and thinthat the domain walls have an in-plane, transversecharacter, 20 and transitions between the magnetic states areaccomplished by the creation, movement or annihilation oftransverse walls. The switching field H C1 represents the fieldat which the onion state is destroyed by the unpinning andmovement of one domain wall, while H C2 is the field atwhich the reverse onion state is formed from a wall-freevortex state by creation of a reverse domain followed byFIG. 5. Field stability ranges for the twisted states seen in threedifferent arrays of 520-nm-diameter Co rings of width 110, 135, and170 nm, respectively. Each bar represents the range over which thetwisted state was seen in an individual ring. Some rings havetwisted states that persist over hundreds of Oe while others show atwisted state only over a small field range.FIG. 6. Top: SEM of several 520 nm diameter, 170 nm widerings. Below, MFM images a–d demonstrate four variants of thetwisted state seen in four different rings. In b the angle betweenthe domain walls is defined. e,f Examples of pinned states.144421-4

MAGNETIC CONFIGURATIONS IN 160–520-NM- ...FIG. 7. Histogram of the angles between the domain walls in Corings, 520 nm in diameter, and 170 nm wide. The distribution ofangles between the walls in the twisted state is centered at 33°. Thedistribution of angles between the walls in the onion state is centeredat 180° while the angles in the pinned states vary.FIG. 8. The simulated hysteresis loop for rings with outer diameterof 360 nm and widths of 110 and 160 nm.PHYSICAL REVIEW B 69, 144421 2004separation of a domain wall pair, at a region of the ringmagnetized antiparallel to the applied field. At H C1 , themovement of one of the domain walls and its combinationwith the other to make a 360° wall produces an intermediatemetastable twisted state; the twisted state then decomposesinto the vortex by the annihilation of the 360° wall at a fieldintermediate between H C1 and H C2 . This intermediate fieldis difficult to measure by conventional magnetometry, becausethe twisted and vortex states have little or no moment,but the transition can be detected using MFM. Many of therings in this work showed the onion-twisted-vortex-reverseonion state sequence upon field cycling. In some rings,twisted states were not seen, which indicates either directtransitions between the onion and vortex states, or a smallstability range of the twisted state compared to the field stepsize between measurements. Larger rings, on the micronscale, have not been reported to show twisted states becausethe 360° wall is unstable in wider structures 15 and easilyannihilates to produce a vortex state.For the ring geometries and film thickness studied here,the ring width is the key parameter in controlling the switchingfields, with ring diameter secondary. Both H C1 and H C2increase for narrower rings, in agreement with previousresults. 2,12,19 H C1 is expected to be lower for wider ringswhere the potential energy landscape in which the wallmoves, which is affected by the various microstructural andshape irregularities in the ring, is flatter. The increase in H C2with decreasing width can be attributed to the increasing difficultyfor narrower rings in rotating the moments away fromthe edge of the ring to form a reverse domain. 21 Changes inthe switching fields with diameter are less dramatic, especiallyfor wider rings. The data suggest little if any increasein H C1 , but a decrease in H C2 with increasing diameter.Both H C1 and H C2 have a wider switching field distributionfor smaller and narrower rings. Data from elliptical rings ofconstant width 19 shows little effect of the radius of curvatureon H C1 , but H C2 is lower when the reverse domain is nucle-FIG. 9. Simulated remanence loop for a ringstructure with outer diameter of 520 nm andwidth of 110 nm. Images of the different statesduring magnetization reversal are also depictedfor the data points at zero field onion state, at500 twisted state, at 800 vortex state, and1100 Oe reverse onion state.144421-5

