Magnetic anisotropy and coercivity of Fe3Se4 nanostructures

Magnetic anisotropy and coercivity of Fe3Se4 nanostructures
Gen Long, Hongwang Zhang, Da Li, Renat Sabirianov, Zhidong Zhang et al.
Citation: Appl. Phys. Lett. 99, 202103 (2011); doi: 10.1063/1.3662388
View online: http://dx.doi.org/10.1063/1.3662388
View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v99/i20
Published by the American Institute of Physics.
Related Articles
Adatom kinetics on nonpolar InN surfaces: Implications for one-dimensional nanostructures growth
Appl. Phys. Lett. 99, 193106 (2011)
Modeling pulsed-laser melting of embedded semiconductor nanoparticles
J. Appl. Phys. 110, 094307 (2011)
Ag-Au nanoclusters: Structure and phase segregation
Appl. Phys. Lett. 99, 171914 (2011)
Epitaxial graphene three-terminal junctions
Appl. Phys. Lett. 99, 173111 (2011)
Spherical magnetic nanoparticles fabricated by electric explosion of wire
AIP Advances 1, 042122 (2011)
Additional information on Appl. Phys. Lett.
Journal Homepage: http://apl.aip.org/
Journal Information: http://apl.aip.org/about/about_the_journal
Top downloads: http://apl.aip.org/features/most_downloaded
Information for Authors: http://apl.aip.org/authors
Downloaded 15 Nov 2011 to 210.72.130.85. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions

APPLIED PHYSICS LETTERS 99, 202103 (2011)
Magnetic anisotropy and coercivity of Fe 3 Se 4 nanostructures
Gen Long, 1 Hongwang Zhang, 1 Da Li, 1,2 Renat Sabirianov, 3 Zhidong Zhang, 2
and Hao Zeng 1,a)
1 University at Buffalo, the State University of New York, Buffalo, New York 14260, USA
2 Shenyang National Laboratory for Materials Science, Institute of Metal Research and International Center
for Materials Physics, Chinese Academy of Sciences, Shenyang, Liaoning 110016, China
3 University of Nebraska-Omaha, Omaha, Nebraska 68182, USA
(Received 10 August 2011; accepted 23 October 2011; published online 15 November 2011)
The hard magnetic properties of Fe 3 Se 4 nanostructures were studied both experimentally and
theoretically. Magnetic measurements showed that Fe 3 Se 4 nanoparticles can exhibit giant coercivity
exceeding 40 kOe at low temperature (10 K). This unusually large coercivity is attributed to the
uniaxial magnetocrystalline anisotropy of the monoclinic structure of Fe 3 Se 4 with ordered cation
vacancies. The measured anisotropy constant is 1.0 10 7 erg/cm 3 , consistent with the result from
first-principles calculations. The magnetization reversal mechanism of the nanoparticles is found to
be incoherent spin rotation. VC 2011 American Institute of Physics. [doi:10.1063/1.3662388]
Fe 7 Se 8 and Fe 3 Se 4 are two iron chalcogenide compounds
known to be ferrimagnetic half-a-century ago. 1–5
The ferrimagnetism is attributed to the ferromagnetically
aligned spins within the c-plane coupled antiferromagnetically
between adjacent planes with ordered iron vacancies. 6,7
The nanostructures of these compounds, on the other hand,
are less studied. 8,9 The lower dimensionality provides additional
tuning capabilities for their magnetism. Two very
recent work reported the synthesis and magnetic properties
of Fe 7 Se 8 and Fe 3 Se 4 nanostructures and positive magnetoresistance
in one-dimensional Fe 3 Se 4 nanowire arrays. 10,11
However, the magnetic anisotropy in these materials,
whether in bulk form or in nanostructures, is poorly known.
In this work, we report the magnetic properties of chemically
synthesized Fe 3 Se 4 nanostructures. By reducing the dimension
of Fe 3 Se 4 , giant coercivity values of 40 kOe have been
realized at low temperatures. Such a large coercivity has not
been reported previously in Fe 3 Se 4 or in any other assynthesized
magnetic systems. The magnetic anisotropy is
measured to be 1.0 10 7 erg/cm 3 , which is confirmed by our
first-principles computation results. It is rare for materials
without rare earth or noble metal elements to possess such
high anisotropy. Its origin is attributed to the monoclinic
structure of Fe 3 Se 4 with ordered iron vacancies.
