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Composition dependence of exchange stiffness in FexPt1-x alloys

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The exchange stiffness constants of chemically disordered FexPt1-x films with thickness around 50 nm were determined by means of ferromagnetic resonance. It was found to increase with increasing Fe content from 6±4pJ/m for x=0.27 to 15±4pJ/m for x=0.67 . Theoretical results from fully relativistic and scalar-relativistic band-structure calculations using the Korringa-Kohn-Rostoker method confirm the experimentally obtained values. In addition, determination of the magnetocrystalline anisotropy by angular-dependent measurements of the ferromagnetic resonance gave the possibility to estimate the exchange length that was found to be 40-50 nm for all compositions investigated in this work.
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Composition dependence of exchange stiffness in Fe
x
Pt
1−x
alloys
C. Antoniak,
1
J. Lindner,
1
K. Fauth,
2
J.-U. Thiele,
3
J. Minár,
4
S. Mankovsky,
4
H. Ebert,
4
H. Wende,
1
and M. Farle
1
1
Fakultät für Physik and Center for Nanointegration Duisburg-Essen (CeNIDE), Universität Duisburg-Essen, Lotharstr. 1,
D-47048 Duisburg, Germany
2
Experimentelle Physik IV, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany
3
Research and Technology Development, Seagate Technology, 47010 Kato Road, Fremont, California 94538, USA
4
Department Chemie und Biochemie, Ludwig-Maximilians-Universität München, Butenandtstr. 11, D-81377 München, Germany
Received 18 March 2010; revised manuscript received 5 July 2010; published 4 August 2010
The exchange stiffness constants of chemically disordered Fe
x
Pt
1−x
films with thickness around 50 nm were
determined by means of ferromagnetic resonance. It was found to increase with increasing Fe content from
64pJ/ m for x =0.27 to 154pJ/ m for x =0.67. Theoretical results from fully relativistic and scalar-
relativistic band-structure calculations using the Korringa-Kohn-Rostoker method confirm the experimentally
obtained values. In addition, determination of the magnetocrystalline anisotropy by angular-dependent mea-
surements of the ferromagnetic resonance gave the possibility to estimate the exchange length that was found
to be 40–50 nm for all compositions investigated in this work.
DOI: 10.1103/PhysRevB.82.064403 PACS numbers: 76.50.g, 71.70.Gm, 75.30.Gw
I. INTRODUCTION
The systematic investigation of spin waves and exchange
stiffness gives the possibility, e.g., to gain more insight into
spin torque and domain-wall depinning which are recently
discussed intensively especially relating to new magneto-
logic or data storage devices. For example, the recently pre-
sented domain-wall logic
1
uses the magnetic domain wall in
nanowires made of soft-magnetic materials like Permalloy as
transition edge in a changing signal. However, reducing the
dimensionality of such components to the nanometer scale
leads to the FePt system as a promising candidate
2
with its
high magnetocrystalline anisotropy in the chemically ordered
state to avoid thermally activated fluctuations of the mag-
netic moments, the so-called superparamagnetism,
3
as dis-
cussed in the literature.
The intense research activities on nanoparticles of
Fe
x
Pt
1−x
alloys over the last decades did not only lead to new
results on the structural and magnetic properties see, e.g.,
Refs. 48 but also reveals some lack of knowledge about
the bulk system. Driven by the on-going discussion about
spin canting effects that may occur in Fe
x
Pt
1−x
nanoparticles,
911
we examined the exchange stiffness in the
corresponding bulk material which is connected to the length
scale of dominating exchange coupling exchange length
which usually suppresses spin canting. Ferromagnetic reso-
nance FMR was used as a powerful tool for the determina-
tion of i the magnetocrystalline anisotropy by angular-
dependent measurements and ii the exchange stiffness
constant A by the analysis of standing spin waves excited in
the material. The results are supported by theoretical calcu-
lations using the spin-polarized relativistic Korringa-Kohn-
Rostoker SPR-KKR method.
12
II. EXPERIMENTAL DETAILS
Epitaxial Fe
x
Pt
1−x
films with thickness around 50 nm were
grown on MgO001 substrates at room temperature by mag-
netron cosputtering from Fe and Pt targets in a vacuum sys-
tem with a base pressure of about 10
−6
Pa. The deposition
rate was about 0.1 nm/s. X-ray diffraction indicates a high
degree of structural order, the mosaic spread is below 1°. The
layer thickness determined by Rutherford backscattering was
found to be 46 6 nm and therefore, the films are expected
to exhibit bulk properties.
