School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 1 Magnetic properties of Ferromagnetic Semiconductor (Ga,Mn)As M. Sawicki Institute of Physics, Polish Academy of Sciences, Warsaw, Poland. In collaboration with: Support by: Japanese ERATO, EU FENIKS, Polish MNiI T. Dietl, et al., Warsaw B. Gallagher, et al., Nottingham L.W. Molenkamp, et al., Wuerzburg H. Ohno, et al., Sendai
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School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 1
Magnetic properties of Ferromagnetic Semiconductor
(Ga,Mn)AsM. Sawicki
Institute of Physics, Polish Academy of Sciences, Warsaw, Poland.
In collaboration with:
Support by: Japanese ERATO, EU FENIKS, Polish MNiI
T. Dietl, et al., WarsawB. Gallagher, et al., NottinghamL.W. Molenkamp, et al., WuerzburgH. Ohno, et al., Sendai
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 2
Outlook• Introduction
- motivation/history
• TC and MS
• Uniaxial magnetic anisotropy due to confinement and/or biaxial (epitaxial) strain- reorientation transition
• Biaxial (cubic, 4-fold) in-plane anisotropy
• Uniaxial in-plane anisotropy - reorientation transition- single domain behaviour
Hole driven ferro-DMS, mostly (Ga,Mn)As
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 3
Spintronics
Making spins to:• store and reveal information in a faster way• transmit information (supplementing charge and light)• process information (supplementing charge)
Substrate
Ferro
Anti Ferro Ferro
Conductor/Oxide
Spin valve (or MTJ) Main applications:• magnetic field sensors• read heads• galvanic isolators• Magnetoresistive RAMs
Why semiconductor spintronics?
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 4
Semiconductor Spin-electronics (Spintronics)
Spin-related phenomena in semiconductors →an additional degree of freedom (spin + charge → spintronics)
spinincluding
magnetism
electronics optics
spintronics
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 5
Ferromagnetic semiconductors
May offer a possibility to replace of ‘All metal’ Spin-Based Electronic Devices
• they posses both spins and mechanism that effectively couples spins with carriers.
• technological compliance with semiconductorindustry.
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 6
Towards ferromagnetic semiconductors
• magnetic semiconductorsmagnetic semiconductors and insulators: short-range antiferromagnetic superexchangeEuTe, ...., NiO, ...short-range ferromagnetic super- or double exchangeEuS, ZnCr2Se4, La1-xSrxMnO3, ...EuS/KCl,...
• diluted magnetic semiconductorsStandard semiconductor + magnetic ion
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 16
Why DMS, why (Ga,Mn)As?
10 100 1000CdTe
InSb
C
ZnO
ZnTeZnSe
InAsInP
GaSb
GaPGaAs
GaNAlAs
AlPGe
Si
Curie temperature (K)
Carrier mediated ferromagnetism in semiconductors:
x = 0.05, p = 3.5×1020 cm-3
T. Dietl, et al., Science 2000
Operational criteria:
• Scaling of TC and Mwith x and p
• Interplay between semiconducting and
ferromagnetic properties
More than 20 compounds showed ferro- coupling so far
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 17
140 150 160 170 180 190 200
M
REM
(MSp
onta
neou
s )
[ a
.u. ]
Temperature [ K ]
χ-1 [ a.u. ]
8% (Ga,Mn)As
(Ga,Mn)As: single phase ferro-DMS
-1 0 1 2 3
-0.05
0.00
0.05
0.10
T = 175 K
T = 172 K8% (Ga,Mn)As
M[1
10](T
) / M
Sat(5
K)
[ r.u
. ]
Magnetic Field [ Oe ]
Remnant Magnetisation
K-Y. Wang, et al., JAP ‘04 & ICPS’27
TC = 173 K
25 nm thick0 2 4 6 8 10
0
100
200
300
T C
( K )
Total xMn ( % )T. Dietl, H. Ohno, F. Matsukura, PRB ‘01
TC ~ xp1/3TF = xeff N0 S(S+1)J2AF ρ(εF)/12kF
TC = 173 K = -100o C
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 18
Y. Ohno et al., Nature’99
Spin-LED
H. Ohno et al., Nature’00
Ferro-FET
Operational criteria for carrier-controlled ferromagnetic semiconductors
Also:• Current induced domain wall switching JC~105 A/cm2
• Electrically assisted magnetisation reversalM. Yamanouchi, et al., Nature’04
D. Chiba, et al., Science’03
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 19
Why DMS, why (Ga,Mn)As?
10 100 1000CdTe
InSb
C
ZnO
ZnTeZnSe
InAsInP
GaSb
GaPGaAs
GaNAlAs
AlPGe
Si
Curie temperature (K)
Carrier mediated ferromagnetism in semiconductors:
x = 0.05, p = 3.5×1020 cm-3
T. Dietl, et al., Science 2000
Operational criteria:
• Scaling of TC and Mwith x and p
• Interplay between semiconducting and
ferromagnetic properties
More than 20 compounds showed ferro- coupling so far
GaAs
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 20
1990 1995 2000 2005 20100
50
100
150
200
250
300
350
Rec
ord
T C (
K)
Date
LT annealing 173 K
TC in (Ga,Mn)As: prospects
Increase Mn incorporation
High index surfaces?
300
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 21
e
e
e
e
e
3d
h
3d4+1 = „3d5” A- S = 5/2, L = 0
v.b.3d5+h = „3d4” A0 J = 1
e
e
e
e
e
3d
h
3d
Mn(...3d54s2) + GaAs = 3d4 (A0) + e+e+ev.b.
e
e
e
e
Mn = spin 5/2 + hole
Mn in GaAs
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 22
Mntotalhole + S=5/2
Mn source
SUBSTRATE
K. Yu, et al.0 2 4 6 8 10
0
4
8
12
16
(Ga,Mn)As
p [
1020
cm-3 ]
x tot [ % ]
zero compensation limit
Something went wrong!
Growth of (Ga,Mn)As
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 23
c-RBS and c-PIXE reveal: in low-temperature MBE grown ferromagnetic (Ga,Mn)As Mn atoms occupy three distinct positions in the lattice
substitutional MnGa, interstitial MnI, and random (MnAs)in proportions depending on annealing.
Mn⁻
Mn++
Ga
As
interstitial MnI:Double donorDoes not play ferroAF bonds to MnGa
Blinowski, Kacman, PRB’03
K. Yu, et al., PRB’02
Mn interstitials
Low temperature annealing!!Potashnik et al.,’02
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 24
Mntotalhole + S=5/2
Mn source
SUBSTRATE
Mn source
SUBSTRATE
MnI2e+?
MnGahole + S=5/2K. Yu, et al.
