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Research Papers in Physics and Astronomy
2012
Tailoring magnetocrystalline anisotropy of FePt by external strain Tailoring magnetocrystalline anisotropy of FePt by external strain
Pavel Lukashev
University of Nebraska-Lincoln
, pavel.lukashev@uni.edu
Nathan Horrell
University of Nebraska - Lincoln
Renat F. Sabirianov
University of Nebraska - Omaha
, rsabirianov@mail.unomaha.edu
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Lukashev, Pavel; Horrell, Nathan; and Sabirianov, Renat F., "Tailoring magnetocrystalline anisotropy of FePt
by external strain" (2012).
Faculty Publications, Department of Physics and Astronomy
. 100.
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Tailoring magnetocrystalline anisotropy of FePt by external strain
Pavel V. Lukashev,
1,3,a)
Nathan Horrell,
2,3
and Renat F. Sabirianov
2,3
1
Department of Physics and Astronomy, University of Nebraska - Lincoln, Lincoln,
Nebraska 68588-0299, USA
2
Department of Physics, University of Nebraska at Omaha, Omaha, Nebraska 68182-0266, USA
3
Nebraska Center for Materials and Nanoscience, University of Nebraska - Lincoln, Lincoln, Nebraska
68588-0299, USA
(Presented 1 November 2011; received 22 September 2011; accepted 14 October 2011; published
online 16 February 2012)
We propose using strain assisted reduction in anisotropy of FePt to control magnetization reversal
in the writing on the magnetic storage devices. Our first-principles calculations show 21% decrease
of the magnetocrystalline anisotropy energy (MAE) with application of 1.5% tensile biaxial strain.
The reduction of MAE is primarily due to the change of the c/a ratio and to some extent due to the
increase in volume. We propose building bilayer (or heterostructure) of FePt and piezoelectric film.
This system is expected to allow the control of anisotropy constant by applying electric field to
the system. Finally, we discuss the possibility of forming medium using bi-layer of FePt and soft
magnetic material with the gradient of anisotropy constant.
V
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2012 American Institute of Physics.
[doi:10.1063/1.3673853]
Thin ferromagnetic films are widely utilized in modern
high density magnetic recording technology. FePt nanopar-
ticles having large magnetocrystalline anisotropy and large
magnetization can provide further increase of perpendicular
recording density. The large coercivity of these materials,
however, requires high magnetic field to “write” bit informa-
tion on them, thus significantly restricting this recording
technology in portable or ultrahigh-speed processing devi-
ces. Thermally assisted magnetization reversal,
1
and the cur-
rent induced magnetization switching
2
have been proposed
to solve this problem. Recently, the formation of exchange
coupled composites of soft and hard phases was proposed to
reduce switching field.
3,4
The switching field could be fur-
ther reduced in a graded anisotropy medium where anisot-
ropy constant varies smoothly across the bit.
5
FePt is well known hard magnetic material with tetrago-
nal ground state L1
0
structure and it preserves its bulk mag-
netic properties at nanoscale. Experimentally prepared 4 nm
FePt nanoparticles show large coercivity of 1.8 T and large
magnetization.
6
Ability to tailor coercivity and anisotropy
constant of FePt could be beneficial for various applications.
The sensiti vity of the anisotropy constant of FePt to the
modification of lattice parameters has been observed both
experimentally
7,8
and theoretically.
9
However, the detailed
analysis of magnetoelastic properties of FePt is lacking.
We show that magnetocrystalline anisotropy of FePt can
be altered significantly by a moderate applied biaxial strain.
We propose two potential implementations of this effect: (1)
forming gradient anisotropy medium, (2) electrically controlla-
ble coercivity of nanoparticle films by forming FePt/piezoelec-
tric bilayers (or heterostructures). These devices could be used
as magnetic recording medium and in sensor applications.
Figure 1 shows the schematic view of the FePt cell in
the ground state L1
0
structure. We perform first principles
calculation of MAE as function of applied biaxial strain. We
use the projector augmented wave (PAW) method,
10
imple-
mentation of PAW in VASP code
11
within a local density
approximation of the density functional theory. We use
k-point sampling of 20 20 20 with Monkhorst-Pack inte-
gration scheme.
12
We use force theorem approach, i.e., MAE is calculated
in pseudoperturbative manner as the difference between the
sums of single particle eigenvalues for the magnetization per-
pendicular (001) and parallel (100) to the easy axis. We per-
form calculations in the wide range of the strain values for
both tensile and compressive strain. Moderate biaxial strain is
usual for tetragonal lattices near interfaces with misfit in lattice
parameters. When in-plane tensile biaxial strain is applied, the
lattice parameter, a, in the plane increases, while lattice
parameter along perpendicular direction, c, decreases. The
experimental lattice parameters for FePt nanoparticles are
a ¼ 0.387 nm, c ¼ 0.373 nm (c/a ¼ 0.96) and the Poisson’s
ratio is 0.33. Because Poisson’s ratio is less than 0.5 the
FIG. 1. (Color online) Tetragonal L1
0
structure - alternating Fe and Pt
atomic planes with square lattice along (001) direction.
a)
Electronic mail: pavel.lukashev@gmail.com.