Room-temperature FMR experiments were performed us-
ing a constant microwave frequency of
10 GHz with a
power of P 5 mW. The sample was centered in a cylindric
microwave cavity operated in the TE
011
mode and a quasi-
static external magnetic field was swept up to
0
H
ext
=1.8 T. For this setup, the magnetic part of the microwave
coupled into the cavity is maximum in the center of the
cavity and aligned parallel to the axis of rotational symmetry
of the cylindric cavity which is perpendicular to the external
quasistatic magnetic field. The electric field component of
the microwave vanishes in the center of the cavity. However,
a sample with finite dimensions may short the electric field
lines off-center. In order to minimize these effects, the
sample was cut into small pieces, about 2 2mm
2
. For this
size, also inhomogeneities of the magnetic field component
are negligible. In general, microwave absorption of the
sample can be detected if the precession frequency of mag-
netization equals the frequency of the irradiated microwave.
In the ground state of the system, all spins of a ferromagnet
are aligned parallel due to the exchange interaction while
precessing around the effective magnetic field H
eff
consisting
of the external magnetic field, anisotropy fields, exchange
field, and the magnetic component of the microwave. This is
the so-called uniform mode of precession.
Spin waves magnons may be excited by the microwave.
A schematic example of a spin wave is shown in Fig. 1.In
this case, the effective magnetic field is parallel to the z
direction and the spin wave propagates along the y direction.
All magnetic moments precess around the field direction in-
cluding the same angle
but with a constant angular differ-
ence
between neighboring moments. Additional surface or
interface pinning of the spins may lead to the occurrence of
standing spin waves. In the case of a magnetic field pointing
PHYSICAL REVIEW B 82, 064403 2010
1098-0121/2010/826/0644036 ©2010 The American Physical Society064403-1
along the sample normal, their possible wave vectors are
given by the condition k
n
=n
/ t, where t denotes the sample
thickness. For small
and small
, the frequency of the
precession around the exchange field can be written as
13
n
=
Dk
n
2
=
D
2
t
2
n
2
, 1
where
=g
B
/ is the magnetogyric ratio depending on the
spectroscopic splitting factor g and D is the spin-wave stiff-
ness related to the exchange stiffness via A =
0
M
s
D/ 2. In a
FMR experiment, standing spin waves yield additional reso-
nances H
n
shifted relatively to the one of the uniform pre-
cession H
uni
,
H
n
= H
uni
2
D
t
2
n
2
. 2
In this work, only spin waves with n =1 could be observed.
For this case, the exchange stiffness can be determined from
the experimental data using the following equation:
A =
1
2
0
M
s
H
uni
H
1
t
2
2
. 3
The magnetocrystalline anisotropy as well as the effective
magnetization were determined by polar and azimuth
angular-dependent measurements at room temperature. Since
the anisotropy may strongly depend on the temperature,
1418
FMR spectra were taken also at 20 K for the sample with the
lowest Curie temperature,
19,20
i.e., Fe
0.26
Pt
0.74
. No shift in the
resonance field compared to room temperature measure-
ments was obtained within experimental errors. Therefore,
FMR measurements at room temperature seemed to be suf-
ficient for all samples investigated in this work.
III. SPR-KKR CALCULATIONS
Band-structure calculations for chemically disordered
Fe
x
Pt
1−x
alloys were performed by means of the fully rela-
tivistic spin-polarized version of the KKR band-structure
method SPR-KKR within the framework of spin density-
functional theory.
12
As structural input for the SPR-KKR cal-
culations, lattice constants of the single-crystalline Fe
x
Pt
1−x
films experimentally investigated in this work were used.
The values obtained by x-ray diffraction can be found
elsewhere
21
and are in agreement to other values reported in
the literature for this system.
22
The SPR-KKR method rep-
resents the electronic structure in terms of the Green’s func-
tion evaluated by means of multiple-scattering theory. This
feature allows to deal with the chemical disorder by using
the coherent potential approximation alloy theory as done in
this work for the chemically disordered Fe
x
Pt
1−x
alloys. Spin
and angular momentum resolved density of states at the Fe
and Pt sites as well as element-specific magnetic moments
have been published elsewhere.
21
In the scalar-relativistic mode, ab initio Heisenberg pair
exchange parameters were calculated using the formulation
of Liechtenstein et al.