Fig. 1(a) shows the magnetic hysteresis loops of the
Fe 3 Se 4 nanoparticles synthesized by our chemical solution
method. 12 The nanoparticles have a shape of faceted nanoplatelets
with average sizes of 100 nm. The paramagnetic
slope at high fields can be attributed to spin canting at the
grain boundaries and particle surfaces. Assuming that spins
in the particle interior remain collinear and reach saturation,
we can subtract the paramagnetic component from the magnetic
hysteresis to extract the behavior of the ferrimagnetic
component including its saturation magnetization (M S ) and
coercivity (H c ). M S is 2.2 emu/g at 293 K which increases
to 12.6 emu/g at 10 K. The M S value of 12.6 emu/g
(83 emu/cm 3 ) corresponds to 2.2 l B per unit cell (defined as
Fe 6 Se 8 ) and is close to earlier experimental results. 5 The
a) Electronic mail: haozeng@buffalo.edu.
most striking behavior of these nanoparticles is their giant
coercivity observed. It can be seen that H c reaches 4 kOe at
room temperature, which rises by an order of magnitude to
40 kOe at 10 K (Fig. 1(a)).
To investigate the origin of such a large coercivity, the
magnetic anisotropy is measured using powderized bulk
samples partially aligned in a magnetic field. As can be seen
from the inset of Fig. 1(b), the predominant diffraction peak
is (020) for the aligned sample, indicating that the easy axis
is the b-axis. The hexagonal symmetry of NiAs-based FeSe
crystal structure is dictating the symmetry axis to be along
its 6-fold symmetry c-axis. However, vacancies in Fe 3 Se 4
order in chains along the b-axis. Because of this, the symmetry
of the lattice reduces to monoclinic and the b-axis
becomes the easy axis. This also suggests that magnetocrystalline
anisotropy is responsible for the observed anisotropy
and large coercivity. This is understandable since the shape
of the nanostructures is more or less isotropic with small aspect
ratio, and also the magnetization of the material is low,
leading to negligible contribution from the shape anisotropy.
The magnetic anisotropy constant (K u ) can be obtained by
extrapolating the magnetic hysteresis loops in both the easy
and hard axes directions. As an example, Fig. 1(b) shows the
hysteresis loops parallel and perpendicular to the easy axes,
measured at 10 K. Note that while the powder sample has
much smaller coercivity than that of the nanoparticles, their
anisotropy values should be comparable since K u is primarily
a material property. From the measured M s and extrapolated
anisotropy field (H K ), the magnetic anisotropy constant K u
can be calculated using K u ¼ 1 2 M SH K . To determine the type
of the magnetocrystalline anisotropy, temperature dependence
of K u was measured (Fig. 2(a)). For uniaxial magnetocrystalline
anisotropy, K u should be proportional to M 3 S ;
while for cubic type, K u should be proportional to M 10 s . 13
Fig. 2(b) shows a plot of K u as a function of M s (log-scale).
A linear fitting gives a slope of 2.6, which indicates that the
anisotropy is predominantly uniaxial. 13
The large K u of 1.1 10 7 erg/cm 3 at 10 K is non-trivial
since the material does not contain any rare-earth or noble
metal element. This makes Fe 3 Se 4 standing out as a
0003-6951/2011/99(20)/202103/3/$30.00 99, 202103-1
VC 2011 American Institute of Physics
Downloaded 15 Nov 2011 to 210.72.130.85. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions

202103-2 Long et al. Appl. Phys. Lett. 99, 202103 (2011)
TABLE I. Calculated MAE and orbital moments (per unit cell) of Fe 3 Se 4 .
a b c
MAE 1.139 meV 0 2.051 meV
Orbital moments 0.16 0.19 0.1
Note: using lattice parameters a ¼ 6.208, b ¼ 3.525, and c ¼ 11.28326 A ;
1 meV/unit cell ¼ 0.6 10 6 erg/cm 3 .
FIG. 1. (Color online) (a) The hysteresis loops of faceted Fe 3 Se 4 nanoparticles
at 10 K and room temperature and (b) the hysteresis loops of a partially
aligned Fe 3 Se 4 powder sample measured parallel and perpendicular to the
easy axis at 10 K. The inset shows that the predominant diffraction peak is
(020).
candidate for hard magnetic material applications, especially
when large magnetization is not needed (e.g., in recording
media). 14 The origin of the large anisotropy is rooted in its
crystal symmetry: Fe 3 Se 4 is in a monoclinic structure, with
ordered Fe vacancies along the b-axis. This vacancy ordering
produces highly anisotropic crystal field and the spin-orbit
coupling thus leads to prominent magnetocrystalline anisotropy.