0 2 4 6 8 100
4
8
12
16
(Ga,Mn)As
p [
1020
cm-3 ]
x tot [ % ]
zero compensation limit
0 2 4 6 8 100
4
8
12
16(Ga,Mn)As
p [
1020
cm-3 ]
x tot [ % ]
zero compensation limit
Annealing
Wang, et al., 2004
Growth of (Ga,Mn)As
p = x
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 25
µtot = MS / x tot
MnI paramagnetic: xeff = xSub
MnI AF to MnGa: xeff = xSub - xI
2
4
6
0 2 4 6 8 102
4
62
4
6
As-Grown
µ tot [
µB/M
n ] Annealed
X [
µ B/M
n sub ]
xtotal [ % ]
X [
µ B/M
n sub ]
MS = N0 xeff ⋅ X + p ⋅ (-1)
(apparent) ‘Magnetisation deficit’
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 26
... summary
• (Ga,Mn)As emerges as the best understood model ferromagnet with a number of attractive functionalities
• Control of magnetism and magnetization direction is possible by external means
• Beginning of the road for high temperature ferromagnetic semiconducting system
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 27
The magnetic anisotropy
- Testing/verification for models- Device engineering
• magnetoresistive AMR ~ cos2(∠ j, M )• spin injection/detection
• utilisation of the magnetic anisotropy
)
InjectorFerromagneticpolarizer
DetectorFerromagnetic
analyser
Datta & Das (1990)
Electrical gate Electric field
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 28
Magnetocrystalline vs. shape anisotropy
Despite the expected for the layered material in-plane arrangement of M(HA = MS), relatively strong perpendicular (uniaxial) magnetic anisotropy has been observed since the very beginning of the studies:
Epitaxial (biaxial) strain ⇒ Splitting of the hole states
hh
lhEne
rgy
M || z
hh
lhEne
rgy
M in plane
Compressive case:
jz = ± 3/2
jz = ± 1/2
⇒ uniaxial anisotropy~ J s •S
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 40
Valence band engineering – (Cd,Mn)Te QW
12% Zn CdTeCdTe
QW 10 nmx = 5.3%
QW 10nmx = 4.9%
QW 15nmx = 5.6%
Cd1-zZnzTe
compressiveεxx= - 0.12%
tensileεxx= 0.13%
tensileεxx= 0.11%
S. TatarenkoJ. Cibert(Grenoble)
e
hhlh
hh lh
e
hhlh
e
Compensation of confinement induced hh/lh splitting by epitaxial tensile strain
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 41
The measurements
σ-σ-σ+
σ+
ENER
GY
∆E ~ M
Faraday configurationσ –
σ+
χ =δ(E– - E+)/δH
at H→0
(Warsaw,Grenoble)
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 42
Tailoring the magnetic anisotropy
(Cd,Mn)Te QWBy strain
no splittingfor B⊥Z
P. Kossacki et al., Physica E’04
hhlh
ee
hhlh
Perp.anisotropyIsing case
χ-1
In-plane likeanisotropy
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 43
hh/lh influence on uniaxial anisotropy
0.0 0.2 0.4 0.6 0.8 1.00.1
1
0.5
x = 5.3%εxx = -0.27%<100>
Hol
e de
nsity
[ 1
020 c
m-3 ]
T / TC
[001]
<110>
5
Easy plane
Easy z-axisM
H
M
H
M
Hlhhh
e
For biaxial compression
EF
Typically, easy axis in plane
Calculations: Dietl, Ohno, Matsukura, PRB 2001
T2d ⇒ D2d symmetry lowering, growth direction is the quantisation axis, hh/lh population plays decisive role
Ku = f ( k⋅p 6×6 H + Hp-d , HStrain )
TC=33K
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 44
hh/lh influence on anisotropy
Two important features emerge:1) Both types of anisotropy possible2) 2nd order phase transition in-between
0.0 0.2 0.4 0.6 0.8 1.00.1
1
0.5
x = 5.3%εxx = -0.27%<100>
Hol
e de
nsity
[ 1
020 c
m-3 ]
T / TC
[001]
<110>
5
M
M
Easy z-axis
Easy plane
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 45
Perpendicular magnetic anisotropy1) For low enough p perpendicular magnetic anisotropy in compressively strained (Ga,Mn)As/GaAs is observed (in-plane for tensile case)
-2000 -1000 0 1000 2000 3000
-1.0
-0.5
0.0
0.5
1.0
M /
MS
at(5
K)
[ a.u
. ]
Magnetic Field [ Oe ]
T = 5 K
H
M
H
M H
M
H
M H
M H
M
HA
xMn=0.023
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 46
0.0 0.2 0.4 0.6 0.8 1.00.1
1
0.5
x = 5.3%εxx = -0.27%<100>
Hol
e de
nsity
[ 1
020 c
m-3 ]
T / TC
[001]
<110>
5
hh/lh influence on anisotropy
2) The reorientation: easy axis ⇔ easy plane
Calculations: Dietl, Ohno, Matsukura, PRB 2001
Easy plane
Easy z-axis
H
M
H
M
H
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 47
The reorientation transition: temperature
0,0 0,2 0,4 0,6 0,8 1,00,1
1(001)
0.5
x = 5.3%εxx = -0.27%
Hol
e de
nsity
[ 1
020 c
m-3 ]
T / TC
[001]
5
-200 0 200-1,0
-0,5
0,0
0,5
1,0
-40 0 40 80-0,4
-0,2
0,0
0,2
0,4
M /
MSa
t (5K
) [
rel.