23
The exchange constant was calcu-
lated for all Fe-Fe, Fe-Pt, and Pt-Pt pairs as a function of
distance. In the case of dominating exchange coupling be-
tween nearest-neighbor atoms, the exchange stiffness can be
written in general for a single-element system as
24
A =
JS
2
a
J
ag
2
s
2
B
2
, 4
where a denotes the lattice constant, J the exchange coupling
constant, and S and
S
the spin moment and the spin mag-
netic moment, respectively.
25
To achieve higher accuracy, in
this work not only nearest-neighbor atoms but contributions
from all atoms within a cluster of radius R =3a were in-
cluded. The values of J for all considered Fe-Fe, Fe-Pt, and
Pt-Pt pairs were weighted by their probability and summed
up assuming complete chemical disorder. For instance, the
probability to find an Fe-Fe pair in an Fe
x
Pt
1−x
alloy is
P
FeFe
=x
2
, an Fe-Pt pair P
FePt
=P
PtFe
=x1−x and a Pt-Pt pair
P
PtPt
=1−x
2
. Thus J can be written for all nearest-neighbor
contributions as J=x
2
J
FeFe
+2x1−xJ
FePt
+1−x
2
J
PtPt
. Since
there is a significant difference in the calculated and experi-
mentally determined values of the Fe spin magnetic moment
for the Fe-rich alloys, experimental values
21
were taken to
determine the value of the exchange stiffness.
IV. RESULTS AND DISCUSSION
A. Spin waves and exchange stiffness
As an example, experimental FMR data for Fe
0.46
Pt
0.54
are
presented in Fig. 2a for two different polar angles
be-
tween the external magnetic field and the sample normal, i.e.,
=0° and
=90°. In this graph, the first derivative of the
absorption signal is shown as a function of the external mag-
netic field. Note that the sharp resonance lines around
0
H
ext
=0.33 T are caused by paramagnetic impurities in the
MgO substrate. The strong shift in the resonance field that
can be assigned to the resonant microwave absorption of the
FePt film is mainly due to the shape anisotropy that favors a
magnetization direction in the sample plane
=90°. For
=0° a second resonance line is visible at
0
H
ext
1.12 T
with a lower intensity compared to the resonance of the uni-
form mode at
0
H
ext
1.28 T. The full angular dependence
is shown in Fig. 2b as contour plot of the first derivative of
the absorption signal as a function of external field value and
polar angle. The absolute values of the gray scale intensities
describe the amplitude of the first derivative of absorbed mi-
crowave power according to the gray scale shown in Fig.
2a. From this plot it can be seen that the spin-wave reso-
nance line is clearly detectable for −10°
10°. From the
resonance position at
=0° the exchange stiffness was cal-
culated according to Eq. 3 for all Fe
x
Pt
1−x
films with their
different compositions.
FIG. 1. Example of a spin wave propagating along the y direc-
tion while the effective field is parallel to the z direction.
ANTONIAK et al. PHYSICAL REVIEW B 82, 064403 2010
064403-2
For comparison the exchange stiffness was also deter-
mined by means of the SPR-KKR method. For this purpose,
the exchange constant of the coupling for Fe-Fe, Fe-Pt, and
Pt-Pt pairs was calculated as a function of distance. This is
shown in Fig. 3 for one example, i.e., Fe
0.46
Pt
0.54
. It is clearly
visible that the exchange is dominated by the coupling be-
tween two nearest-neighbor Fe atoms. The coupling constant
is about 14 meV yielding a ferromagnetic coupling. This
value exhibits only a weak dependence on the composition in
the range investigated in this work not shown here.Inthe
case of two neighboring Pt atoms or an Fe-Pt pair the ex-
change coupling is about one order of magnitude smaller.
For next-nearest-neighbor Fe atoms the coupling prefers an
antiferromagnetic spin arrangement, for third-nearest neigh-
bors the coupling is ferromagnetic again. At distances above
twice the lattice constant, the coupling constant almost van-
ishes. For the case of bcc Fe as a reference, an exchange
stiffness of 24 pJ/m was calculated which is in good agree-
ment to the experimentally obtained values of 21 and 25
pJ/m reported in the literature.