To verify this, we performed first-principles calculations
of the magnetocrystalline anisotropy energy (MAE) of
Fe 3 Se 4 using the projector augmented-wave (PAW) method
and its implementation in the Vienna ab-initio simulation
package (VASP) code within the Perdew-Burke-Ernzerhof
(PBE) generalized gradient approximation. The lattice parameters
and the atomic positions were taken from the experimental
data. The calculations were performed without
symmetry operations and with 9 16 5 division of Brillouin
zone.
The results of the calculation are presented in Table I. The
calculated easy axis is b and the MAE is of the order of
1.2 10 7 erg/cm 3 . These are in agreement with experimental
findings. The magnetic structure of the compound in the
ground state is ferrimagnetic. The calculated difference in
energy of the ferromagnetic and ferrimagnetic structures is
0.447 eV/unit cell. The total magnetic moment per unit cell
(Fe 6 Se 8 )is4.34l B (4.15 l B spin moment). This value is nearly
twice as large as the experimental value of 2.2 l B /unit cell. In
ferrimagnetic materials, the total magnetization is obtained
from the difference of two large magnetization values in sublattices
and somewhat larger discrepancies can be expected compared
with the computational results for ferromagnetic
systems. Ma et al. 15 argue that in a-FeSe the corresponding
long-range ordering moment measured by experiments should
be smaller than the calculated one, because the calculations are
done based on the magnetic unit cell and the low-energy spin
fluctuations, as well as their interactions with itinerant electrons
are frozen by the finite-size excitation gap.
Coercivity depends on both magnetic anisotropy and the
magnetization reversal mechanisms. To see whether our particles
are multi-domain or single-domain, we estimate the
critical radius for a single-domain particle following:
r C 9 ðAK uÞ 1=2
pMS
2 ; (1)
where A is the exchange stiffness constant. 13 A is unknown
experimentally for Fe 3 Se 4 , and thus calculated from firstprinciples
by linear muffin-tin orbital method (LMTO) using
analytical formula derived in the frame of second-order perturbation
expansion. 16,17 Results of exchange parameters are
shown in Table II. The exchange coupling in the plane is
mainly ferromagnetic while that between the planes is antiferromagnetic.
The exchange stiffness can then be estimated
using
D ¼ 2l B
3M
X
J ij R 2 ij : (2)
TABLE II. Calculated pair exchange parameters of Fe 3 Se 4 .
j
Pair (types) J ij (mRy) R ij (A )
FIG. 2. (Color online) (a) The measured K u as a function of temperature
and (b) K u as a function of M S plotted in the logarithmic scale. The line is a
linear fitting giving a slope of 2.6. The errors in the measurements are represented
by the size of the data points.
1-2 0.47 2.9242
1-2 0.04 7.18
1-2 0.12 4.5800
1-1 0.07 6.7689
1-1 0.64 3.525
1-1 0.04 6.208
2-2 0.95 3.26
2-2 0.22 5.49
2-2 0.03 3.525
2-2 0.02 6.208
Downloaded 15 Nov 2011 to 210.72.130.85. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions

202103-3 Long et al. Appl. Phys. Lett. 99, 202103 (2011)
FIG. 3. (Color online) (a) H c as a function of temperature and (b) H c as a
function of M S 2 . The line is a linear fitting. The errors in the measurements
are represented by the size of the data points.
The calculated exchange stiffness D ¼ 100 meV*A 2 corresponds
to an exchange stiffness constant A ¼ 0.4 10 6 erg/
cm. r c is thus obtained to be about 800 nm at 10 K and
2000 nm at 300 K, much larger than the particle sizes of our
synthesized samples. Therefore, we conclude that all nanostructures
studied here are single-domain particles. The coherence
radius r coh , below which the particle reverses its
magnetization by coherent rotation, is estimated to be
100 nm at 10 K using
r coh ¼ C
A 1=2
MS
2 ; (3)
where C is an aspect ratio dependent constant, taken to be
1.44 for a sphere. 13 Since the particle sizes of our samples
range from 100 nm to 500 nm, the magnetization reversal
most likely proceeds by incoherent rotation modes such as
curling.
To study the role of thermal fluctuations, coercivity H c
as a function of temperature were measured. It is observed
that H c drops rapidly with increasing temperature, as shown
in Fig. 3(a). The temperature dependence of coercivity for
nanostructures has contributions from two sources: the temperature
dependence of anisotropy and thermal fluctuations.