CASTAÑO, ROSS, EILEZ, JUNG, AND FRANDSENated in the more sharply curved section of the ring.The size of the 360° wall in the ring is governed by competitionbetween exchange energy, which is minimized by agreater separation between the two constituent 180° walls,and magnetostatic attraction between the constituent wallsdue to their stray fields. The circumferential length of the360° wall, and the arc angle which it subtends at the centerof the ring, therefore depend on the geometry of the ring.The length of the 360° wall is smaller in narrower ringsbecause the total exchange energy is smaller, allowing thewalls to approach more closely, while in rings with the samewidth, the length of the wall along the circumference is similarfor different ring diameters. In the example of Fig. 9, thearc angle subtended by the 360° wall is similar to that measuredexperimentally.The behavior of rings, as with other lithographically patternedmagnetic elements for example, Ref. 22, shows considerablevariability between nominally identical structures.The switching fields for transitions between micromagneticconfigurations depend on defects or imperfections in thering, which affect domain wall generation, pinning, andmovement. For a twisted state to form at all, one wall in theonion state must move before the other. In a perfectly symmetricalring the two walls are expected to move simultaneouslyand the ring would switch from the onion to reverseonion state without forming intermediate states. 5 In practice,some edge roughness or microstructural irregularity will alwaysbreak the symmetry of the system. Edge roughness orgrain size are more significant in smaller patterned structures,leading to the greater switching field distributions andtwisted state stability ranges seen in the smaller and narrowerrings. Notably, in a few rings the pinning sites are strongenough to lead to ‘‘pinned states’’ with domain walls presentat positions different from those characteristic of either onionor twisted states. We observed twisted and pinned statesmore frequently in rings with greater edge roughness. Thetwisted state can be reproduced by micromagnetic simulations,because the edge roughness due to the discretizationand the random 3D magnetocrystalline anisotropy includedin the simulations break the symmetry of the ring.From the equal probability of appearance of the four variantsFig. 6 of the twisted states, it appears that the choice ofwhich wall moves first, and which direction it moves aroundthe ring, is random. This choice ultimately determines thecirculation direction of the resulting vortex state. By pinningone wall, for instance, with a notch, some control can beimposed over the eventual circulation direction of thevortex, 11 and therefore also over which variant of the precedingtwisted state forms.The minor loop data shows that, as expected, the formationof an onion state from a vortex state occurs at H C2irrespective of the direction of the applied field. A similarresult was reported for micron-size rings, in which the onionstate formed at the same field H C2 for both the minor andmajor loops. 5 However, if the field direction is instead reversedwhen the ring is magnetized in a twisted state, thefield will act to separate the two 180° walls and recreate theoriginal onion state. Since domain wall nucleation is not required,the recreation of the onion state is expected to occurPHYSICAL REVIEW B 69, 144421 2004at a field smaller than H C2 . Observations on several ringsconfirmed this expectation qualitatively.This work has shown that small rings commonly reversevia intermediate metastable twisted states. The remanentstate of a ring could conceivably be chosen from one of eightpossibilities two onion states, four variants of the twistedstate, and two different vortex states, or even more complexconfigurations 15 under appropriate field cycling, providedthat pinning sites for the walls can be controlled. This couldbe useful in devices such as magnetic random access memories,where each ring might store several bits. Readback ofthe various states could be accomplished by making the ringsfrom magnetoresistive multilayer stacks, and measuring theresistance of the ring under a small perturbing field. A onebit-per-ringscheme using two twisted states has already beenproposed. 