26,27
The values for the
Fe
x
Pt
1−x
system are summarized in Table I. Since there are
various definitions of the exchange stiffness, for a better
comparison the sum A
=
j
J
0j
r
0j
2
in millielectron volt per
angstrom is given in addition which is also sometimes called
exchange stiffness in the literature. Again, the values of A
for all considered Fe-Fe, Fe-Pt, and Pt-Pt pairs were
weighted by their probability and summed up. Its value is
related to the exchange stiffness A as defined in this work by
the inverse volume of the unit cell. Both experimentally and
theoretically obtained values of the exchange stiffness are
shown in Fig. 4 as a function of Fe content. In the experi-
mental data, there is an increase in the exchange stiffness
with increasing Fe content from 6 4pJ/ m for x =0.27 to
15 4pJ/ m for x=0.67. The results from SPR-KKR calcu-
lations are in good agreement to these values. The trend of
increasing exchange coupling with increasing Fe content can
be qualitatively understood in terms of both structural and
compositional changes: the higher Fe content leads to a
smaller lattice constant and therefore the exchange stiffness
increases as can be seen from Eq. 4. However, this is only
true for moderate changes in the lattice constants since large
changes may change the value of the exchange coupling con-
stant J significantly and may even yield an antiferromagnetic
coupling. With respect to the compositional changes, by
summing over all contributions of nearest-neighbor Fe and
Pt atoms, the fraction of Fe-Fe contributions increases with
increasing Fe content. Since these contributions are the ones
with the highest exchange coupling, the exchange stiffness
increases according to Eq. 4. For all compositions, the ex-
change stiffness is smaller than in bcc-Fe bulk material.
Comparison with the value for FePt in the chemically or-
dered fct state reported in the literature, i.e., 10 pJ/m,
28
sug-
gests that there is no measurable influence on the exchange
TABLE I. Calculated and experimentally obtained values of the
exchange stiffness. Note that the Fe contents of the measured
samples slightly differ from the nominal values cf. Fig. 4.
Fe content
A
meV/Å
A
pJ/m
A
exp
pJ/m
0.32 170 4.5 6.2 4.0
0.40 320 8.7 11.4 4.0
0.48 370 10.2 11.9 4.0
0.60 400 11.5 10.3 4.0
0.68 430 13.0 15.0 4.0
0.72 470 13.9
FIG. 2. a FMR spectra of epitaxial Fe
0.46
Pt
0.54
at room temperature and
rf
10 GHz for two different angles between the external
magnetic field and the sample normal. The first derivative of absorbed microwave power is plotted against the external magnetic field. b
Contour plot of the first derivative of absorbed microwave power as a function of external magnetic field value and polar angle.
FIG. 3. Exchange coupling for Fe-Fe, Fe-Pt, and Pt-Pt pairs as a
function of radial distance r in units of the lattice constant a.
COMPOSITION DEPENDENCE OF EXCHANGE STIFFNESS PHYSICAL REVIEW B 82, 064403 2010
064403-3
stiffness of the crystal symmetry in this case.
B. Magnetic anisotropies and exchange lengths
In order to calculate the exchange length, i.e., the width of
a 180° domain wall, the magnetocrystalline anisotropy con-
stant has to be known since the anisotropy energy and ex-
change coupling are competing values in this case according
to the following equation for the exchange length assuming a
Bloch-type domain wall:
xc
=
A/K
4
, 5
where K
4
is the cubic fourth-order term of the magnetocrys-
talline anisotropy density sometimes denoted as K
1
in the
literature. In the case of our Fe
x
Pt
1−x
films, the anisotropy
constant was extracted from angular-dependent FMR mea-
surements. Both polar and azimuthal angles were varied. In
Fig. 5 the experimental FMR spectra are shown depending
on the external magnetic field and azimuth angle as contour
plot with the gray scale relating to the amplitude of the first
derivative of absorbed microwave power similar to Fig. 2b.
The Fe content of the samples is increasing from the left to
the right 27 at. %, 46 at. %, 58 at. %, and 67 at. % Fe.
The decrease in the mean resonance field with increasing Fe
content indicates the increase in the effective magnetization.
In addition, the linewidth becomes smaller for higher Fe con-
tents that may indicate an increase in relaxation times. How-
ever, a discussion of relaxation in FMR is beyond the scope
of the paper. The magnetic anisotropy has been analyzed by
the angular dependence of the resonance field which is plot-
ted in Fig. 5 lower panel. It is clearly indicating the four-
fold anisotropy. Additionally, a twofold anisotropy contribu-
tion is visible. The easy direction of magnetization changes
between x =0.46 and x =0.58 from the 111 directions to the
100 directions as it is known, e.g., for the composition-
dependent magnetocrystalline anisotropy of Fe
x
Ni
1−x
alloys.
Also in the case of Fe
x
Pt
1−x
alloys, changes in the easy di-
rection of magnetization as a function of composition
20
and
temperature
29
are reported.
In our case, the transition can be seen in Fig. 5 since for
a and b maximum resonance fields are obtained for
=0°, 90°, 180°, and 270° whereas in c and d minimum
resonance fields are obtained at these angles. Note that the
twofold anisotropy contribution does not follow this trend: in
all cases it is along a direction including an angle of 5° with
the 100 direction of the substrate leading to a slight asym-
metry in the angular-dependent resonance fields. This indi-
cates an anisotropy due to steps of the substrate or may be
growth induced. The latter seems to be a more likely expla-
nation since the films are quite thick and therefore, substrate-
FIG. 4. Exchange stiffness in fcc-Fe
x
Pt
1−x
films as a function of
Fe content obtained by KKR calculations open symbols and FMR
experiments at room temperature filled symbols. The solid line is
a guide to the eye. Experimental value for bcc Fe is taken from Ref.
26.
FIG. 5. Upper graphics: contour plot of the first derivative of absorbed microwave power as a function of external magnetic field value
and azimuth angle of a Fe
0.27
Pt
0.73
, b Fe
0.46
Pt
0.54
, c Fe
0.58
Pt
0.42
, and d Fe
0.67
Pt
0.33
at room temperature and
rf
10 GHz. Lower
graphics: extracted azimuthal dependence of the FMR resonance field. Symbols refer to experimental data and lines refer to simulations.
ANTONIAK et al. PHYSICAL REVIEW B 82, 064403 2010
064403-4
induced anisotropies at the interface should not be measur-
able. However, its origin is not clear up to now but is of less
importance since we will only roughly estimate the values of
the exchange length.
The magnetocrystalline anisotropies were quantified by
simulation of the azimuth and polar angle dependence of the
resonance field using a program developed by Anisimov
based on the Landau-Lifshitz-Gilbert formalism.
30
In this
software, the resonance field is described in terms of mini-
mization of the free-energy density including second- and
fourth-order anisotropy contributions and the Zeeman
energy.
31
The resonance field is calculated for any chosen
pairs of polar and azimuthal angle,
and
, respectively,
according to Ref. 32,
2
=
1
M
2
F
␪␪
F
␾␾
sin
2
+
cos
sin
F
1
M
2
F
␪␾
sin
cos
sin
F
sin
2
, 6
where F
x
F
xy
denotes the first second derivative of the
free-energy density to the angle xxy. Both experimental
polar and azimuthal angular dependence of the resonance
field were fitted using the same set of fitting parameters, i.e.,
an effective magnetization, the spectroscopic splitting factor
g, K
4
and in addition, a uniaxial anisotropy in the sample
plane as discussed before. The dependence on the polar
angle is not shown here. We obtained values of K
4
ranging
between 2.81.0 and 7.1 0.5 kJ/ m
3
for all compositions
except Fe
0.58
Pt
0.42
. For the latter case, a smaller value of
1.6 0.5 kJ/ m
3
was found by simulation of the experimen-
tal data. This may be related to the transition of the easy
direction of magnetization near that composition as men-
tioned above. All these values are rather small compared,
e.g., to bulk Fe in the bcc state but of the same order of
magnitude as in the case of pure Fe in the fcc state.
33
Using the values of K
4
and the corresponding exchange
stiffnesses, the exchange length is found to range between 40
and 50 nm for all compositions investigated in this work.
This value is about twice the value of bulk bcc Fe
xc
=23.3 nm Ref. 27兲兴.
V. CONCLUSION
By analyses of angular-dependent FMR and spin-wave
resonance, the composition dependence of exchange stiff-
ness, magnetocrystalline anisotropy, and exchange length in
Fe
x
Pt
1−x
films with compositions 0.27x 0.67 were deter-
mined. As the main result, the exchange stiffness constant
was found to increase with increasing Fe content from 64
to 15 4pJ/ m. These values are in good agreement to the
SPR-KKR results presented here. In addition, we found a
clear indication of a transition of the in-plane easy direction
of magnetization from 111 directions for Fe contents below
the equiatomic composition to 100 for Fe-rich composi-
tions. The exchange length calculated from exchange stiff-
ness and magnetocrystalline anisotropy was about 40–50 nm
and does not show any composition dependence within ex-
perimental errors.
Concerning the question raised in the introduction one
may conclude that spin canting effects in chemically disor-
dered Fe
x
Pt
1−x
nanoparticles with diameters around 5 nm and
below are unlikely since this diameter is only about a tenth
of the bulk exchange length. In order to induce spin canting
effects, the magnetic anisotropy of the nanoparticles would
have to be 100 times larger than in the corresponding bulk
material which was never observed.
ACKNOWLEDGMENTS
We thank M. Acet and H. C. Herper U. Duisburg-Essen
for helpful discussions. This work was financially supported
by the DFG within the framework of SFB 445.
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25
Note that in the SPR-KKR package the definition of the ex-
change constant is different. It is based on the Heisenberg
Hamiltonian written as H
xc
=−
i j
J
ij
e
ˆ
i
e
ˆ
j
, where e
ˆ
i
and e
ˆ
j
are
unit vectors pointing into the direction of the local magnetic
moments. Thus, the absolute values of the moments in units of
B
are already included in J
ij
.
26
P. Vavassori, D. Bisero, F. Carace, A. di Bona, G. C. Gazzadi, M.
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29
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A. Anisimov, simulation package Cubic films.
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ANTONIAK et al. PHYSICAL REVIEW B 82, 064403 2010
064403-6
... At 22°C, the model phenomenological exchange constant within the Fe 55 Pt 45 layer, as 10.2 and 11.9 ± 4 × 10 −9 erg/cm, respectively. The model optimized value of A for Fe 55 Pt 45 is lower than that observed in Ref. [31], but this can be explained by the different thickness and deposition parameters of our films compared to [31]. To evaluate a model value for A for Fe 49 Rh 51 at room temperature is more complex because the FM moment of Fe 49 Rh 51 is minimal at 22°C. ...
... At 22°C, the model phenomenological exchange constant within the Fe 55 Pt 45 layer, as 10.2 and 11.9 ± 4 × 10 −9 erg/cm, respectively. The model optimized value of A for Fe 55 Pt 45 is lower than that observed in Ref. [31], but this can be explained by the different thickness and deposition parameters of our films compared to [31]. To evaluate a model value for A for Fe 49 Rh 51 at room temperature is more complex because the FM moment of Fe 49 Rh 51 is minimal at 22°C. ...
Article
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Equiatomic Fe50Rh50, with its highly unusual antiferromagnetic to ferromagnetic phase transition at approximately 370 K, provides the ability to create artificial multifunctional materials when combined with high-anisotropy magnetic thin films in an exchange-mediated structure. We investigate the temperature dependence of switching in L10Fe55Pt45/Fe49Rh51 bilayer thin films, where the Fe49Rh51 assists the switching of the Fe55Pt45 at modestly increased temperatures. A simple layered macrospin model is able to capture the switching characteristics of these films and shows good agreement with experimental results. Patterned L10Fe55Pt45/Fe49Rh51structures, measured using the anomalous Hall effect, show a similar temperature-dependent switching behavior, paving the way for reduced switching fields in future applications including heat-assisted bit-patterned-media recording and spintronic devices.
... A is the exchange stiffness of the FeCr NPs, and K the anisotropy constant. The used value of 2.28E-11 Jm -1 for A was estimated as the 95% of the reported exchange stiffness for pure Fe [33], as it has been stated that Cr addition of up to 30% to Fe 1-x Cr x bulk alloys decrease the Fe exchange stiffness by only 5 % [34]. K was estimated by using the equation 3 for which the anisotropy field (H k ) was determined from the magnetisation hysteresis loops at 700 K, by taking a straight line through the data around the origin and determining the field at the point where the line significantly diverge from the hysteresis loop. ...
Article
We have studied the effect of phase separation on the magnetic and magneto-caloric properties of the CoFeNi0.5Cr0.5-Alx (x= 0.0, 1.0 and, 1.5) system. Results show that a collaborative behaviour amongst FeCr-rich segregated nanoparticles (NPs) increases the saturation magnetisation (Ms) whilst the Curie temperature (Tc) is controlled by the amount of added Al. With a strong ferromagnetic coupling between segregated FeCr-NPs, the CoFeNi0.5Cr0.5-Al1.0 sample shows the highest Ms (100 Am²kg⁻¹) with an increase of 61% over the Al-free CoFeNi0.5Cr0.5 sample. It is argued that as the ferromagnetic interaction increases in a degenerated super-spin-glass like state of the NPs the field induced phase transition is broadened whilst the magnetic entropy decreases. In turn, the CoFeNi0.5Cr0.5-Al1.0 sample shows the highest refrigerant capacity (17.1 Jkg⁻¹ at μ0ΔH = 1.0 T), and the smallest measured magnetic entropy change (ΔSmpeak = 0.22 Jkg⁻¹K⁻¹). We found that the enhanced magnetic and refrigerant capacity by mean of phase separation and NPs clustering are amongst the highest reported for the multi-component alloys being investigated for energy applications in the high temperature range.
... If the square root of 15 nm 2 is regarded as the experimental error, this suggests that the anomalous anisotropy field originates within a region smaller than 4 nm. However, the estimated value of A = 35 ± 7 pJ/m in HPT-Fe is significantly greater than that of 21-25 pJ/m in normal Fe [44,45]. This contrasts with previous reports on nanocrystalline Ni and Co, where the values of A were consistent with normal Ni and Co, respectively [34][35][36]. ...
Article
Full-text available
The formation of nanosized spin misalignment can be observed in pure Fe processed via high-pressure torsion (HPT) straining. The magnetic field dependence of the small-angle neutron-scattering profiles indicates that spin misalignment is conserved in magnetic fields up to 10 T. This result demonstrates that HPT straining provides anomalous magnetic anisotropy in pure Fe due to the high densities of the grain boundaries and lattice defects.
... However, while the acoustic branches of the ES and GSE/LLG models do not match at relatively high energy, they show a rather similar exchange stiffness, D, at low k. It is 24 , all three models are within the error range Interestingly, the exchange stiffness for the ESM is slightly lower than that of the LLG value, despite its Curie temperature being slightly higher. Such small anomaly is then explained with the contribution of the high-k spin-wave excitations to the T C . ...
Preprint
L$1_0$ FePt is a technologically important material for a range of novel data storage applications. In the ordered FePt structure the normally non-magnetic Pt ion acquires a magnetic moment, which depends on the local field originating from the neighboring Fe atoms. In this work a model of FePt is constructed, where the induced Pt moment is simulated by using combined longitudinal and rotational spin dynamics. The model is parameterized to include a linear variation of the moment with the exchange field, so that at the Pt site the magnetic moment depends on the Fe ordering. The Curie temperature of FePt is calculated and agrees well with similar models that incorporate the Pt dynamics through an effective Fe-only Hamiltonian. By computing the dynamic correlation function the anisotropy field and the Gilbert damping are extracted over a range of temperatures. The anisotropy exhibits a power-law dependence with temperature with exponent $n\approx2.1$. This agrees well with what observed experimentally and it is obtained without including a two-ion anisotropy term as in other approaches. Our work shows that incorporating longitudinal fluctuations into spin dynamics calculations is crucial for understanding the properties of materials with induced moments.
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FeCoB films with different B doping contents and different thicknesses were deposited by composition gradient sputtering. The results show that in-plane anisotropy fields and exchange constants change with the increasing B contents and increasing thickness, respectively. Both results of the composition-gradient films and the thickness-dependent films and the micromagnetic simulation indicate that multiple order spin-wave resonances are easy to obtain in the films with the large in-plane anisotropy field. We observed four resonance peaks including three perpendicular standing spin waves. The hysteresis loop and magnetic domain results indicate that such films also have good magnetic softness and an in-plane homogeneous domain structure.
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Possible engineering of spin polarization through a multistranded magnetic quantum network in the presence of light irradiation is reported. Each site of the network is associated with a net magnetic moment which provides a spin-dependent scattering via spin-spin exchange interaction, yielding a finite spin polarization across the network. The quantum system is described within a tight-binding framework where the irradiation effect is incorporated through Floquet-Bloch prescription. The spin-polarization coefficient, measured by determining spin-dependent transmission probabilities following the Green's function formalism, shows several atypical features with irradiation parameters. Apart from getting a high degree of spin polarization, a complete phase reversal can be achieved. These two issues are extremely important in designing efficient spin-based electronic devices. A detailed mathematical description is given to decouple the Hamiltonian of a generalized multistranded magnetic ladder into distinct one-dimensional lattices in separate spin subspaces for any arbitrary orientation of local spin, which clearly illustrates the allowed energy spin subbands. Effects of system size and uncorrelated disorder on spin polarization are critically examined. Finally, we discuss the possible experimental realization of our magnetic quantum systemto regulate the degree and phase of spin polarization by irradiating a magnetic sample, and thus we believe that the present analysis may provide a route of engineering spin-dependent electron transfer through a spin-polarized device.
