Magnetic anisotropy and coercivity of Fe3Se4 nanostructures
Magnetic anisotropy and coercivity of Fe3Se4 nanostructures
Magnetic anisotropy and coercivity of Fe3Se4 nanostructures
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
<strong>Magnetic</strong> <strong>anisotropy</strong> <strong>and</strong> <strong>coercivity</strong> <strong>of</strong> <strong>Fe3Se4</strong> <strong>nanostructures</strong><br />
Gen Long, Hongwang Zhang, Da Li, Renat Sabirianov, Zhidong Zhang et al.<br />
Citation: Appl. Phys. Lett. 99, 202103 (2011); doi: 10.1063/1.3662388<br />
View online: http://dx.doi.org/10.1063/1.3662388<br />
View Table <strong>of</strong> Contents: http://apl.aip.org/resource/1/APPLAB/v99/i20<br />
Published by the American Institute <strong>of</strong> Physics.<br />
Related Articles<br />
Magnetization enhancement <strong>and</strong> cation valences in nonstoichiometric (Mn,Fe)3-δO4 nanoparticles<br />
J. Appl. Phys. 111, 074309 (2012)<br />
Tunable emission in surface passivated Mn-ZnS nanophosphors <strong>and</strong> its application for Glucose sensing<br />
AIP Advances 2, 012183 (2012)<br />
A sintered nanoparticle p-n junction observed by a Seebeck microscan<br />
J. Appl. Phys. 111, 054320 (2012)<br />
Gram scale synthesis <strong>of</strong> high magnetic moment Fe100−xCox alloy nanoparticles: Reaction mechanism,<br />
structural <strong>and</strong> magnetic properties <strong>and</strong> its application on nanocomposite<br />
J. Appl. Phys. 111, 07B539 (2012)<br />
Textured Nd2Fe14B flakes with enhanced <strong>coercivity</strong><br />
J. Appl. Phys. 111, 07A735 (2012)<br />
Additional information on Appl. Phys. Lett.<br />
Journal Homepage: http://apl.aip.org/<br />
Journal Information: http://apl.aip.org/about/about_the_journal<br />
Top downloads: http://apl.aip.org/features/most_downloaded<br />
Information for Authors: http://apl.aip.org/authors<br />
Downloaded 05 Apr 2012 to 210.72.130.187. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_<strong>and</strong>_permissions
APPLIED PHYSICS LETTERS 99, 202103 (2011)<br />
<strong>Magnetic</strong> <strong>anisotropy</strong> <strong>and</strong> <strong>coercivity</strong> <strong>of</strong> Fe 3 Se 4 <strong>nanostructures</strong><br />
Gen Long, 1 Hongwang Zhang, 1 Da Li, 1,2 Renat Sabirianov, 3 Zhidong Zhang, 2<br />
<strong>and</strong> Hao Zeng 1,a)<br />
1 University at Buffalo, the State University <strong>of</strong> New York, Buffalo, New York 14260, USA<br />
2 Shenyang National Laboratory for Materials Science, Institute <strong>of</strong> Metal Research <strong>and</strong> International Center<br />
for Materials Physics, Chinese Academy <strong>of</strong> Sciences, Shenyang, Liaoning 110016, China<br />
3 University <strong>of</strong> Nebraska-Omaha, Omaha, Nebraska 68182, USA<br />
(Received 10 August 2011; accepted 23 October 2011; published online 15 November 2011)<br />
The hard magnetic properties <strong>of</strong> Fe 3 Se 4 <strong>nanostructures</strong> were studied both experimentally <strong>and</strong><br />
theoretically. <strong>Magnetic</strong> measurements showed that Fe 3 Se 4 nanoparticles can exhibit giant <strong>coercivity</strong><br />
exceeding 40 kOe at low temperature (10 K). This unusually large <strong>coercivity</strong> is attributed to the<br />
uniaxial magnetocrystalline <strong>anisotropy</strong> <strong>of</strong> the monoclinic structure <strong>of</strong> Fe 3 Se 4 with ordered cation<br />
vacancies. The measured <strong>anisotropy</strong> constant is 1.0 10 7 erg/cm 3 , consistent with the result from<br />
first-principles calculations. The magnetization reversal mechanism <strong>of</strong> the nanoparticles is found to<br />
