Magnetic anisotropy and coercivity of Fe3Se4 nanostructures

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.
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