In the Stoner-Wohlfarth model, the energy barrier to magnetization
reversal by coherent rotation of a particle is given by
K u V. Using the room temperature value of K u and volume
calculated from the coherent radius of 100 nm, the lower
bound of the anisotropy barrier is found to be more than 3
orders of magnitude larger than the thermal energy k B T.
Since the particle sizes are larger than 100 nm, the thermal
fluctuation does not play a role here. Due to the dominating
role of magnetocrystalline anisotropy and negligible thermal
effects, H c should be proportional to the anisotropy field and,
therefore, its temperature dependence should scale linearly
with Ms 2 . As shown in Fig. 3(b), H c vs. Ms 2 indeed obeys a
linear relationship. H c expected from a random assembly of
non-interacting nanoparticles undergoing coherent rotation
would be 0.5 H K . 18 The measured H c is somewhat smaller
than but fairly close to 0.5H K , suggesting that the magnetization
reversal mechanism of the sample is close to the transition
from incoherent rotation to coherent rotation.
In conclusion, Fe 3 Se 4 nanostructures exhibit giant coercivity
at low temperatures. This unusually large coercivity
originates from the large magnetocrystalline anisotropy of
the monoclinic structure of Fe 3 Se 4 with ordered Fe vacancies.
The magnetocrystalline anisotropy constant calculated
from first-principles agrees with the measured value. The
coercivity measured at different temperatures scales linearly
with Ms 2 , confirming the origin of the coercivity to be the
uniaxial magnetocrystalline anisotropy. The magnetization
reversal mechanism is found to be incoherent spin rotation.
This work is supported by NSF DMR0547036, NSF
MRSEC, DOE, the National Basic Research Program (No.
2010CB934603) of China, the National High Technology
Research and Development Program (863 Program:
2010AA03A402) of China. Da Li thanks the Chinese Academy
of Sciences for financial support.
1 T. Hirone and S. Chiba, J. Phys. Soc. Jpn. 11, 666 (1956).
2 A. Okazaki and K. Hirakawa, J. Phys. Soc. Jpn. 11, 930 (1956).
3 K. Hirakawa, J. Phys. Soc. Jpn. 12, 929 (1957).
4 T. Kamimura, K. Kamigaki, T. Hirone, and K. Sato, J. Phys. Soc. Jpn. 22,
1235 (1967).
5 P. Terzieff and K. L. Komarek, Monatsch. Chem. 109, 1037 (1978).
6 A. Okazaki, J. Phys. Soc. Jpn. 16, 1162 (1961).
7 Y. Takemura, H. Suto, N. Honda, K. Kakuno, and K. Saito, J. Appl. Phys.
81, 5177 (1997).
8 K. D. Oyler, X. L. Ke, I. T. Sines, P. Schiffer, and R. E. Schaak, Chem.
Mater. 21, 3655 (2009).
9 L. Q. Chen, H. Q. Zhan, X. F. Yang, Z. Y. Sun, J. Zhang, D. Xu, C. L.
Liang, M. M. Wu, and J. Y. Fang, Cryst. Eng. Commun. 12, 4386 (2010).
10 C. R. Lin, Y. J. Siao, S. Z. Lu, and C. Gau, IEEE Trans. Magn. 45, 4275
(2009).
11 D. Li, J. J. Jiang, W. Liu, and Z. D. Zhang, J. Appl. Phys. 109, 07C705
(2011).
12 H. W. Zhang, G. Long, D. Li, R. Sabirianov, and H. Zeng, Chem. Mater.
23, 3769 (2011).
13 B. D. Cullity, Introduction to Magnetic Materials (Addison Wesley Publishing
Company, Reading, MA, 1972).
14 R. C. O’Handley, Modern Magnetic Materials: Principles and Applications
(Wiley, New York, 2000).
15 F. Ma, W. Ji, J. Hu, Z. Y. Lu, and T. Xiang, Phys. Rev. Lett. 102, 177003
(2009).
16 R. F. Sabiryanov, S. K. Bose, and O. N. Mryasov, Phys. Rev. B. 51, 8958
(1995).
17 A. L. Liechtenstein, M. I. Katsnelson, V. P. Antropov, and V. A. Gubanov,
J. Magn. Magn. Mater. 67, 65 (1987).
18 E. C. Stoner and E. P. Wohlfarth, Philos. Trans. R. Soc. London, Ser. A
240, 599 (1948).
Downloaded 15 Nov 2011 to 210.72.130.85. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions