magnetic properties of ferromagnetic semiconductor...

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


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


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?


Semiconductor Spin-electronics (Spintronics)

Spin-related phenomena in semiconductors →an additional degree of freedom (spin + charge → spintronics)

spinincluding

magnetism

electronics optics

spintronics


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.


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

II-VI: Cd1-xMnxTe, ..., Hg1-xMnxSe, ...IV-VI: Sn1-xMnxTe, ..., Pb1-xEuxSIII-V: In1-xMnxSb, ..., Ga1-xErxNIV: Ge1-xMnx, ..., Si1-xCex


History of DMS


Most of DMS: random antiferromagnet

short range antiferromagneticsuperexchange

B


Evidences for antiferromagnetic interactions: magnetic susceptibility

Curie-Weiss law

χ = C/(T − Θ)

C = gµBS(S+1)xNo/3kB

Θ < 0 antiferro

A. Lewicki et al.


Magnetisation of localized spins

M(T,H) = gµBSxeffNoBS[gµBH/kB(T + TAF)]

antiferromagnetic interactions

xeff < x

TAF > 0

Modified Brillouin function

Y. Shapira et al.no spontaneous magnetisation …


Determination of sp-d exchange integrals:- giant splitting of exciton states

J. Gaj et al., R. Planel,..A. Twardowski et al.G. Bastard, …

geff > 102

σ-σ-σ+

σ+

ENER

GY

v.b.

c.b.

∆E ~ M ~ BS(H)

-- s-d: Isd ≡ αNo ≈ 0.2 eV no s-d hybridization => potential s-d exchange

-- p-d: Ipd ≡ βNo ≈ - 1.0 eVlarge p-d hybridization and large intra-site Hubbard U => kinetic p-d exchange


Effect of acceptor doping on magnetic susceptibility in Zn1-xMnxTe:P

0 5 10 15

0

1

2

3

4

5

p ≈ 5×1018 cm-3

p ≈ 1017 cm-3

px = 0.023

p -Zn

1-xMn

xTe

χ-1 [

a.u

. ]

Temperature [ K ]

TCW

Sawicki et al. (Warsaw) pss’02Kępa et al. (Warsaw, Oregon) PRL’03

χ-1 vs. T


Ferromagnetic temperature in p-(Zn,Mn)Te

Ferrand et al. (Grenoble, Warsaw) PRB’01Sawicki et al. (Warsaw) pss’02

1

10

1

10

3030Fe

rrom

agne

tic T

emp.

TF

/ xef

f(K

) 1017 1018 1019 10205x1020

Hole concentration (cm-3)

( Zn ,Mn )Te:P

( Zn ,Mn )Te:N

InsulatingMetallic

• ferromagnetism disappears in the absence of holes• ferromagnetism on both sides of metal-insulator transition


Ferromagnetism in DMS – the origin-- carriers localized by impurities (BMP): inoperative

Bhatt et al., Dugaev et al., Inoue et al., Das Sarma et al., Dagotto et al.,

...-- delocalized carriers (Zener/RKKY model)

Ryabchenko, et al., Dietl et al., MacDonald et al., Boselli et al.,Petukhov, Sham et al., …

k

EF

Mn

Mn Mn

MnMn

Mn world + Mn Mn

Mn

Exchange spin splitting redistributes the carriers between spin subbands

thus lowering their energy

T ≤ TC

EF

k

hole world


Ferromagnetism in DMS – the origin-- carriers localized by impurities (BMP): inoperative

Bhatt et al., Dugaev et al., Inoue et al., Das Sarma et al., Dagotto et al.,

...-- delocalized carriers (Zener/RKKY model)

Ryabchenko, et al., Dietl et al., MacDonald et al., Boselli et al.,Petukhov, Sham et al., …

Mn

Mn Mn

MnTC = xeff N0 S(S+1)J2AF ρ(εF)/12kFholes!!! = valence band k

EF

Exchange spin splitting redistributes the carriers between spin subbands

thus lowering their energy

T ≤ TC

-- s-d: Isd ≡ αNo ≈ 0.2 eV no s-d hybridization

-- p-d: Ipd ≡ βNo ≈ - 1.0 eVlarge p-d hybridization


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


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


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


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


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


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


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


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


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 [ % ]