be incoherent spin rotation. VC 2011 American Institute <strong>of</strong> Physics. [doi:10.1063/1.3662388]<br />
Fe 7 Se 8 <strong>and</strong> Fe 3 Se 4 are two iron chalcogenide compounds<br />
known to be ferrimagnetic half-a-century ago. 1–5<br />
The ferrimagnetism is attributed to the ferromagnetically<br />
aligned spins within the c-plane coupled antiferromagnetically<br />
between adjacent planes with ordered iron vacancies. 6,7<br />
The <strong>nanostructures</strong> <strong>of</strong> these compounds, on the other h<strong>and</strong>,<br />
are less studied. 8,9 The lower dimensionality provides additional<br />
tuning capabilities for their magnetism. Two very<br />
recent work reported the synthesis <strong>and</strong> magnetic properties<br />
<strong>of</strong> Fe 7 Se 8 <strong>and</strong> Fe 3 Se 4 <strong>nanostructures</strong> <strong>and</strong> positive magnetoresistance<br />
in one-dimensional Fe 3 Se 4 nanowire arrays. 10,11<br />
However, the magnetic <strong>anisotropy</strong> in these materials,<br />
whether in bulk form or in <strong>nanostructures</strong>, is poorly known.<br />
In this work, we report the magnetic properties <strong>of</strong> chemically<br />
synthesized Fe 3 Se 4 <strong>nanostructures</strong>. By reducing the dimension<br />
<strong>of</strong> Fe 3 Se 4 , giant <strong>coercivity</strong> values <strong>of</strong> 40 kOe have been<br />
realized at low temperatures. Such a large <strong>coercivity</strong> has not<br />
been reported previously in Fe 3 Se 4 or in any other assynthesized<br />
magnetic systems. The magnetic <strong>anisotropy</strong> is<br />
measured to be 1.0 10 7 erg/cm 3 , which is confirmed by our<br />
first-principles computation results. It is rare for materials<br />
without rare earth or noble metal elements to possess such<br />
high <strong>anisotropy</strong>. Its origin is attributed to the monoclinic<br />
structure <strong>of</strong> Fe 3 Se 4 with ordered iron vacancies.<br />
Fig. 1(a) shows the magnetic hysteresis loops <strong>of</strong> the<br />
Fe 3 Se 4 nanoparticles synthesized by our chemical solution<br />
method. 12 The nanoparticles have a shape <strong>of</strong> faceted nanoplatelets<br />
with average sizes <strong>of</strong> 100 nm. The paramagnetic<br />
slope at high fields can be attributed to spin canting at the<br />
grain boundaries <strong>and</strong> particle surfaces. Assuming that spins<br />
in the particle interior remain collinear <strong>and</strong> reach saturation,<br />
we can subtract the paramagnetic component from the magnetic<br />
hysteresis to extract the behavior <strong>of</strong> the ferrimagnetic<br />
component including its saturation magnetization (M S ) <strong>and</strong><br />
<strong>coercivity</strong> (H c ). M S is 2.2 emu/g at 293 K which increases<br />
to 12.6 emu/g at 10 K. The M S value <strong>of</strong> 12.6 emu/g<br />
(83 emu/cm 3 ) corresponds to 2.2 l B per unit cell (defined as<br />
Fe 6 Se 8 ) <strong>and</strong> is close to earlier experimental results. 5 The<br />
a) Electronic mail: haozeng@buffalo.edu.<br />
most striking behavior <strong>of</strong> these nanoparticles is their giant<br />
<strong>coercivity</strong> observed. It can be seen that H c reaches 4 kOe at<br />
room temperature, which rises by an order <strong>of</strong> magnitude to<br />
40 kOe at 10 K (Fig. 1(a)).<br />
To investigate the origin <strong>of</strong> such a large <strong>coercivity</strong>, the<br />
magnetic <strong>anisotropy</strong> is measured using powderized bulk<br />
samples partially aligned in a magnetic field. As can be seen<br />
from the inset <strong>of</strong> Fig. 1(b), the predominant diffraction peak<br />