4 Even if only the vortex states are used for datastorage, to take advantage of their zero stray fields, 3 transitionsbetween them are likely to involve onion or twistedintermediate states, and the switching process will thereforedepend on the behavior of domain walls within the rings. Aswith conventional magnetic random access memory cellsmade from elongated or tapered elements, the ultimate usefulnessof such devices will depend on whether the intrinsicvariability between the elements can be controlled. This dependson controlling microstructural inhomogeneity, for example,by using an amorphous or single crystal material, orone with a low magnetocrystalline anisotropy, and reducingedge roughness by improvements in the lithography and patterningprocesses.V. CONCLUSIONSFerromagnetic thin-film rings with diameters of 160–520nm, made from 12-nm-thick Co, commonly transform froman onion bidomain to a vortex flux-closed state via anintermediate metastable twisted state, which contains a 360°wall. Twisted states can be stable over a wide field range, andhave a distinctive micromagnetic structure in which the spatialextent of the 360° wall, determined by exchange andmagnetostatic interactions, depends on the ring width. Micromagneticmodeling also reproduces the formation of thetwisted state during the reversal of a ring. The measuredswitching fields for transitions between the onion, vortex andtwisted states increase with decreasing ring width, vary lessstrongly with diameter, and show significant switching fielddistribution. The transitions between the states depend on themovement, creation and annihilation of domain walls and aretherefore highly sensitive to microstructural and shape irregularities.ACKNOWLEDGMENTSThe authors thank Henry I. Smith for the use of facilitiesat the Nanostructures Laboratory at MIT, and Dario Gil andFeng Zhang for useful discussions. This work was supportedby the Cambridge-MIT Institute, the German Academic ExchangeService DAAD, and the Danish Technical ResearchCouncil.144421-6

MAGNETIC CONFIGURATIONS IN 160–520-NM- ...* Electronic address: caross@mit.edu† Present address: Departamento de Quimica-Fisica, Universidaddel Pais Vasco, P.O. Box 644, 48080 Bilbao, Spain.‡ Permanent address: Department of Physics, Technical Universityof Denmark, Lyngby DK 2800, Denmark.1 B. Cullity, Introduction to Magnetism and Magnetic MaterialsAddison-Wesley, Reading, MA, 1973.2 M. Klaui, C. A. F. Vaz, L. Lopez-Diaz, and J. A. C. Bland, J.Phys.: Condens. Matter 15, R985 2003.3 J. G. Zhu, Y. Zheng, and G. A. Prinz, J. Appl. Phys. 87, 66682000.4 X. Zhu and J. G. Zhu, IEEE Trans. Magn. 39, 2854 2003.5 J. Rothman, M. Klaui, L. Lopez-Diaz, C. A. F. Vaz, A. Bleloch, J.A. C. Bland, Z. Cui, and R. Speaks, Phys. Rev. Lett. 86, 10982001.6 S. P. Li, W. S. Lew, J. A. C. Bland, M. Natali, A. Lebib, and Y.Chen, J. Appl. Phys. 92, 7397 2002.7 M. Rahm, J. Raabe, R. Pulwey, J. Biberger, W. Wagscheider, D.Weiss, and C. Meier, J. Appl. Phys. 91, 7980 2002.8 J. Bekaert, D. Buntinx, C. Van Haesendonck, V. V. Moshchalkov,J. de Boeck, G. Borghs, and V. Metlushko, Appl. Phys. Lett. 81,3413 2002.9 C. A. F. Vaz, L. Lopez-Diaz, M. Klaui, J. A. C. Bland, T. L.Monchesky, J. Unguris, and Z. Cui, Phys. Rev. B 67 14,140405 2003.10 X. Zhu, P. Grutter, V. Metlushko, and B. Ilic, J. Appl. Phys. 93,7059 2003.PHYSICAL REVIEW B 69, 144421 200411 M. Klaui, J. Rothman, L. Lopez-Diaz, C. A. F. Vaz, and J. A. C.Bland, Appl. Phys. Lett. 78, 3268 2001.12 Y. G. Yoo, M. Klaui, C. A. F. Vaz, L. J. Heyderman, and J. A. C.Bland, Appl. Phys. Lett. 82, 2470 2003.13 M. Klaui, C. A. F. Vaz, J. A. C. Bland, W. Wernsdorfer, G. Faini,and E. Cambril, Appl. Phys. Lett. 81, 108 2002.14 X. Zhu, P. Grutter, V. Metlushko, B. Ilic, Y. Hao, F. J. Castaño, S.Haratani, C. A. Ross, B. Vogeli, and H. I. Smith, J. Appl. Phys.93, 8540 2003.15 F. J. Castaño, C. A. Ross, C. Frandsen, A. Eilez, D. Gil, H. I.Smith, M. Redjdal, and F. B. Humphrey, Phys. Rev. B 67 18,184425 2003.16 S. P. Li, D. Peyrade, M. Natali, A. Lebib, Y. Chen, U. Ebels, L. D.Buda, and K. Ounadjela, Phys. Rev. Lett. 86, 1102 2001.17 J. G. Goodberlet, J. T. Hastings, and H. I. Smith, J. Vac. Sci.Technol. B 19, 2499 2001.18 X. Zhu, P. Grutter, V. Metlushko, and B. Ilic, J. Appl. Phys. 91,7340 2002.19 F. J. Castaño, C. A. Ross, and A. Eilez, J. Phys. D 36, 20312003.20 R. D. McMichael and M. J. Donahue, IEEE Trans. Magn. 33,4167 1997.21 M. Klaui, C. A. F. Vaz, J. A. C. Bland, T. L. Monchesky, B.Unguris, E. Bauer, S. Cherifi, S. Heun, A. Locatelli, L. J. Heyderman,and Z. Cui, Phys. Rev. B 68, 134426 2003.22 F. J. Castaño, Y. Hao, M. Hwang, C. A. Ross, B. Vögeli, H. I.Smith, and S. Haratani, Appl. Phys. Lett. 79, 1504 2001.144421-7