0 2 4 6 8 100

4

8

12

16(Ga,Mn)As

p [

1020

cm-3 ]

x tot [ % ]


Annealing

Wang, et al., 2004

Growth of (Ga,Mn)As

p = x


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’


... 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


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


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:

(In,Mn)As/GaAs – Munekata ‘93some (Ga,Mn)As/InGaAs – Ohno, Shono ’96-’00QW (Cd,Mn)Te – Haury ‘97(Ga,Al,Mn)As/GaAs – Takamura ’02(Ga,Mn)As/GaAs – Sawicki ’02

HA >> MS ⇒ magnetocrystalline anisotropy dominates over the shape effects

H

MM

MS in 5% (Ga,Mn)As ≅ 600 Oe22000 Oe for Fe


Magnetic anisotropy in cubic materials

Td symmetry of the host lattice⇓

magnetic anisotropy is expected on<100> and <111> directions


MA of p-DMS: the epitaxial origin

H

MM

H

M

H

M

Tensile strain⇓

PerpendicularMagnetic Anisotropy

Compressive strain⇓

In planeMagnetic Anisotropy

Shen et al. 1997 (Sendai)

Marginal role of the shape anisotropy!!Ks = M 2(Da – Dc ) / 2

+ lots of confusing information? [100], [110] ?

about in plain easy axis


Excellent micromagnetic properties

• Large values of Ka (= MSHa / 2) and Ahinder domain formation

• Dilute systems: low MS

1 m

m

Welp et al., PRL’03

Domain wall energy E = (Ka A)1/2

(Ga,Mn)As


Magnetic anisotropy – the origin

It is the anisotropy of the carrier-mediatedexchange interaction stemming from

spin-orbit coupling of hole gas.

•EPR studies shows that Mn single ion anisotropy is negligible

• p-d Zener Model - Mn - Mn interaction is mediated by holes, characterised by a non-zero orbital momentum

Fedorych et al., 2002

Dietl, Ohno, Matsukura, PRB 2001(cf. Abolfath, Jungwirth, Brum, MacDonald, PRB 2001 )


Valence band structure (Zinc-blende Γ7 and Γ8)

Schrödinger equation: ( ) Ψ=Ψ++ EHHHkp bspd

basis function:

↑+= )(2

11 iYXu [ ]↑−↓+= ZiYXiu 2)(

61

2[ ]↓+↑−= ZiYXu 2)(

61

3,

,↓−= )(2

14 iYXiu [ ]↑+↓+= ZiYXu )(

31

5[ ]↓+↑−−= ZiYXiu )(

31

6,

,,

.

-2 0 2-0,4

-0,3

-0,2

-0,1

0,0

0,1

(x107)[111]L X

E (e

V)

k (cm-1)

GaAs

Γ[100]

1

0

1

2(x107)

(x107)

k z (cm

-1)

k y (c

m-1 )

kx (cm -1)

(x107)

Fermi Surface at EF = 100 meV


Dispersion of strained (Ga,Mn)As

-2 0 2-0.4

-0.3

-0.2

-0.1

0.0

0.1

(x107)[111]L X

E (e

V)

k (cm-1)

GaAs

Γ[100]

-2 0 2-0.4

-0.3

-0.2

-0.1

0.0

0.1

(x107)[111]L X

E (e

V)

k (cm-1)

GaAsεxx = -0.01

Γ[100]

Fermi Surface at EF = 100 meV

1

0

1

2

0

1

2

(x107)

(x107)

k z (c

m-1

)

k y (c

m-1 )

kx (cm -1)

(x107)1

0

1

2(x107)

(x107)

k z (cm

-1)

k y (c

m-1 )

kx (cm -1)

(x107)


Uniaxial MA – epitaxial origin

GaAsGaAs

(GaMn)As

growthaxis (001)

CompressiveBiaxial strain

(GaMn)As Td

Td Td

D2d

Pseudomorphic low temperature MBE growth:



hh, lh

Energy

hh

lh

Compressive

jz = ± 3/2

jz = ± 1/2

strain

hh

lh

0Tensile

confinement

0

1. strain, confinement or both split the hh from lh


MIS M: M. S awicki on (Ga,Mn)As - Moscow 29/06/2005 29

Ferromagnetism in DMS – the originMn

Mn Mn

Mn

T ≤ TC

k

EF


hh

Ene

rgy

hh

Ene

rgy

M || z M in plane

Compressive case, low hole density

• hh. subband occupied easy [001] (KU > 0; strong)