is (020) for the aligned sample, indicating that the easy axis<br />
is the b-axis. The hexagonal symmetry <strong>of</strong> NiAs-based FeSe<br />
crystal structure is dictating the symmetry axis to be along<br />
its 6-fold symmetry c-axis. However, vacancies in Fe 3 Se 4<br />
order in chains along the b-axis. Because <strong>of</strong> this, the symmetry<br />
<strong>of</strong> the lattice reduces to monoclinic <strong>and</strong> the b-axis<br />
becomes the easy axis. This also suggests that magnetocrystalline<br />
<strong>anisotropy</strong> is responsible for the observed <strong>anisotropy</strong><br />
<strong>and</strong> large <strong>coercivity</strong>. This is underst<strong>and</strong>able since the shape<br />
<strong>of</strong> the <strong>nanostructures</strong> is more or less isotropic with small aspect<br />
ratio, <strong>and</strong> also the magnetization <strong>of</strong> the material is low,<br />
leading to negligible contribution from the shape <strong>anisotropy</strong>.<br />
The magnetic <strong>anisotropy</strong> constant (K u ) can be obtained by<br />
extrapolating the magnetic hysteresis loops in both the easy<br />
<strong>and</strong> hard axes directions. As an example, Fig. 1(b) shows the<br />
hysteresis loops parallel <strong>and</strong> perpendicular to the easy axes,<br />
measured at 10 K. Note that while the powder sample has<br />
much smaller <strong>coercivity</strong> than that <strong>of</strong> the nanoparticles, their<br />
<strong>anisotropy</strong> values should be comparable since K u is primarily<br />
a material property. From the measured M s <strong>and</strong> extrapolated<br />
<strong>anisotropy</strong> field (H K ), the magnetic <strong>anisotropy</strong> constant K u<br />
can be calculated using K u ¼ 1 2 M SH K . To determine the type<br />
<strong>of</strong> the magnetocrystalline <strong>anisotropy</strong>, temperature dependence<br />
<strong>of</strong> K u was measured (Fig. 2(a)). For uniaxial magnetocrystalline<br />
<strong>anisotropy</strong>, K u should be proportional to M 3 S ;<br />
while for cubic type, K u should be proportional to M 10 s . 13<br />
Fig. 2(b) shows a plot <strong>of</strong> K u as a function <strong>of</strong> M s (log-scale).<br />
A linear fitting gives a slope <strong>of</strong> 2.6, which indicates that the<br />
<strong>anisotropy</strong> is predominantly uniaxial. 13<br />
The large K u <strong>of</strong> 1.1 10 7 erg/cm 3 at 10 K is non-trivial<br />
since the material does not contain any rare-earth or noble<br />
metal element. This makes Fe 3 Se 4 st<strong>and</strong>ing out as a<br />
0003-6951/2011/99(20)/202103/3/$30.00 99, 202103-1<br />
VC 2011 American Institute <strong>of</strong> Physics<br />
Downloaded 05 Apr 2012 to 210.72.130.187. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_<strong>and</strong>_permissions
202103-2 Long et al. Appl. Phys. Lett. 99, 202103 (2011)<br />
TABLE I. Calculated MAE <strong>and</strong> orbital moments (per unit cell) <strong>of</strong> Fe 3 Se 4 .<br />
a b c<br />
MAE 1.139 meV 0 2.051 meV<br />
Orbital moments 0.16 0.19 0.1<br />
Note: using lattice parameters a ¼ 6.208, b ¼ 3.525, <strong>and</strong> c ¼ 11.28326 A ;<br />
1 meV/unit cell ¼ 0.6 10 6 erg/cm 3 .<br />
FIG. 1. (Color online) (a) The hysteresis loops <strong>of</strong> faceted Fe 3 Se 4 nanoparticles<br />
at 10 K <strong>and</strong> room temperature <strong>and</strong> (b) the hysteresis loops <strong>of</strong> a partially<br />
aligned Fe 3 Se 4 powder sample measured parallel <strong>and</strong> perpendicular to the<br />
easy axis at 10 K. The inset shows that the predominant diffraction peak is<br />
