Diluted Magnetic Semiconductors- An Introduction -

International Conference and School on Spintronics and Quantum Information Technology (Spintech VI)

School Lecture 2 “Diluted Magnetic Semiconductors”

Matsue, Japan, August 1, 2011

Hideo Ohno1,2

1Center for Spintronics Integrated Systems, Tohoku University, Sendai, Japan

2Laboratory for Nanoelectronics and Spintronics, Research Institute of Electrical Communication, Tohoku University, Sendai, Japan

1. What you need to know about nonmagnetic semiconductors• Band structure

2. How you make a semiconductor magnetic• Doping and sp-d exchange

3. The consequences of exchange interaction• Spin-split bands and ferromagnetism

4. Making “use” of ferromagnetism in semiconductors• Electrical control of ferromagnetism• Current induced domain wall motion• Tunneling with magnetism

I am indebted to lecturers of earlier Spintechs, many collaborators, particularly Tomasz Dietl and Fumihiro Matsukura, for a number of materials used here.

1. What you need to know about nonmagnetic semiconductors

• Band structure

Electronic band structureFrom Wikipedia, the free encyclopedia

taken from Walter A. Harrison “Electronic Structure and the Properties of Solids–The Physics of Chemical Bond –, 1980

J. R. Chelikowsky and M. L. Cohen, Phys. Rev. B14, 556 (1976)

Bottom of the conduction band: Ga 4sTop of the valence band: As 4p

εs(Ga)

εs(As)

εp(As)

εp(Ga)

Density of states

up spin states down spin states

conduction band

valence band

EC

EV

2. How you make a semiconductor magnetic

• Doping and sp-d exchange

Making semiconductor magnetic

SiIII-VII-VI…

EuSCuCr2Se4…

diluted magnetic semiconductors

Magnetic ion: Mn

Hund rule: Distributing n electrons over 2(2l+1) degenerate atomic orbitals, the lowest energy state is the state that maximize the total spin angular momentum S

Mn: l=2, n=5 -> S=5/2

http://physics.nist.gov

- intra site correlation energy U = En+1 – En

for n = 5, U ≈≈≈≈ 15 eV

- intra-site exchange interaction: ferromagnetic

Hund’s rule: S the highest possiblefor n = 5, ES=3/2 −−−− ES=5/2 ≈≈≈≈ 2 eV

- transition metal atoms, 3d n4s1, e.g., Mn: ferromagnetic

ES=2 −−−− ES=3 ≈≈≈≈ 1.2 eVJs-d ≈≈≈≈ 0.4 eV

4s

3d

Magnetic ion: Mn

II-VI Diluted Magnetic Semiconducotors

+ =

Density of states with transition metal impurity

d states

majority spin states minority spin states

0

0

sdH xN

E xN

αα

= − ⋅

∆ =

s S

S

0

0

pdH xN

E xN

β

β

= − ⋅

∆ =

s S

S

s-d exchange interaction

(potential exchange)

p-d exchange interaction

(hybridization; kinetic exchange)

0

0 0

: Mn composition

: Density of cation site

, : Exchange energy

x

N

N Nα β

( ) ( ) ( ) ( )01n n n n nH x U xU xJ= − − + − − − ⋅r R r R r R s S

( )

( ) ( ) ( )

( )

0

0;

;

nn

BB

B

xxN

V

xN gg

g

µµ

µ

→

→ − = −

→ − =

∑S S r

M rM r S r

MM M r

Virtual crystal approximation

molecular-field approximation

mean-field approximation

III-V Diluted Magnetic Semiconductors

+ =

(Ga,Mn)As, (In,Mn)As, (Ga,Mn)Sb

h

h

hnot to scale

kinetic, Coulomb, central cell correction, p-d exchange interaction

Mn in GaAs

Mn on Ga site: 113 meV acceptor

• d5+hole (weak coupling) ←• d4

• d5+hole (strong coupling)

22

0 00

expe r

H T V xNr r

βε

= − − − − ⋅

s S N0β = -0.9 eV

from spectroscopy

theory: Bhattacharjee & C. Benoit a la Guillaume, Solid State Commun. 113, 17 (2000) exp: M. Linnarsson et al. Phys. Rev. B 55, 6938 (1997)

3. The consequences of exchange interaction

• Spin -split bands and ferromagnetism

Magnetization of localized spins – no holes

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

antiferromagnetic interactions

xeff < x

TAF > 0

Modified Brillouin function

Y. Shapira et al.

no spontaneous magnetization

Density of states with transition metal impurity

d states

majority spin states minority spin states

0E xN α∆ = S

0E xN β∆ = S

s-d exchange interaction

p-d exchange interaction

J. Gaj, Spintech III

-8000o

Faraday effect

xN0|α<S>|

xN0|β<S>|

xN0|β<S>|/3

Splitting of the bands

EC

EV

k

σ+σ−

+1/2

−1/2

−3/2

+3/2

E

σ−

σ+

∆E=2geffµBHS, S=1/2

•geff～400 > 0

•Follows M not H

Measurements of the band splitting

SPINTECH II Joel Cibertmagnetoreflectance: Aggarwal et al. Phys. Rev. B34, 5894 (1986)

sp-d exchange

(Cd,Mn)Te

(Cd,Mn)Se

(Cd,Mn)S

(Zn,Mn)Te

(Zn,Mn)Se

(Cd,Fe)Se

(Zn,Fe)Se

(Cd,Co)Se

material

0.22

0.26

0.22

0.19

0.26

0.25

0.22

0.28

N0α (eV)

-0.88

-1.24

-1.8

-1.09

-1.32

-1.45

-1.74

-1.87

N0β (eV)

1

2

3

4

ZnO

ZnS

ZnSeCdTe

ZnTeCdSe

CdS

0.5 0.6 0.7 0.80.40.4

|N0β|

(eV

)

a (nm)

circles: photoemissionsquares: optical spectroscopy

3. The consequences of exchange interaction

• Spin -split bands and ferromagnetism

GaAs (or InAs) + Mn

Material Science

- MBE system - 250oC

(Ga,Mn)As (1x2)

Single crystal (Ga,Mn)As

0 5 10 15 20

Inte

nsity

(ar

b. u

nit)

time (sec)

shutter opening(Ga,Mn)AsT

S = 250oC

Molecular beam epitaxy of (Ga,Mn )As

250oC Zinc-blende

HT-GaAs c(4x4)

LT-GaAs (1x1)

(Ga,Mn)As (1x2)

320oC MnAs segregation

170oC Polycrystalline

(Ga,Mn)As spotty

(Ga,Mn)As spotty A. Shen et al., J. Cryst. Growth 175/176, 1069 (1997).

[-110] azimuth

ZB-(Ga,Mn)As can be grown by selecting appropriate growth temperature

Highest Mn composition without segregation is about 10%.

Molecular beam epitaxy of (Ga,Mn )As

Extended X-ray-Absorption Fine Structure (EXAFS)

· X-ray is absorbed by target atom → creation of photoelectron· Photoelectron is scattered by adjacent atoms· Interference of photoelectron and reflected photoelectron· Oscillating structure in absorption spectra includes the information of

local structure around target atom

Incident X-ray Transmitted X-ray

Sample

X-ray

Target atom Adjacent atoms

Absorption edge

Abs

orpt

ion

coef

ficie

nt

Incident X-ray energy

0.0 0.3 0.6

R (nm)

Mn inGaAs (cal.)

MnAs (cal.)

x = 0.005

MnAs

x = 0.074

4As12As

12Ga

12Mn6As

6As

6Mn

2Mn

6As

12Mn6As6As6Mn2Mn

6As

4As 12As12Ga

12Ga 12As4As

FT

(kχ)

(ar

b. u

nits

)

(Ga,Mn)As

Most of Mn substitute III-cation site (Mn2+ → acceptor)

R. Shioda et al., Phys. Rev. B 58, 1100 (1998).

Local Structures - Extended X-ray-Absorption Fine Structure (EXAFS)

Atom Probe Microscopy of (Ga,Mn )As

Surface direction

~ 4

5 nm

~ 90 nm

~ 42 nm~ 1

0 nm

Ga

Mn

As

Analysis direction

M. Kodzuka, T. Ohkubo, K. Hono (NIMS) F. Matsukura, and H. Ohno (Tohoku), Ultramicroscopy 2009

(Ga,Mn)As

Magnetism, transport, and more materials science

Magnetization of (Ga,Mn )As

(Ga,Mn)As & (In,Mn)As: Mn acts as a source of spin and hole

D. Chiba et al., APL 90, 122503 (2007)

Ferromagnetism in (In,Mn)As: H. Ohno et al., Phys Rev. Lett. 1992and in (Ga,Mn)As: H. Ohno et al., Appl. Phys. Lett. 1996

xeff = 0.09, t = 5 nm

-0.5 0.0 0.5-0.04

0.00

0.04

0 50 1000.00

0.03

x = 0.035T = 5 K

B // plane B ⊥ plane B ⊥ plane

(from transport)

M (

T)

B (T)

-0.02 0.00 0.02-0.03

0.00

0.03

M

r (T

)

T (K)

RHall = (R0/d)B + (RS/d)M⊥

H. Ohno et al. Appl. Phys. Lett. 1996H. Ohno Science 1998

RHall = VHall/IRsheet ∝ Vsheet/I

Magnetization and transport of (Ga,Mn )As

Hall Effects

Ordinary Hall effect Anomalous Hall effect Spin Hall effect

0

10

20

30

(a)

RH

all (

Ω)

22 24 26 2829.5

30.0

30.5

experimental linear fit

B (T)

RH

all (

Ω)

0 5 10 15 20 25 30-0.20

-0.16

-0.12

-0.08

-0.04

0.00

B (T)

(b)

1.8K

10K 50mK

100K

∆ρ/ρ

0

xMn=0.053

p = 3.5 x 1020 cm-3

(30% of Mn)

Hall 0

0

( )

1

SR B R M

R B

Bqpd

ρ ⊥∆ = ∆ +≈ ∆

= ∆

Low -temperature & high -field measurements

T. Omiya et al. Physica E, 2000

Ga0.947Mn0.053As

21 3[ ] 1.2 10 cmMn −= ×

10 100

10-2

10-1

100

Ta = 260oC

Ta = 220oC

Ta = 310oC

as-grown

annealed for 15 min(Ga,Mn)As x = 0.05

TS = 210oC

As4/Ga ~ 3

ρ (Ω

cm)

T (K)

0.5670

0.5672

0.5674

0.5676

220 240 260 280 300 320

70

80

90

100

5

6

7

a (n

m)

Ta (oC)

TC (

K)

(x1019)

p (cm-3)

T. Hayashi et al., Appl. Phys. Lett. 78, 1691 (2001).

See also K. W. Edmonds et al., Appl. Phys. Lett. 81, 4991 (2002).

Low -temperature annealing

Low-temperature annealing 220-250 oC· Decreases lattice constant

· Increases electrical conductivity· Increases hole concentration

· Increases ferromagnetic transition temperature

Correlation between TC and p

Mn i

Ferromagnetism

Like other thermodynamic quantities, Fc[M] is expected to be weakly perturbed by static disorder

We suggest that the holes in the extended or weakly localized states mediate the long-range interactions between the localized spins on both sides of the MIT in the III-V and II-VI magnetic semiconductors.

Mn spinsCarrier spins0≠M

β

exchange

p-d Zener model of ferromagnetism

( ) ( )B

FFc k

EASSxNT

12

1 20 βρ+=

T. Dietl, et al. Science 287, 1019 (2000) and PRB 63, 195205 (2001)

Ferromagnetic (Ga,Mn)AsMn acts as a source of spin and hole

also Koenig et al. Phys. Rev. Lett. 2000

s><−= SxNH pd β0

H. Ohno et al. Appl. Phys. Lett. 1996H. Ohno Science 1998

22

2 2

total Mn c

c

Mn

F F F

MH

χχ

∆ = ∆ + ∆

= −

( )Tk

SSxNg

B

BMn 3

1022 += µχ ( )2

c B FEχ µ ρ=

TC by the p-d Zener model

Mn spinsCarrier spins0≠M

β

exchange

( )

22

22

2 22 20

2 2

( )1

812

3

ctotal

Mn

F

BB

B

MF H

EM

gg xN S S

k T

χχ

ρ βµµ

∆ == −

= − +

2

2

2

B

B

EH

M

g

µβ

µ

∆=

=

0

0

∆ 2

∆

B

B

B

E H

E xN S

M xN g S

ME

g

µ

β

µ

βµ

=

=

=

∆ =

22

2 2

( )( )

8F F

cB

A EF M M

g

ρ βµ

∆ ≈ −

( ) ( ) 20 1

12F

cB

xN S S ET

k

ρ β+=

TC by the p-d Zener model

Basis functionsΨΨ EHkp =

k·p matrix

γ1 = 6.85, γ2 = 2.1, γ3 = 2.58, ∆ = 0.34 eV for GaAs

21kP γ= ( )222

2 2 zyx kkkQ −+= γ ( ) zyx kikkL −−= 332 γ ( )[ ]yxyx kkikkM 322

2 23 γγ −−−=, , ,

Valence band structure ( ΓΓΓΓ7, ΓΓΓΓ8)

T. Dietl, H. Ohno and F. Matsukura, Phys. Rev. B63, 195205 (2001)

Valence band structure with p-d exchange ( ΓΓΓΓ7, ΓΓΓΓ8)

ΨΨ EHH pdkp =+ )(

zSxNB β061−= ββ xx b= ββ zz b=

SSw zz = ( ) SSiSw yx ±=±

21222

zyx SSSS ++=

,

,

,

p-d exchange interaction matrix

T. Dietl, H. Ohno and F. Matsukura, Phys. Rev. B63, 195205 (2001)

Exchange energy: N0ββββ

Core level photoemission and modeling:N0β = -1.2 ± 0.2 eV

Okabayashi et al., Phys. Rev. B58, 1998.

Comparison of exp. and calculated TC

0 1 2 3 4 50

50

100

150

, exp. , cal.

(In,Mn)As, x = 0.03

(Ga,Mn)As, x = 0.053

(x1020)

T

C (

K)

Hole concentration, p (cm-3)

Fermi surface of (Ga,Mn)As

Strain induced -anisotropy: Theory vs. Experiment

0

50

100

150

M // [100] : in-plane M // [110] : in-plane M // [001] : ⊥ plane

x=0.05N

0β=-1.2 eV

AF=1.2

compressive strain 0.3 %

TC (

K)

0 1 2 3 4 5

0

50

100

tensile strain 0.7 %

(x1020)

p (cm-3)

-0.10

-0.05

0.00

0.05

0.10

0.15

1.5-µm (Ga0.965Mn0.035)As/LT-GaAs

200-nm (Ga0.957Mn0.043)As/(In0.16Ga0.84)As

^

0o

15o

30o

60o

RH

all (

KΩ

)

-0.5 0.0 0.5-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

T=2.3 K

B (T)

T=10 K

tensile strain

compressive strain

easy

axis

Bθ

easy

axis

Bθ

Theory Experiment

Hole bands are responsible for the anisotropy

Acceptor doping and susceptibility of Zn 1-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

1019 10201

10

100

TC (

K)

p (cm-3)

exp, cal, (Ga,Mn)As, x = 0.053

, (In,Mn)As, x = 0.03

, (Zn,Mn)Te, xeff

= 0.015

Comparison of Experimental and Calculated TC

exp.:(Ga,Mn)As:T. Omiya et al., Physica E 7, 976 (2000). (In,Mn)As: D. Chiba et al., J. Supercond. and Novel Mag.16, 179 (2003). (Zn,Mn)Te: D. Ferrand et al., Phys. Rev. B 63, 085201 (2001).

N0β comparison

p-d exchange energy

4. Making “use” of ferromagnetism in semiconductors

• Electrical control of ferromagnetism• Current induced domain wall motion• Tunneling with magnetism

4. Making “use” of ferromagnetism in semiconductors

• Electrical control of ferromagnetism• Current induced domain wall motion• Tunneling with magnetism

Electric-field control of ferromagnetism

-1.0 -0.5 0 0.5 1.0

-50

-25

0

25

50

22.5 K

0 V +1.5 MV/cm -1.5 MV/cm 0 V

R H

all (

Ω)

B (mT)

H. Ohno et al., Nature 408, 944 (2000).

(In,Mn)AsInAs(Al0.6Ga0.4)Sb

AlSbGaAs sub.

5 nm

10 nm400 nm100 nm

(In0.97Mn0.03)Aspolyimide

Au/Cr

800 nm

95/5 nm RHall = (R0/d)B + (RS/d)M⊥

(In,Mn)As

52 56 60 64 68 720.0

0.2

0.4

0.6

0.8

0 1 2 30

50

100

T (K)

RS

Hal

l (kΩ

)

0 MV/cm +5 MV/cm -5 MV/cm

(x1020)

TC

(K

)

p (cm-3)

Electric-field control: the case of (Ga,Mn )As

(Al0.80Ga0.20)As

(In0.13Ga0.87)As

GaAs

(001) GaAs sub.

7 nm

30 nm500 nm100 nm

(Ga0.953Mn0.047)As

Al2O3

Au/Cr

50 nm

100/5 nm

D. Chiba et al. Appl. Phys. Lett. 2006

(In,Mn)As, H. Ohno et al., Nature 408, 944 (2000).

See also Y. Nishitani et al., Phys. Rev. B 81, 045208 (2010) and M. Sawicki, et al., Nature Physics, 6, 22 (2010)

Field -effect structures of (Ga,Mn )As

K. Olejník et al., Phys. Rev. B 78, 054403 (2008); M. S. H. Owen et al., New J. Phys. 11, 023008 (2009).

backgate structure ferroelectric-gate structure

I. Stokichnov et al., Nature Mater. 7, 464 (2008).

M. Overby et al., Appl. Phys. Lett 92, 192501 (2008); A. W. Rushforth et al., Phys. Rev. B 78, 085314 (2008); S. T. B. Goennenwein et al., phys. stat. sol. (RRL) 2, 96 (2008); C. Bihler et al., Phys. Rev. B 78, 045203 (2008).

(Ga,Mn)As

PZT

piezoelectric hybrid structure

electric double layer

M. Endo et al., Appl. Phys. Lett.96, 022515 (2010).

Electric-field control of magnetization direction

-4 -2 0 2 4-10

-5

0

5

10

Gate electric Field E (MV/cm)

H = 0

M A

ngle

ϕ (

deg.

)

[100] axis

2K

Ga0.9Mn0.1As

D. Chiba et al. Nature (2008).

FePt, FePd: M. Weisheit et al., Science (2007).

Multiferroics ：：：： T. Arima et al., PASPS13 (2009/1/27).

Au/ ultrathin Fe: T. Maruyama et al., Nature Nanotechnology (2009). CoFeB: M. Endo, S. Kanai, S. Ikeda, F.

Matsukura, and H, Ohno, Appl. Phys. Lett. 2010

Electric-field effects on metals

All at room temperatureO-23 Kanai et al.

4. Making “use” of ferromagnetism in semiconductors

• Electrical control of ferromagnetism• Current induced domain wall motion• Tunneling with magnetism

Welp et al., PRL 2003

5 µm

compressive strain in-plane easy axis

90o domains

1 mm

tensile strainperpendicular easy axis

stripe domains

Shono et al., APL 2000

Well defined domains: (Ga,Mn)As

S. I. GaAs (001) sub.GaAs 100 nm

buffer layer

channel layer

In0.22Al0.78As 75 nmGa0.955Mn0.045As 30 nm

easy axis

In0.18Al0.82As 75 nmIn0.13Al0.87As 75 nm

In0.065Al0.935As 75 nm

Current induced domain wall motion

Sample structure

Preparation of domain wall

Patterning of coercive force Hc by etching of (Ga,Mn)As Hc

’ Hc

etching

≠≠≠≠

20 nm 30 nm

Tc ~ 112 K Tc ~ 115 K

Au/Cr electrode 60 µm 20 µm

5 µm

[-110]

[110] (I) (II)

perpendicular easy axis

0 2 4 6 8 10 120

5

10

15

20 107 K 107 K 106 K 105 K 104 K 103 K 102 K 101 K 100 K

v eff (

m/s

)

j (A/cm2)

100 K

x105

M. Yamanouchi et al., Phys. Rev. Lett. 96, 096601 (2006)

Current induced domain wall motion

jcurrent

electron

Mn

Adiabatic spin transfer (conservation of angular momentum)

Mechanism

EF

d state

• Square root dependenceG. Tatara and H. Kohno, Phys. Rev. Lett. 92, 086601 (2004).

2/122 )( CjjAv −=

Domain wall motion: Theory

P

Kej wC

ℏπδ2=

Me

gPA B

2

µ=P : spin polarizationg : g factor of Mn spinµB : Bohr magnetone : charge of electronM : magnetizationK : transverse anisotropyδw : DW width

(Spin transfer)

Current induced domain wall motion

0 2 4 6 8 10 12

0

5

10

15

20 107 K 107 K 106 K 105 K 104 K 103 K 102 K 101 K 100 K

veff (

m/s)

j (A/cm2)

100 K

x105

P

Kej wC

ℏπδ2=

Me

gPA B

2

µ=

102 103 104 105 106 1070.0

0.5

1.0

1.5

2.0

2.5

exp. (square root)

exp. (linear)

A (

m3 /C

)

temperature (K)

x10-9

102 103 104 105 106 1070

2

4

6

8

exp. (linear)

exp. (square root)

j C (

A/c

m2 )

temperature (K)

x105

102 103 104 105 106 1070.0

0.5

1.0

1.5

2.0

2.5

theory

exp. (square root)

exp. (linear)

A (

m3 /C

)

temperature (K)

x10-9

102 103 104 105 106 1070

2

4

6

8

theory

j C (

A/c

m2 )

temperature (K)

Transfer factor and threshold current density

M. Yamanouchi et al., Phys. Rev. Lett. 96, 096601 (2006)

P

Kej wC

ℏπδ2=

(Ga,Mn)As(T/Tc ~ 0.9)

Metal(in plane)

Metal (perpendicular)

K (hard axisanisotropy, J/m3)

60 4x105 105

δw (domain wall width, nm)

20 100 10

P (spin polarization, %)

20 60 60

jC (A/m2) 6x109 7x1013 2 x1012

4. Making “use” of ferromagnetism in semiconductors

• Electrical control of ferromagnetism• Current induced domain wall motion• Tunneling with magnetism

Sample A-1

-0.4 -0.2 0.0 0.2 0.40

100

200

300

2

3

4

5

MR

(%

)

0.39 K+0.5 mV

R(k

ΩΩ ΩΩ)

B [100] (T)

-50 -25 0 25 500

100

200

300

B[100](mT)M

R (

%)

290 %, P = 77 %

Tunnel Magnetoresistance (TMR)

D. Chiba et al. Physica E 2004

20 nm (Ga0.926Mn0.074)As 230-240

6 nm GaAs 250

20 nm (Ga0.956Mn0.044)As 250

50 nm GaAs:Be 560

p+- GaAs (001) sub

2

2

1

2

P

PTMR

−=

Resonant Tunneling Diode with a Ferromagnetic Emitt er

H. Ohno et al. Appl. Phys. Lett., 1998

Resonant Tunnel Diode with a Ferromagnetic Emitter

Sample structures(Ga0.965Mn0.035)As 200 nm

GaAs 15 nmAlAs 5 nmGaAs dW nmAlAs 5 nmGaAs 5 nm

GaAs:Be (5x1017cm-3) 150 nmGaAs:Be (5x1018cm-3) 150 nm

p+ GaAs sub.

Ultra-high doping of Mn in III-V compounds

T. Jungwirth et al., Phys. Rev. B76, 125206 (2007)

Spintech VI, O-10

(Formation of 2D holes in GaAs:Be explains the resonant tunnel-like feature and the thickness dependence)

arXiv 1102.3267v2 (Spintech VI poster FP-42)

Diluted Magnetic Semiconductors

1. What you need to know about nonmagnetic semiconductors• Band structure

2. How you make a semiconductor magnetic• Doping and sp-d exchange

3. The consequences of exchange interaction• Spin-split bands and ferromagnetism

4. Making “use” of ferromagnetism in semiconductors• Electrical control of ferromagnetism• Current induced domain wall motion• Tunneling with magnetism