~ J s •S

lh lh

1. strain, confinement or both split the hh from lh2. if M ≠ 0 the lower energy state: • for hh (l=±1) when k ⊥ M

jz = ± 3/2

jz = ± 1/2




Mn Mn

Mn

T ≤ TC

k

EF


hh

lh

Ene

rgy

M || z

hh

lh

Ene

rgy

M in plane

hh

~ J s •S

• hh. subband occupied easy (001) (KU < 0; weak)

Tensile case, low hole density

1. strain, confinement or both split the hh from lh2. if M ≠ 0 the lower energy state: • for lh (l=0) when k || M

jz = ± 3/2

jz = ± 1/2




Mn Mn

Mn

T ≤ TC

k

EF

Magnetic anisotropy – epitaxial origin

• hh. subband occupied perpendicular anisotropy (strong)• lh. subband occupied in-plane anisotropy (weak)

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


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


The measurements

σ-σ-σ+

σ+

ENER

GY

∆E ~ M

Faraday configurationσ –

σ+

χ =δ(E– - E+)/δH

at H→0

(Warsaw,Grenoble)


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


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


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


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

. ]


T = 5 K

H

M

H

M H

M

H

M H

M H

M

HA

xMn=0.023


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


Easy plane

Easy z-axis

H

M

H

M

H


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


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


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


22 K

Compressed(Ga,Mn)As

By temperature(and hole density)

χ-1

In-plane likeanisotropy


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


Easy plane

Easy z-axis M

M


M. S awicki on magnetic anisotropy - S endai 28/07/2005 26

-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

ρ Hal

l(B) [

Ωcm

]

Magnetic Field [T]

T=10K

w/ illumination w/o illumination

0 10 20 30 40 50 600

1

2

3

4

5

6

7

8

Mag

netiz

atio

n (e

mu/

cm3 )

Temperature (K)

H=10oe normal to plane

H

M

H

M

Mz=M

HHM

Mz<M

The reorientation transition: hole density

Gate

Compensation

H. Ohno et al., Nature’00

Light InMnAsInMnAs/Ga/GaSbSb heterojunctionheterojunction

Koshihara et al.,’97; X. Liu et al., ‘04

– Hydrogenation

– LT annealing

Lemaitre et al., 27 ICPS ‘04Brandt et al., ‘04

Thevenard, et al., ‘05Penn State ’02, Nottingham ’03, & everywhere else

pb < pc < pd < pe

ρ Hal

l~ M

⊥


-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


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


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


Control of the magnetism in nano scale

Controlling quantum magnetic dots

Patterning magnetic nanostructuresPatterning magnetic nanostructuresFerromagnetic Quantum Wires Ferromagnetic Quantum Dot

Array


....summary

Confinement and Strain induced magnetocrystallineanisotropy observed.- character- magnitude- reorientation transition

consistent with p-d Zener model


The epitaxially induced D2d symmetry suggests 4-fold (biaxial) magnetic in-plane anisotropy

The in-plane magnetic anisotropy


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>


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?


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-

-


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. ]


[010]

[-110]

HH

H

[010]=

T = 5 K

[100]

-

A proof of:• Formation of macroscopically

large domains• 4-fold magnetic symmetry


0 1000 2000 3000 4000 500010

15

20

25

30

35

40

Sam

ple

Mom

ent

[ a

.u. ]


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


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Mom

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[ a

.u. ]



[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]


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

. ]


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

. ]


T=135K

M. Sawicki, et al.,, PRB ‘05

T / TC = 0.65 T / TC = 0.90

(near perfect single domain behaviour!!)


Not sensitive to the state of the surface;surface/interface anisotropy not important


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

. ]


x0.50

[110]

[-110]

Before: 50nm2x etch

4x etch: 25nm



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.....



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



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

~


M. S awicki on magnetic anisotropy - S endai 28/07/2005 45


[100]

71%

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ple

Mom

ent

[ a

.u. ]


[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 ⇒


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)


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

magnetic properties of ferromagnetic semiconductor...

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