(020).<br />
c<strong>and</strong>idate for hard magnetic material applications, especially<br />
when large magnetization is not needed (e.g., in recording<br />
media). 14 The origin <strong>of</strong> the large <strong>anisotropy</strong> is rooted in its<br />
crystal symmetry: Fe 3 Se 4 is in a monoclinic structure, with<br />
ordered Fe vacancies along the b-axis. This vacancy ordering<br />
produces highly anisotropic crystal field <strong>and</strong> the spin-orbit<br />
coupling thus leads to prominent magnetocrystalline <strong>anisotropy</strong>.<br />
To verify this, we performed first-principles calculations<br />
<strong>of</strong> the magnetocrystalline <strong>anisotropy</strong> energy (MAE) <strong>of</strong><br />
Fe 3 Se 4 using the projector augmented-wave (PAW) method<br />
<strong>and</strong> its implementation in the Vienna ab-initio simulation<br />
package (VASP) code within the Perdew-Burke-Ernzerh<strong>of</strong><br />
(PBE) generalized gradient approximation. The lattice parameters<br />
<strong>and</strong> the atomic positions were taken from the experimental<br />
data. The calculations were performed without<br />
symmetry operations <strong>and</strong> with 9 16 5 division <strong>of</strong> Brillouin<br />
zone.<br />
The results <strong>of</strong> the calculation are presented in Table I. The<br />
calculated easy axis is b <strong>and</strong> the MAE is <strong>of</strong> the order <strong>of</strong><br />
1.2 10 7 erg/cm 3 . These are in agreement with experimental<br />
findings. The magnetic structure <strong>of</strong> the compound in the<br />
ground state is ferrimagnetic. The calculated difference in<br />
energy <strong>of</strong> the ferromagnetic <strong>and</strong> ferrimagnetic structures is<br />
0.447 eV/unit cell. The total magnetic moment per unit cell<br />
(Fe 6 Se 8 )is4.34l B (4.15 l B spin moment). This value is nearly<br />
twice as large as the experimental value <strong>of</strong> 2.2 l B /unit cell. In<br />
ferrimagnetic materials, the total magnetization is obtained<br />
from the difference <strong>of</strong> two large magnetization values in sublattices<br />
<strong>and</strong> somewhat larger discrepancies can be expected compared<br />
with the computational results for ferromagnetic<br />
systems. Ma et al. 15 argue that in a-FeSe the corresponding<br />
long-range ordering moment measured by experiments should<br />
be smaller than the calculated one, because the calculations are<br />
done based on the magnetic unit cell <strong>and</strong> the low-energy spin<br />
fluctuations, as well as their interactions with itinerant electrons<br />
are frozen by the finite-size excitation gap.<br />
Coercivity depends on both magnetic <strong>anisotropy</strong> <strong>and</strong> the<br />
magnetization reversal mechanisms. To see whether our particles<br />
are multi-domain or single-domain, we estimate the<br />
critical radius for a single-domain particle following:<br />
r C 9 ðAK uÞ 1=2<br />
pMS<br />
2 ; (1)<br />
where A is the exchange stiffness constant. 13 A is unknown<br />
experimentally for Fe 3 Se 4 , <strong>and</strong> thus calculated from firstprinciples<br />
by linear muffin-tin orbital method (LMTO) using<br />
analytical formula derived in the frame <strong>of</strong> second-order perturbation<br />
expansion. 16,17 Results <strong>of</strong> exchange parameters are<br />
shown in Table II. The exchange coupling in the plane is<br />
mainly ferromagnetic while that between the planes is antiferromagnetic.<br />
The exchange stiffness can then be estimated<br />
using<br />
D ¼ 2l B<br />
3M<br />
X<br />
J ij R 2 ij : (2)<br />
TABLE II. Calculated pair exchange parameters <strong>of</strong> Fe 3 Se 4 .<br />
