Magnetic properties of Ferromagnetic Semiconductor (Ga,Mn)As M. - - PowerPoint PPT Presentation

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 1

Magnetic properties of Ferromagnetic Semiconductor (Ga,Mn)As

• M. Saw icki
• M. Saw icki

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

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) spin

including magnetism

electronics

• ptics

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 semiconductor

industry.

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 6

Towards ferromagnetic semiconductors

• magnetic semiconductors

magnetic semiconductors and insulators: short-range antiferromagnetic superexchange EuTe, ...., NiO, ... short-range ferromagnetic super- or double exchange EuS, ZnCr2Se4, La1-xSrxMnO3, ... EuS/KCl,...

• diluted magnetic semiconductors

Standard semiconductor + magnetic ion II-VI: Cd1-xMnxTe, ..., Hg1-xMnxSe, ... IV-VI: Sn1-xMnxTe, ..., Pb1-xEuxS III-V: In1-xMnxSb, ..., Ga1-xErxN IV: Ge1-xMnx, ..., Si1-xCex

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 7

History of DMS

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 8

Most of DMS: random antiferromagnet

short range antiferromagnetic superexchange

B

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 9

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.

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 10

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 …

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 11

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+

ENERGY

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 eV

large p-d hybridization and large intra-site Hubbard U => kinetic p-d exchange

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 12

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

5 10 15 1 2 3 4 5

p ≈ 5×10

18 cm

• 3

p ≈ 10

17 cm

• 3

p

x = 0.023

p -Zn1-xMnxTe χ

• 1 [ a.u. ]

Temperature [ K ]

TCW

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

χ-1 vs. T

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 13

Ferromagnetic temperature in p-(Zn,Mn)Te

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

1 10 1 10 30 30 Ferromagnetic Temp. T

F / x eff (K)

10

17

10

18

10

19

10

20

5x10

20

Hole concentration (cm

• 3)

(Zn,Mn )Te:P (Zn,Mn )Te:N

Insulating Metallic

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

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 14

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 M n Mn Mn Mn Mn world

+

Mn Mn Mn Exchange spin splitting redistributes the carriers between spin subbands thus lowering their energy

T ≤ TC

EF

k

hole world

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 15

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 Mn

TC = xeff N0 S(S+1)J2AF ρ(εF)/12kF

holes!!! = 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 eV

large p-d hybridization

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 16

Why DMS, why (Ga,Mn)As?

10 100 1000

CdTe InSb C ZnO ZnTe ZnSe InAs InP GaSb GaP GaAs GaN AlAs AlP Ge 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 M

with 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

MREM (MSpontaneous ) [ a.u. ]

Temperature [ K ]

χ

• 1

[ a.u. ]

8% (Ga,Mn)As

(Ga,Mn)As: single phase ferro-DMS

• 1

1 2 3

• 0.05

0.00 0.05 0.10

T = 175 K T = 172 K

8% (Ga,Mn)As

M[110](T) / MSat(5K) [ r.u. ]

Magnetic Field [ Oe ]

Remnant Magnetisation K-Y. Wang, et al., JAP ‘04 & ICPS’27

TC = 173 K

25 nm thick

2 4 6 8 10

100 200 300

TC ( K )

Total xMn ( % )

• T. Dietl, H. Ohno, F. Matsukura, PRB ‘01

TC ~ xp1/3

TF = 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 reversal
• M. 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 1000

CdTe InSb C ZnO ZnTe ZnSe InAs InP GaSb GaP GaAs GaN AlAs AlP Ge 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 M

with 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 2010 50 100 150 200 250 300 350

Record TC (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

3d

h

3d

Mn(...3d54s2) + GaAs =

3d4 (A0) + e+e+e v.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

Mntotal

hole + S=5/2

Mn source SUBSTRATE

• K. Yu, et al.

2 4 6 8 10 4 8 12 16

(Ga,Mn)As

p [ 10

20 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 donor Does not play ferro AF 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

Mntotal

hole + S=5/2

Mn source SUBSTRATE Mn source SUBSTRATE

MnI

2e+?

MnGa

hole + S=5/2

• K. Yu, et al.

2 4 6 8 10 4 8 12 16

(Ga,Mn)As

p [ 10

20 cm

• 3 ]

x tot [ % ]

zero compensation limit

2 4 6 8 10 4 8 12 16

(Ga,Mn)As

p [ 10

20 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

2 4 6 8 10

2 4 6 2 4 6

As-Grown µtot [ µB/Mn ] Annealed

X [ µB/Mnsub ]

xtotal [ % ]

X [ µB/Mnsub ]

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

)

Injector

Ferromagnetic polarizer

Detector

Ferromagnetic 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:

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

HA >> MS ⇒ magnetocrystalline anisotropy dominates

• ver the shape effects

H

M

MS in 5% (Ga,Mn)As ≅ 600 Oe 22000 Oe for Fe

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 29

Magnetic anisotropy in cubic materials Td symmetry of the host lattice

⇓

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

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 30

MA of p-DMS: the epitaxial origin

H

M

H

M

H

M

Tensile strain ⇓ Perpendicular Magnetic Anisotropy Compressive strain ⇓ In plane Magnetic 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

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 31

Excellent micromagnetic properties

• Large values of Ka (= MSHa / 2) and A

hinder domain formation

• Dilute systems: low MS

1 mm

Welp et al., PRL’03

Domain wall energy E = (Ka A)1/2 (Ga,Mn)As

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 32

Magnetic anisotropy – the origin

It is the anisotropy of the carrier-mediated exchange 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 )

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 33

Valence band structure (Zinc-blende Γ7 and Γ8)

Schrödinger equation: (

)

Ψ = Ψ + + E H H Hkp

bs pd

basis function:

↑ + = ) ( 2 1

1

iY X u

[ ]

↑ − ↓ + = Z iY X i u 2 ) ( 6 1

2

[ ]

↓ + ↑ − = Z iY X u 2 ) ( 6 1

3

, , ↓ − = ) ( 2 1

4

iY X i u

[ ]

↑ + ↓ + = Z iY X u ) ( 3 1

5

[ ]

↓ + ↑ − − = Z iY X i u ) ( 3 1

6

, , , .

• 2

2

• 0,4
• 0,3
• 0,2
• 0,1

0,0 0,1

(x10

7)

[111] L X

E (eV) k (cm

• 1)

GaAs

Γ

[100]

1 1 2 (x10

7)

(x10

7)

kz (cm

• 1)

ky (cm

• 1)

kx (cm

• 1)

(x10

7)

Fermi Surface at EF = 100 meV

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 34

Dispersion of strained (Ga,Mn)As

• 2

2

• 0.4
• 0.3
• 0.2
• 0.1

0.0 0.1

(x10

7)

[111] L X

E (eV) k (cm

• 1)

GaAs

Γ

[100]

• 2

2

• 0.4
• 0.3
• 0.2
• 0.1

0.0 0.1

(x10

7)

[111] L X

E (eV) k (cm

• 1)

GaAs

εxx = -0.01

Γ

[100]

Fermi Surface at EF = 100 meV

1 1 2 1 2 (x10

7)

(x10

7)

kz (cm

• 1)

ky (cm

• 1)

kx (cm

• 1)

(x10

7)

1 1 2 (x10

7)

(x10

7)

kz (cm

• 1)

ky (cm

• 1)

kx (cm

• 1)

(x10

7)

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 35

Uniaxial MA – epitaxial origin

GaAs GaAs

(GaMn)As

growth axis (001)

Compressive Biaxial strain

(GaMn)As

Td Td Td D2d

Pseudomorphic low temperature MBE growth:

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 36

Uniaxial MA – epitaxial origin

hh, lh Energy hh lh

Compressive

jz = ± 3/2 jz = ± 1/2

strain hh lh

Tensile

confinement

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

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 37

Ferromagnetism in DMS – the origin

Mn Mn Mn Mn

T ≤ TC

k

EF

Uniaxial MA – epitaxial origin

hh Energy hh Energy

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 lh
• 2. if M ≠ 0 the lower energy state: • for hh (l=±1) when k ⊥ M

jz = ± 3/2 jz = ± 1/2

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 38

Ferromagnetism in DMS – the origin

Mn Mn Mn Mn

T ≤ TC

k

EF

Uniaxial MA – epitaxial origin

hh lh Energy

M || z

hh lh Energy

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 lh
• 2. if M ≠ 0 the lower energy state:
• for lh (l=0) when k || M

jz = ± 3/2 jz = ± 1/2

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 39

Ferromagnetism in DMS – the origin

Mn 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 lh Energy

M || z

hh lh Energy

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

CdTe CdTe

QW 10 nm

x = 5.3%

QW 10nm

x = 4.9%

QW 15nm

x = 5.6%

Cd1-zZnzTe

compressive εxx= - 0.12% tensile εxx= 0.13% tensile εxx= 0.11%

• S. Tatarenko
• J. Cibert

(Grenoble)

e hh lh hh lh e hh lh 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+

ENERGY

∆E ~ M Faraday configuration σ – 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 QW By strain

no splitting for B⊥Z

• P. Kossacki et al.,

Physica E’04

hh lh e e hh lh

Perp. anisotropy Ising case

χ-1

In-plane like anisotropy

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 1.0 0.1 1 0.5

x = 5.3%

εxx = -0.27%

<100>

Hole density [ 10

20 cm

• 3 ]

T / TC

[001]

<110>

5

Easy plane Easy z-axis

M

H

M

H

M

H

lh hh 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 possible 2) 2nd order phase transition in-between

0.0 0.2 0.4 0.6 0.8 1.0 0.1 1 0.5

x = 5.3%

εxx = -0.27%

<100>

Hole density [ 10

20 cm

• 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 anisotropy

1) For low enough p perpendicular magnetic anisotropy in compressively strained (Ga,Mn)As/GaAs is observed (in-plane for tensile case)

• 2000
• 1000

1000 2000 3000

• 1.0
• 0.5

0.0 0.5 1.0

M / MSat(5K) [ a.u. ] Magnetic Field [ Oe ]

T = 5 K

H

M

H

M

H

M

H

M

H M H

M

H A

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 1.0 0.1 1 0.5

x = 5.3%

εxx = -0.27%

<100>

Hole density [ 10

20 cm

• 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 1,0 0,1 1

(001)

0.5

x = 5.3%

εxx = -0.27%

Hole density [ 10

20 cm

• 3 ]

T / TC

[001]

5

• 200

200

• 1,0
• 0,5

0,0 0,5 1,0

• 40

40 80

• 0,4
• 0,2

0,0 0,2 0,4

M / MSat (5K) [ rel. u. ]

5 K

Magnetic Field [ Oe ]

22 K

H

M

H

M

H

M

H

M

H

M

Perpendicular In-plane

xMn=0.053

H

M

• M. Sawicki, et al., PRB ‘04

Temperature influence on hh/lh population 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 QW By strain

no splitting for B⊥Z

• P. Kossacki et al.,

Physica E’04

Perp. anisotropy Ising case

• 2000 -1000

1000 2000 3000

T = 5 K

• 400

400 800

Magnetic Field [ Oe ]

22 K

Compressed (Ga,Mn)As By temperature

(and hole density)

χ-1

In-plane like anisotropy

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 49

lh hh e

EF

lh hh e

EF

The reorientation transition: hole density

0.0 0.2 0.4 0.6 0.8 1.0 0.1 1 0.5

x = 5.3%

εxx = -0.27%

<100>

Hole density [ 10

20 cm

• 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

• 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

ρHall(B) [Ωcm]

Magnetic Field [T]

T=10K w/ illumination w/o illumination

10 20 30 40 50 60 1 2 3 4 5 6 7 8

Magnetization (emu/cm

Temperature (K) H=10oe normal to plane

H

M

H

M

Mz=M

H

M

Mz<M

The reorientation transition: hole density

Gate Compensation

• H. Ohno et al., Nature’00

Light InMnAs

InMnAs/Ga /GaSb Sb heterojunction heterojunction

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

– Hydrogenation – LT annealing

Lemaitre et al., 27 ICPS ‘04 Brandt et al., ‘04 Thevenard, et al., ‘05 Penn State ’02, Nottingham ’03, & everywhere else

pb < pc < pd < pe

ρHall ~ M⊥

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 51

• 200

200

• 1,0
• 0,5

0,0 0,5 1,0

• 40

40 80

• 0,4
• 0,2

0,0 0,2 0,4

M / MSat (5K) [ rel. u. ]

5 K

Magnetic Field [ Oe ]

22 K

H

M

H

M

H

M

H

M

H

M

Perpendicular In-plane

xMn=0.053

H

M

Hole density change: LT annealing

Post growth LT annealing increases hole density Annealing influence on magnetic anisotropy/ REM(T) needed reorientation 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 1,0 0,1 1

0.5

x = 5.3%

εxx = -0.27%

Hole density [ 10

20 cm

• 3 ]

T / TC

5

Easy plane Easy z-axis

5 10 15 20 5 10 15 20

In-plane component

• f REM [ a.u. ]

Temperature [ K ]

5 10 15 20 5 10 15 20

As grown 28 h ann. 57 h ann.

Perpendicular component

• f REM [ a.u. ]

Temperature [ K ]

Hole density change: LT annealing

Post growth LT annealing increases hole density Annealing influence on magnetic anisotropy/ reorientation transition

• M. Sawicki, et al., PRB ‘04

a n n e a l i n g a n n e a l i n g

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 nanostructures Patterning magnetic nanostructures

Ferromagnetic 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 magnetocrystalline

anisotropy 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 1,0

0,1 1 10

<110> x = 5.3% <100>

Hole density [ 10

20 cm

• 3 ]

T / TC

[001]

<110>

Calculations: Dietl, Ohno, Matsukura, PRB 2001

Easy plane:

‘cubic’ anisotropy 4-fold symmetry

Easy z-axis

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

45 90 135 180 225 315

[100] [110] [110]

H

1 m = M /MS

1/√2 [110]

H

2KC/MS

<100>

T << TC

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

1 m = M /MS

1/√2 [110]

H

2KC/MS

<100>

45 90 135 180 225 315

[100] [110] [110]

71%

1000 2000 3000 4000 5000

10 15 20 25 30 35 40

Sample Moment [ a.u. ]

Magnetic Field [ Oe ]

[010] [-110]

H H 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

1000 2000 3000 4000 5000

10 15 20 25 30 35 40

Sample Moment [ a.u. ]

Magnetic Field [ Oe ]

Temperature dependence of in-plane magnetic anisotropy

[100]

71%

[110] [-110]

10 20 30 40 50 60

10 20 30 40 Ga1-xMnxAs x = 6.5%

A [100] B [-110] C [100] D [110]

REM Moment [ a.u. ]

Temperature [ K ]

biaxial anisotropy 4-fold symmetry winning at low T

uniaxial anisotropy 2-fold symmetry winning 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 anisotropy dominating temperature range

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 60

1000 2000 3000 4000 5000

10 15 20 25 30 35 40

Sample Moment [ a.u. ]

Magnetic Field [ Oe ]

Temperature dependence of in-plane magnetic anisotropy

[100]

71%

[110] [-110]

10 20 30 40 50 60

10 20 30 40 Ga1-xMnxAs x = 6.5%

A [100] B [-110] C [100] D [110]

REM Moment [ 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

10 20 30

• 6
• 3

3 6

_ [110] [110] Ga1-xMnxAs x = 3 % Magnetisation [ a.u. ] Magnetic Field [ Oe ]

T = 15 K

• 100
• 50

50 100 150

• 2
• 1

1 2

_ [110] [110]

(Ga,Mn)As x = 6.7 % Magnetisation [ 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 nm Not sensitive to etching

Welp et al., ‘04 Nottingham, ‘04

• 100
• 50

50 100 150

• 2
• 1

1 2

x0.81

T = 0.92 TC

6% (Ga,Mn)As 50 nm Annealed

Sample Moment [ a.u. ]

Magnetic Field [ Oe ]

x0.50

[110] [-110]

Before: 50nm

2x 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

40 80 120 160 2 4 6

MREM ( emu/cm

3 )

(Ga,Mn)As

x = 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

2 4 6 8 10 4 8 12 16

_ [110] - easy

(Ga,Mn)As

p ( 10

20 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-plane magnetic anisotropy

[100]

71%

1000 2000 3000 4000 5000

10 15 20 25 30 35 40

Sample Moment [ a.u. ] Magnetic Field [ Oe ]

[110] [-110]

T = 5 K

10 20 30 40 50 60

10 20 30 40

Ga1-xMnxAs x = 6.5%

A [100] B [-110] C [100] D [110]

REM Moment [ 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 transition when KC = KU

Em = – KC /4 sin4(2θ) + KU sin2θ – MHcos(ϕ – θ)

KC~ MS

4

KU~ MS

2

⇐ expected ⇒

School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 67

5 10 15 20 0,1 1 10

Phenomenological description of magnetic anisotropy in single domain (Ga,Mn)As

• K. Wang, et al., cond-mat ‘05

KC~ MS

4

KU~ MS

2

⇐ expected ⇒

M[-110]

2+ M[110] 2 = MS 2

• 1000

1000 2000 3000

• 20
• 10

10 20

(2KC+ 2KU) / MS (2KC- 2KU) / MS

T = 5 K

M (emu/cm

3)

H (Oe)

• 100

100 200

• 6
• 3

3 6

T = 50 K

H (Oe) M (emu/cm

3)

20 40 60 5 10 15

KU, KC (10

3erg/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

Conclusions

Magnetic anisotropy in hole-controlled ferro-DMS:

• magnetic anisotropy – effect of s-o interaction in the valence band
• z-axis (perpendicular)/in plane anisotropies controlled by

confinement and epitaxial strain

• in-plane anisotropy: competition of biaxial(cubic) and

uniaxial anisotropy – origin not yet understood

• three Spin Reorientation Transitions observed:

— perpendicular ⇔ in plane — <100> ⇔ [-110] — [-110] ⇔ [110] possibility of easier magnetisation manipulation

• phenomenological self-consistent description possible

in single domain model