8/6/2019 90-Degree Bloch Domain Wall Structure in a Cubic
Crystal With a Negative Magnetic Anisotropy
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90-DEGREE BLOCH DOMAIN WALL STRUCTURE IN A CUBIC CRYSTAL WITH
A
NEGATIVE MAGNETIC ANISOTROPY
Svitlana . Dyachenko, Bogdan . anygin, lexandr V. ychko
National Taras Shevchenko University of Kyiv, RadioPhysics
Faculty, prosp. Acad. Glushkova, 2,building 5,
[email protected]
An influence of strong sample demagnetization field on the
structure of plane 90-degree Bloch
domain walls in a cubic (001)-crystal with a negative first
constant of magnetic anisotropy is considered.
1. For some samples (thin films, magnetic particles, etc.) their
demagnetization field becomes the factor
influencing a structure of a domain wall [1]. It may be
connected with a deviation of a magnetization vector
M from medium easy magnetization axes at presence of enough
strong sample demagnetization fields. In
particular, strong demagnetization field in thin epitaxial
magnetic ferrite-garnet (001)-films results in a
reorientation of the M in domain volumes from easy magnetization
axes to the film plane [2].
At homogeneous magnetization distribution, the volume
orientation of the M in the thin plate is
determined by minimum of energy density Ae = Me + MAe , where
MAe and Me - volume energy density of the
magnetic anisotropy and demagnetization field Hd respectively
[1]: Me = (MHd)/2=23
22 M ;
MAe = ( ) ..K +++ 2
3
2
1
2
3
2
2
2
2
2
11 , where M saturation magnetization (M=M, - unit vector);
= ),,(321
;1
,2
and3
directing cosines in coordinate system Oxyz with axes along
-,
- and - direction accordingly;1
K first magnetic anisotropy constant. For (001)-plate at
p = ||/2 12 KM 50. and
1K
8/6/2019 90-Degree Bloch Domain Wall Structure in a Cubic
Crystal With a Negative Magnetic Anisotropy
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( ),e A = ++++
8}2sin2sincos4)2cos3(2cos2cos2cos)2cos1)(2cos2(cos3{ p ++++
)4cos3212cos28(4cos)2cos44cos3(2cos44cos9)2cos2cos(1297{
)4cos2cos45(4cos2cos4 +++++
512/])4cos2cos2835(4cos)4cos2cos43(7[4cos
)3coscos7(4sin4sin8)cos3(cos4sin2sin61 ++
3. Orientation dependencies of specific energy sin/ are
presentedFig.. Here is an angle between(001)- and DW planes. DW
parameters (for equilibrium orientation) dependencies on sample
demagnetization field are resulted in Fig.b.
Fig. a
0
10
30
50
20
40
60
/ sin (A| ) , a.u. 1/2
K |1
0 8040-40-80
, .deg
p=3
p=20
p=0.5
Fig. b
50
70
. / (A ) , / (A/| ) a.u
|K | K |1 1
/ (A|K |)1/ (A/ |K |)1
1
40
60
2
3
4
0 5 10 15 20p ,a.u .
, deg.
For p 0.5 possible equilibrium DW orientations are set by the
expression:
[ ++++= 12cos10cos98cos136cos394cos372cos3023p
( )( )]/11sin9sin67sin5sin243sin3sin492cos32 ++++
( )( )]} 7sin5sin23sin12sin92cos328cos6cos54cos102cos21254 ++++
.
DW have equilibrium orientations in a range00 90813 . . With p
growth the general tendency of
specific energy sin/ increase is remained for DW.
Depending on DW orientation their thickness [4] is determined by
the following expression:
( )( ++
=
4cos22cos44cos2cos2389/2cos3
2cos3
sin2arccos||/8 1 pKA
( )( ))21
6sin24sin42sin82sin4cos2cos4528cos6cos4 ++++ p
General tendency of DW thickness decrease is kept with growthp
for examined DW.
1. A. Hubert, R. Shafer Magnetic domains. The analysis of
magnetic microstructures. Berlin: Springer-
Verlag, 1998.
2. Sohatsky V., Kovalenko V. //Journal De Physique IV. Colloque
CI. Suppl. Journ. De Physique III.-1996.-
V.7,3.-P.C1-699 - C1-702.
3. O.A. Antonyuk, A.V. Tychko, V.F. Kovalenko // Alloys and
Compounds. 2004. 369. 112-116.
4. B.A. Lilley //Phill. Mag. 1950. 41. 319. 792-813.