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L10 FePt is a technologically important material for a range of novel data storage applications. In the ordered FePt structure the normally nonmagnetic Pt ion acquires a magnetic moment, which depends on the local field originating from the neighboring Fe atoms. In this work a model of FePt is constructed in which the induced Pt moment is simulated by using combined longitudinal and rotational spin dynamics. The model is parameterized to include a linear variation of the moment with the exchange field, so that at the Pt site the magnetic moment depends on the Fe ordering. The Curie temperature of FePt is calculated and agrees well with similar models that incorporate the Pt dynamics through an effective Fe-only Hamiltonian. By computing the dynamic correlation function the anisotropy field and the Gilbert damping are extracted over a range of temperatures. The anisotropy exhibits a power-law dependence on the magnetization with exponent n≈2.1. This agrees well with what was observed experimentally, and it is obtained without including a two-ion anisotropy term as in other approaches. Our work shows that incorporating longitudinal fluctuations into spin dynamics calculations is crucial for understanding the properties of materials with induced moments.
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Single-layer Fex Ni1 - x thin magnetic films have been investigated by the spin-wave resonance technique in the entire concentration range. The surface anisotropy and exchange stiffness constants for the films with a Ni content from 30 to 80 at % have been measured from the experimental standing spin wave spectra. The surface exchange spin wave penetration depth δC = 20–30 nm has been determined from the dependences of the surface anisotropy and exchange coupling constants on the Fe20Ni80 film thickness in the range of 250–400 nm.
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We have systematically investigated the Gilbert damping constant α for L10-FePd films using the time-resolved magneto-optical Kerr effect (TRMOKE). The field angle dependence of TRMOKE signals was measured and analyzed. The field angle dependence of the lifetime of magnetization precession was explained by evaluating extrinsic contributions such as the anisotropy distribution and two-magnon scattering. The crystalline uniaxial perpendicular magnetic anisotropy constant Ku and α values were evaluated for FePd films for various L10 order parameters S. Ku values of approximately 15 Merg/cm3 were obtained for films with large-S values (i.e., over 0.8). In addition, α for the low-S film was found to be approximately 0.007 and decreased with increasing S. Smaller values of α (of 0.002–0.004) were obtained for films with S values of approximately 0.6–0.8. Results revealed that FePd films have both large-Ku and small-α values, which is a useful property for low-power magnetization switching while maintaining high thermal stability in spin-transfer-torque magnetoresistive random access memory applications.
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Full-text available
The effective magnetic anisotropy Keff of chemically disordered Fe70Pt30 particles with a mean diameter of 2.3 nm is shown to be temperature dependent between 50 K and 350 K. From the determination of the blocking temperatures by field-cooled and zero-field-cooled magnetisation measurements and ferromagnetic resonance experiments, that is in two different time windows, we find Keff = (8.4 ± 0.9)×105 J/m3 at 23 K. This is found to be one order of magnitude larger than the bulk material value for the disordered phase. This value is confirmed by quantitative simulations of the experimentally determined zero-field-cooled magnetisation and can be explained by the large contribution of surface anisotropy, small deviations from a spherical shape and the presence of an approximately one monolayer thick iron oxide shell.
Article
The effect of surface anisotropy on the magnetic ground state of a ferromagnetic nanoparticle is investigated using atomic Monte Carlo simulation for spheres of radius R=6a and R=15a, where a is the interatomic spacing. It is found that the competition between surface and bulk magnetocrystalline anisotropy imposes a ``throttled'' spin structure where the spins of outer shells tend to orient normal to the surface while the core spins remain parallel to each other. For large values of surface anisotropy, the spins in sufficiently small particles become radially oriented either inward or outward in a ``hedgehog'' configuration with no net magnetization. Implications for FePt nanoparticles are discussed.
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It is possible to excite exchange and magnetostatic spin waves in a ferromagnet by a uniform rf field, provided that spins on the surface of the specimen experience anisotropy interactions different from those acting on spins in the interior. Modes with an odd number of half-wavelengths should be excited in a flat plate. The definition of what is meant by a different anisotropy interaction is worked out and is a rather lenient condition. Experiments which would determine the exchange energy constant should be possible using sufficiently thin platelets of single crystals having parallel faces. It is perhaps not unlikely that the theory may account for the observation by Waring and Jarrett of a large number of resonance peaks in NiMnO3.
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