u. ]
5 K
Magnetic Field [ Oe ]
22 K
HH
M H
M
H
M
H
M
H
M
Perpendicular In-planexMn=0.053
HH
M
M. Sawicki, et al., PRB ‘04
Temperature influence on hh/lhpopulation ratio:
hωs ~ M = f(T)
Easy z-axis
Easy plane
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 48
Tailoring the magnetic anisotropy
(Cd,Mn)Te QWBy strain
no splittingfor B⊥Z
P. Kossacki et al., Physica E’04
Perp.anisotropyIsing case
-2000 -1000 0 1000 2000 3000
T = 5 K
-400 0 400 800
Magnetic Field [ Oe ]
22 K
Compressed(Ga,Mn)As
By temperature(and hole density)
χ-1
In-plane likeanisotropy
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 49
lhhh
e
EF
lhhh
e
EF
The reorientation transition: hole density
0.0 0.2 0.4 0.6 0.8 1.00.1
1
0.5
x = 5.3%εxx = -0.27%<100>
Hol
e de
nsity
[ 1
020 c
m-3 ]
T / TC
[001]
<110>
5
Calculations: Dietl, Ohno, Matsukura, PRB 2001
Easy plane
Easy z-axis M
M
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 50
M. S awicki on magnetic anisotropy - S endai 28/07/2005 26
Thevenard, et al., ‘05Penn State ’02, Nottingham ’03, & everywhere else
pb < pc < pd < pe
ρ Hal
l~ M
⊥
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 51
-200 0 200-1,0
-0,5
0,0
0,5
1,0
-40 0 40 80-0,4
-0,2
0,0
0,2
0,4
M /
MSa
t (5K
) [
rel.
u. ]
5 K
Magnetic Field [ Oe ]
22 K
HH
M H
M
H
M
H
M
H
M
Perpendicular In-planexMn=0.053
HH
M
Hole density change: LT annealingPost growth LT annealing increases hole density Annealing influence on magnetic anisotropy/ REM(T) neededreorientation transition
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 52
0,0 0,2 0,4 0,6 0,8 1,00,1
1
0.5
x = 5.3%εxx = -0.27%
Hol
e de
nsity
[ 1
020 c
m-3 ]
T / TC
5
Easy plane
Easy z-axis
5 10 15 200
5
10
15
20
In-p
lane
com
pone
nt
of R
EM
[ a.u
. ]
Temperature [ K ]
5 10 15 200
5
10
15
20
As grown28 h ann.57 h ann.
Perp
endi
cula
r com
pone
nt
of R
EM
[ a.u
. ]
Temperature [ K ]
Hole density change: LT annealingPost growth LT annealing increases hole density Annealing influence on magnetic anisotropy/reorientation transition
M. Sawicki, et al., PRB ‘04
an
ne
alin
ga
nn
ea
ling
TTr
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 53
Control of the magnetism in nano scale
Controlling quantum magnetic dots
Patterning magnetic nanostructuresPatterning magnetic nanostructuresFerromagnetic Quantum Wires Ferromagnetic Quantum Dot
Array
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 54
....summary
Confinement and Strain induced magnetocrystallineanisotropy observed.- character- magnitude- reorientation transition
consistent with p-d Zener model
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 55
The epitaxially induced D2d symmetry suggests 4-fold (biaxial) magnetic in-plane anisotropy
The in-plane magnetic anisotropy
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 56
4-fold in-plane magnetic anisotropy
0,0 0,2 0,4 0,6 0,8 1,00,1
1
10<110>
x = 5.3%
<100>
Hol
e de
nsity
[ 1
020 c
m-3 ]
T / TC
[001]
<110>
Calculations: Dietl, Ohno, Matsukura, PRB 2001
Easy plane:‘cubic’ anisotropy4-fold symmetry
Easy z-axis
0
45
90
135
180
225 315
H = 0
[110][-110]
[100]
[010]
M
Can we observe this?