0021-8979/2012/111(7)/07A318/3/$30.00
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2012 American Institute of Physics111, 07A318-1
JOURNAL OF APPLIED PHYSICS 111, 07A318 (2012)
volume will increase with applied tensile biaxial strain. Thus,
there are two different constituents to the change in MAE: (1)
volume change, (2) change in c/a ratio.
Figure 2 shows MAE of FePt as a function of biaxial
strain. As one can see MAE decreases when tensile strain is
applied. MAE is equal to 2.98 eV/f.u. at the equilibrium lat-
tice parameter (in good agreement with previous calculation
and experimental results), but can be reduced by about 21 %
when 1.5% in-plane tensile strain is applied. Inset in Fig. 2
shows c/a and volume as functions of applied strain. There is
2% volume change and 4% change in c/a at 2% biaxial
strain, the two possi ble mechanisms of MAE variation.
In order to separate the contribution due to the volume
change we analyze MAE as a function of the cell volume at
the fixed c/a ratio. The increase in volume by 1.5% results in
reduction of MAE by about 4%. This is very small compared
with 21% MAE reduction due to 1.5% tensile strain.
Next we fix the volume at the value of unstrained cell
(see the zero point on the inset in Fig. 2) and vary the c/a ra-
tio. The change in c/a, i.e. the elongation of FePt unit cell is
expected to give considerable change to the orientation and
length of FePt bonds which results in anisotropy variation.
The distance between Fe and Pt layer changes as well. MAE
as a function of c/a ratio is shown in Fig. 3. This dependence
is nearly linear at both tensile and compressive strains. In the
considered range of c/a ratio our results are consistent with
earlier reports.
9
It is interesting to note that the effect of the
volume increase is very minor compared with the change in
c/a ratio.
To better understand the nature of the MAE change
under external stress we consider the electronic band struc-
ture of FePt. Figure 4 shows the energy band structure and
the k-point resolved contribution to MAE defined as
MAEðk resolvedÞ¼
X
N
bands
i¼1
ð001Þ
i
n
i
ð100Þ
i
n
i
(1)
along the symmetry lines for lattice constants corresponding to
the unstrained cell (a) and 2% tensile strain (b). Here
ð001Þ;ð100Þ
i
is the eigenvalue of i
th
band, while n
i
is its occupation number.
Fig. 4 shows that bands in the minority spin channel are shifted
lower relative to the Fermi level in case of the tensile strain
(due to the increased exchange splitting). As a result of this
shift two bands move below the Fermi level and reduce their
contribution to MAE.
This sensitivity of MAE to the external strain can be
used for electric control of anisotropy in hetrostructures of
two ferroic materials, i.e., FePt and a piezoelectric film. The
piezoelectric materials in these systems provide a biaxial
strain that can be modified by an applied external electric
field. This strain, transferred to FePt layer, should change
MAE of FePt layer. Observation of the coercivity change in
FIG. 2. (Color online) MAE as a function of in-plane biaxial strain. MAE
reduces with positive value of Da=a
0
(tensile strain). Inset: DV=V
0
and c/a
as a function of an in-plane biaxial strain.
FIG. 3. MAE as function of the ratio of lattice parameters c/a at fixed cell
volume corresponding to experimental data. MAE reduces by about 20% at
3% c/a reduction.
FIG. 4. (Color online) (a) Band structure of FePt for the unstrained cell
(lower panel) and corresponding contributions to MAE (top panel). (b) Band
structure of FePt under 2% tensile strain (lower panel) and corresponding
contributions to MAE (top panel).
07A318-2 Lukashev, Horrell, and Sabirianov J. Appl. Phys. 111, 07A318 (2012)
Fe films deposited on top of BaTiO
3
ferroelectric was
recently reported.
13
Traditional ferroelectrics such as BaTiO
3
or PZT can provide about 0.1% strain. The new “relaxor” fer-
roelectrics such as lead magnesium niobate compounds could
provide up to 2% strain with applied voltage, about 10 times
that in conventional ferroelectrics.
14
Recently a recording gradient medium was proposed by
Suess.
5
Strain gradient in FePt can be used to make a struc-
ture with gradual change in the local anisotropy constant.
Strain gradient can be obtained in trilayer where FePt is
sandwiched by two materials with sufficiently different lat-
tice parameters. For example, FePt can be made unstrained
(or possibly strained compressively) to keep/increase its ani-
sotropy constant at one interface while at the other interface
FePt layer would have tensile strain. One of the interfaces
can be made of the magnetically soft material to further pro-
vide a gradient of anisotropy constant. The non-uniform pro-
file of anisotropy const ant across such column should reduce
considerably the coercivity preserving the thermal stability.
In summary, we have shown that application of the 1.5%
biaxial strain reduces MAE of FePt by about 21% which is
primarily due to the reduction of the c/a ratio. The reduction
of MAE can be used in magnetization reversal in the writing
on the magnetic storage devices. The required strain can be
obtained by placing layer of FePt on piezoelectric film and by
applying electric field to the system. Another possible appli-
cation of the strain controlled MAE is the gradient medium
composed of FePt and soft magnetic material.
P.V.L. thanks Sitaram S. Jaswal for reviewing the paper
and for helpful suggestions. This work was supported by the
National Science Foundation through the Materials Research
Science and Engineering Center (NSF-DMR-0820521) at the
University of Nebraska.
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07A318-3 Lukashev, Horrell, and Sabirianov J. Appl. Phys. 111, 07A318 (2012)