j<br />
Pair (types) J ij (mRy) R ij (A )<br />
FIG. 2. (Color online) (a) The measured K u as a function <strong>of</strong> temperature<br />
<strong>and</strong> (b) K u as a function <strong>of</strong> M S plotted in the logarithmic scale. The line is a<br />
linear fitting giving a slope <strong>of</strong> 2.6. The errors in the measurements are represented<br />
by the size <strong>of</strong> the data points.<br />
1-2 0.47 2.9242<br />
1-2 0.04 7.18<br />
1-2 0.12 4.5800<br />
1-1 0.07 6.7689<br />
1-1 0.64 3.525<br />
1-1 0.04 6.208<br />
2-2 0.95 3.26<br />
2-2 0.22 5.49<br />
2-2 0.03 3.525<br />
2-2 0.02 6.208<br />
Downloaded 05 Apr 2012 to 210.72.130.187. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_<strong>and</strong>_permissions
202103-3 Long et al. Appl. Phys. Lett. 99, 202103 (2011)<br />
FIG. 3. (Color online) (a) H c as a function <strong>of</strong> temperature <strong>and</strong> (b) H c as a<br />
function <strong>of</strong> M S 2 . The line is a linear fitting. The errors in the measurements<br />
are represented by the size <strong>of</strong> the data points.<br />
The calculated exchange stiffness D ¼ 100 meV*A 2 corresponds<br />
to an exchange stiffness constant A ¼ 0.4 10 6 erg/<br />
cm. r c is thus obtained to be about 800 nm at 10 K <strong>and</strong><br />
2000 nm at 300 K, much larger than the particle sizes <strong>of</strong> our<br />
synthesized samples. Therefore, we conclude that all <strong>nanostructures</strong><br />
studied here are single-domain particles. The coherence<br />
radius r coh , below which the particle reverses its<br />
magnetization by coherent rotation, is estimated to be<br />
100 nm at 10 K using<br />
<br />
r coh ¼ C<br />
A 1=2<br />
MS<br />
2 ; (3)<br />
where C is an aspect ratio dependent constant, taken to be<br />
1.44 for a sphere. 13 Since the particle sizes <strong>of</strong> our samples<br />
range from 100 nm to 500 nm, the magnetization reversal<br />
most likely proceeds by incoherent rotation modes such as<br />
curling.<br />
To study the role <strong>of</strong> thermal fluctuations, <strong>coercivity</strong> H c<br />
as a function <strong>of</strong> temperature were measured. It is observed<br />
that H c drops rapidly with increasing temperature, as shown<br />
in Fig. 3(a). The temperature dependence <strong>of</strong> <strong>coercivity</strong> for<br />
<strong>nanostructures</strong> has contributions from two sources: the temperature<br />
dependence <strong>of</strong> <strong>anisotropy</strong> <strong>and</strong> thermal fluctuations.<br />
In the Stoner-Wohlfarth model, the energy barrier to magnetization<br />
reversal by coherent rotation <strong>of</strong> a particle is given by<br />
K u V. Using the room temperature value <strong>of</strong> K u <strong>and</strong> volume<br />
calculated from the coherent radius <strong>of</strong> 100 nm, the lower<br />
bound <strong>of</strong> the <strong>anisotropy</strong> barrier is found to be more than 3<br />
orders <strong>of</strong> magnitude larger than the thermal energy k B T.<br />
Since the particle sizes are larger than 100 nm, the thermal<br />
fluctuation does not play a role here. Due to the dominating<br />
role <strong>of</strong> magnetocrystalline <strong>anisotropy</strong> <strong>and</strong> negligible thermal<br />
effects, H c should be proportional to the <strong>anisotropy</strong> field <strong>and</strong>,<br />
therefore, its temperature dependence should scale linearly<br />
with Ms 2 . As shown in Fig. 3(b), H c vs. Ms 2 indeed obeys a<br />
linear relationship. H c expected from a r<strong>and</strong>om assembly <strong>of</strong><br />
non-interacting nanoparticles undergoing coherent rotation<br />
would be 0.5 H K . 18 The measured H c is somewhat smaller<br />
than but fairly close to 0.5H K , suggesting that the magnetization<br />
reversal mechanism <strong>of</strong> the sample is close to the transition<br />
from incoherent rotation to coherent rotation.<br />
In conclusion, Fe 3 Se 4 <strong>nanostructures</strong> exhibit giant <strong>coercivity</strong><br />
at low temperatures. This unusually large <strong>coercivity</strong><br />
originates from the large magnetocrystalline <strong>anisotropy</strong> <strong>of</strong><br />
the monoclinic structure <strong>of</strong> Fe 3 Se 4 with ordered Fe vacancies.<br />
The magnetocrystalline <strong>anisotropy</strong> constant calculated<br />
from first-principles agrees with the measured value. The<br />
<strong>coercivity</strong> measured at different temperatures scales linearly<br />
with Ms 2 , confirming the origin <strong>of</strong> the <strong>coercivity</strong> to be the<br />
uniaxial magnetocrystalline <strong>anisotropy</strong>. The magnetization<br />
reversal mechanism is found to be incoherent spin rotation.<br />
This work is supported by NSF DMR0547036, NSF<br />
MRSEC, DOE, the National Basic Research Program (No.<br />
2010CB934603) <strong>of</strong> China, the National High Technology<br />
Research <strong>and</strong> Development Program (863 Program:<br />
2010AA03A402) <strong>of</strong> China. Da Li thanks the Chinese Academy<br />
<strong>of</strong> Sciences for financial support.<br />
1 T. Hirone <strong>and</strong> S. Chiba, J. Phys. Soc. Jpn. 11, 666 (1956).<br />
2 A. Okazaki <strong>and</strong> K. Hirakawa, J. Phys. Soc. Jpn. 11, 930 (1956).<br />
3 K. Hirakawa, J. Phys. Soc. Jpn. 12, 929 (1957).<br />
4 T. Kamimura, K. Kamigaki, T. Hirone, <strong>and</strong> K. Sato, J. Phys. Soc. Jpn. 22,<br />
1235 (1967).<br />
5 P. Terzieff <strong>and</strong> K. L. Komarek, Monatsch. Chem. 109, 1037 (1978).<br />
6 A. Okazaki, J. Phys. Soc. Jpn. 16, 1162 (1961).<br />
7 Y. Takemura, H. Suto, N. Honda, K. Kakuno, <strong>and</strong> K. Saito, J. Appl. Phys.<br />
81, 5177 (1997).<br />
8 K. D. Oyler, X. L. Ke, I. T. Sines, P. Schiffer, <strong>and</strong> R. E. Schaak, Chem.<br />
Mater. 21, 3655 (2009).<br />
9 L. Q. Chen, H. Q. Zhan, X. F. Yang, Z. Y. Sun, J. Zhang, D. Xu, C. L.<br />
Liang, M. M. Wu, <strong>and</strong> J. Y. Fang, Cryst. Eng. Commun. 12, 4386 (2010).<br />
10 C. R. Lin, Y. J. Siao, S. Z. Lu, <strong>and</strong> C. Gau, IEEE Trans. Magn. 45, 4275<br />
(2009).<br />
11 D. Li, J. J. Jiang, W. Liu, <strong>and</strong> Z. D. Zhang, J. Appl. Phys. 109, 07C705<br />
(2011).<br />
12 H. W. Zhang, G. Long, D. Li, R. Sabirianov, <strong>and</strong> H. Zeng, Chem. Mater.<br />
23, 3769 (2011).<br />
13 B. D. Cullity, Introduction to <strong>Magnetic</strong> Materials (Addison Wesley Publishing<br />
Company, Reading, MA, 1972).<br />
14 R. C. O’H<strong>and</strong>ley, Modern <strong>Magnetic</strong> Materials: Principles <strong>and</strong> Applications<br />
(Wiley, New York, 2000).<br />
15 F. Ma, W. Ji, J. Hu, Z. Y. Lu, <strong>and</strong> T. Xiang, Phys. Rev. Lett. 102, 177003<br />
(2009).<br />
16 R. F. Sabiryanov, S. K. Bose, <strong>and</strong> O. N. Mryasov, Phys. Rev. B. 51, 8958<br />
(1995).<br />
17 A. L. Liechtenstein, M. I. Katsnelson, V. P. Antropov, <strong>and</strong> V. A. Gubanov,<br />
J. Magn. Magn. Mater. 67, 65 (1987).<br />
18 E. C. Stoner <strong>and</strong> E. P. Wohlfarth, Philos. Trans. R. Soc. London, Ser. A<br />
240, 599 (1948).<br />
Downloaded 05 Apr 2012 to 210.72.130.187. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_<strong>and</strong>_permissions