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 57
Field induced coherent rotation
0
45
90
135
180
225 315
[100]
[110]
[110]H
1m = M /MS
1/√2
[110]
H
2KC/MS
<100>
T << TC
0
45
90
135
180
225 315
H[110] = 0
[110][110]
- H[110] > 0
–
-[100]
[010][010]
M M-
-
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 58
Field induced coherent rotation: low T
1m = M /MS
1/√2
[110]
H
2KC/MS
<100>
0
45
90
135
180
225 315
[100]
[110][110]
71
%
0 1000 2000 3000 4000 500010
15
20
25
30
35
40
Sam
ple
Mom
ent
[ a
.u. ]
Magnetic Field [ Oe ]
[010]
[-110]
HH
H
[010]=
T = 5 K
[100]
-
A proof of:• Formation of macroscopically
large domains• 4-fold magnetic symmetry
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 59
0 1000 2000 3000 4000 500010
15
20
25
30
35
40
Sam
ple
Mom
ent
[ a
.u. ]
Magnetic Field [ Oe ]
Temperature dependence of in-planemagnetic anisotropy
[100]
71
%
[110][-110]
0 10 20 30 40 50 600
10
20
30
40
Ga1-xMnxAs x = 6.5%
A [100] B [-110] C [100] D [110]
REM
Mom
ent
[ a.
u. ]
Temperature [ K ]
biaxial anisotropy4-fold symmetrywinning at low T
uniaxial anisotropy2-fold symmetrywinning at high T
T = 5 K
H = 0
cf. Katsumoto et al., Hrabovsky et al., Tang et al., Welp et al., Ferre et al., Liu et al.,...,& EVERYONE ELSE. The new reorientation transition when system
crosses from biaxial to uniaxial anisotropydominating temperature range
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 60
0 1000 2000 3000 4000 500010
15
20
25
30
35
40
Sam
ple
Mom
ent
[ a
.u. ]
Magnetic Field [ Oe ]
Temperature dependence of in-planemagnetic anisotropy
[100]
71
%
[110][-110]
0 10 20 30 40 50 600
10
20
30
40
Ga1-xMnxAs x = 6.5%
A [100] B [-110] C [100] D [110]
REM
Mom
ent
[ a.
u. ]
Temperature [ K ]
T = 5 K
H = 0
As grown samples: Uni_easy [-110]Cubic_easy <100> Uni_hard [110]
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 61
In-plane uniaxial magnetic anisotropy
Strong uniaxial behaviour with either [-110] or [110] the easy axis, seen on all studied samples,
usually dominating close to TC
-10 0 10 20 30-6
-3
0
3
6 _
[110]
[110]
Ga1-xMnxAs x = 3 %
Mag
netis
atio
n
[ a.u
. ]
Magnetic Field [ Oe ]
T = 15 K
-100 -50 0 50 100 150
-2
-1
0
1
2 _[110][110]
(Ga,Mn)Asx = 6.7 %
Mag
netis
atio
n
[ a.u
. ]
Magnetic Field [ Oe ]
T=135K
M. Sawicki, et al.,, PRB ‘05
T / TC = 0.65 T / TC = 0.90
(near perfect single domain behaviour!!)
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 62
Not sensitive to the state of the surface;surface/interface anisotropy not important
In-plane uniaxial magnetic anisotropy
Precluded by symmetry considerations. Not expected in D2d.Thickness independent: seen from 7 µm down to 5 nmNot sensitive to etching
Welp et al., ‘04 Nottingham, ‘04
-100 -50 0 50 100 150
-2
-1
0
1
2
x0.81
T = 0.92 TC
6% (Ga,Mn)As 50 nm Annealed Sa
mpl
e M
omen
t [
a.u
. ]
Magnetic Field [ Oe ]
x0.50
[110]
[-110]
Before: 50nm2x etch
4x etch: 25nm
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 63
In-plane uniaxial magnetic anisotropy
D2d → C2v symmetry lowering:
(In C2v [110] and [-110] are not equivalent)- Mn concentration gradient along growth axis
- preferential incorporation of Mn during
growth
Sadowski et al., 2004
Welp et al., 2004
More information required.....
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 64
In-plane uniaxial magnetic anisotropy
TR
[110] easy
[-110]easy
0 40 80 120 1600
2
4
6
MR
EM
( em
u/cm
3 ) (Ga,Mn)Asx = 8.4%Annealed
[110]
Temperature ( K )
[110]_
There are samples with the easy axis switching from [-110] to [110] on increasing T
M. Sawicki, et al., PRB’05
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 65
In-plane uniaxial magnetic anisotropy
M. Sawicki, et al., PRB’05
There are samples with the uniaxial easy axis switching from [-110] to [110] on increasing T;It switches also upon annealing if p > 6×1020 cm-3
0 2 4 6 8 100
4
8
12
16
_[110] - easy
(Ga,Mn)As
p (
1020
cm-3 )
x ( % )
[110] - easy
~
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 66
M. S awicki on magnetic anisotropy - S endai 28/07/2005 45
Temperature dependence of in-planemagnetic anisotropy
[100]
71%
0 1000 2000 3000 4000 500010
15
20
25
30
35
40
Sam
ple
Mom
ent
[ a
.u. ]
Magnetic Field [ Oe ]
[110]
[-110]
T = 5 K
0 10 20 30 40 50 600
10
20
30
40
Ga1-xMnxAs x = 6.5%
A [100] B [-110] C [100] D [110]
REM
Mom
ent
[ a.
u. ]
Temperature [ K ]
H = 0
M(T) in presence of two competing in-plane anisotropies: single domain case
K. Wang, et al., cond-mat ‘05
Two ‘competing’ terms⇓
Magnetic easy axis reorientation transitionwhen KC = KU
Em = – KC /4 sin4(2θ) + KU sin2θ – MHcos(ϕ –θ) KC~ MS
4 KU~ MS2⇐ expected ⇒
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 67
5 10 15 200,1
1
10
Phenomenological description of magnetic anisotropy in single domain (Ga,Mn)As
K. Wang, et al., cond-mat ‘05
KC~ MS4 KU~ MS
2⇐ expected ⇒ M[-110]2+ M[110]
2 = MS2
-1000 0 1000 2000 3000-20
-10
0
10
20
(2KC+ 2KU) / MS(2KC- 2KU) / MS
T = 5 K
M
(em
u/cm
3 )
H (Oe)
-100 0 100 200-6
-3
0
3
6
T = 50 K
H (Oe)
M
(em
u/cm
3 )
0 20 40 600
5
10
15
KU, K
C
(103 er
g/cm
3 )
T (K) MS ( emu/cm3 )
KU = b MS(2.1±0.1)
KC = a MS(3.8±0.2)
KC = KU
Em = – KC /4 sin4(2θ) + KU sin2θ – MHcos(ϕ –θ)
School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 68
ConclusionsMagnetic anisotropy in hole-controlled ferro-DMS:magnetic anisotropy – effect of s-o interaction in the valence bandz-axis (perpendicular)/in plane anisotropies controlled byconfinement and epitaxial strainin-plane anisotropy: competition of biaxial(cubic) anduniaxial anisotropy – origin not yet understoodthree Spin Reorientation Transitions observed:— perpendicular ⇔ in plane— <100> ⇔ [-110]— [-110] ⇔ [110]possibility of easier magnetisation manipulation
phenomenological self-consistent description possiblein single domain model