Electric-field controlled semiconductor spintronic devicesElectric-field controlled semiconductor spintronic devices

Tomas Jungwirth Institute of Physics ASCR

Alexander Shick

University of Nottingham

Bryan Gallagher, Tom Foxon, Richard Campion, Kevin Edmonds,

Andrew Rushforth, Devin Giddings et al.

Hitachi Cambridge University of Texas and Texas A&M

Jorg Wunderlich, Bernd Kaestner Allan MacDonald, Jairo Sinova David Williams

Spin-orbit couplingSpin-orbit coupling Dirac eq. in external field V(r) & 2nd-order in v /c around non-relativistic limit

ee--

effSO BsH

p)V(cm2

1B

22eff

V

BBeffeff

pss

e.g. GaAs valence band As p-orbitals large SO

Beff Bex + Beff

e.g. GaMnAs valence band FM & large SO

SpintronicsSpintronics

FerromagnetismFerromagnetism Coulomb repulsion & Pauli exclusion principle

spin coupled tomomentum andcrystal fields

macroscopicmoment

kx

ky

kx

ky

AuAu

Current spintronics - two terminal AMR or GMR devices

[010]

Magnetization[110]

[100]

[110][010]

Current

1. Current driven magnetization reversal

2. Spintronic transistor

3. Electric-field induced spin-polarization in non-magnetic systems

Coulomb blockade AMRspintronic SETin thin-film GaMnAs

Spin Hall effect inducededge spin polarizationin GaAs 2DHG

Electrical control of spintronic devicesElectrical control of spintronic devices

Parkin, US Patent (2004)

Magnetic race track memory

Yamanouchi et al., Nature (2004)

2 orders of magnitude lower criticalcurrents in dilute moment (Ga,Mn)As than in conventional metal FMsSinova, Jungwirth et al., PRB (2004)

Coulomb blockade AMR

Spintronic transistor - magnetoresistance controlled by gate voltage

Strong dependenceon field anglehints to AMR origin

Huge hysteretic low-field MR

Sign & magnitudetunable by smallgate valtages

Wunderlich, Jungwirth, Kaestner et al., cond-mat/0602608

Bptp

B90

B0

I

AMR nature of the effect

normal AMR Coulomb blockade AMR

Single electron transistor

Narrow channel SETdots due to disorder potential fluctuations

(similar to non-magnetic narrow-channel GaAs or Si SETs)

CB oscillationslow Vsd blockeddue to SE charging

magnetization angle

CB oscillation shifts by magnetication rotations

At fixed Vg peak valleyor valley peak

MR comparable to CBnegative or positive MR(Vg)

GMMGG0

20

C

C

e

)M(V&)]M(VV[CQ&

C2

)QQ(U

electric && magneticmagnetic

control of Coulomb blockade oscillations

n-1 n n+1 n+2n-1 n n+1 n+2

EC

QQindind = = nnee

QQindind = (= (n+1/2)n+1/2)eeQ0

Q0

e2/2C

Coulomb blockade AMR

Q

0

'D

'

e

)M(Q)Q(VdQU

[010]

M[110]

[100]

[110][010]

SO-coupling (M)

• CBAMR if change of CBAMR if change of ||((MM)| ~ )| ~ ee22//22CC ~ 10Kelvin from exp. consistent

• In room-T ferromagnet change of |In room-T ferromagnet change of |((MM)|)|~100Kelvin~100Kelvin

• CBAMR works with dot both ferro CBAMR works with dot both ferro or paramegneticor paramegnetic

Different doping expected in leads an dots in narrow channel GaMnAs SETs

Calculated doping dependence of(M1)-(M2)

• Huge, hysteretic, low-field MR tunable by small gate voltage changes • Combines electrical transistor action with permanent storage

• Non-hysteretic MR and large B - chemical potential shifts due to Zeeman effect Ono et al. '97, Deshmukh et al. '02

• Small MR - subtle effects of spin-coherent and resonant tunneling through quantum dots Ono et al. '97, Sahoo '05

CBAMR SET

Other FERRO SETs

Spin Hall effect

Spin-orbit only & electric fields only

Wunderlich, Kaestner, Sinova, Jungwirth, Phys. Rev. Lett. '05

Nomura, Wunderlich, Sinova, Kaestner, MacDonald,Jungwirth, Phys. Rev. B '05

Detection through circularlypolarized electroluminescence

y

zx

applied electricalcurrent

induced transversespin accummulationspin (magnetization)

component

Testing the co-planar spin LED only first

p-n junction current only (no SHE driving current)

p -AlG a As

i-G a As

n- -d o p e d AlG a As

e tc he d

2DHG2DHG

2DEG2DEG

0

-10

-20

10

20

Cir

c. p

olar

izat

ion

[%] EL EL

peak

Bz=0• Can detect spin polarization due to Zeemen effect

• Zero perp-to-plane component of polarization at Bz=0 and Ip=0

0

-5

-10

5

10

Cir

c. p

olar

izat

ion

[%]

• In-plane HH spin-splitting due to SO-coupling

• Non-zero in-plane component of EL polarization at Bx=0 and Ip=0

-1

0

1

Pol

ariz

atio

n in

%

1.505 1.510 1.515 1.520

-1

0

1

Energy in eV

Pol

ariz

atio

n in

%

n

n

py

xz

LED 1

LED 2

10m channel

SHE experimentsSHE experiments

- show the SHE symmetries

- edge polarizations can be separated over large distances with no significant effect on the magnitude

1.5m channel

y

zx

applied electricalcurrent

induced transversespin accummulationspin (magnetization)

component

=0

Murakami et al. '03, Sinova et al.'04, Nomura et al. '05, ...

effSO BsH

p)V(cm2

1B

22eff

y

x

Ex

Theory: 8% over 10nm accum. lengthfor the GaAs 2DHG

Consistent with experimental 1-2% polarization over detection length of ~100nm

y [kF-1]

0 10 20 30 40 50

j yz (y)

/Ex

Sz (

y)/E

x

SSzzedgeedge L Lsoso ~ j ~ jzz

bulkbulk t tsoso

Spin injection from SHE GaAs channel Electrical measurement of SHE in Al

Valenzuela, Tinkham '06Kato et al. '04, Sih et al. '06

skewscattering

=0

Other SHE experiments:

100's of theory papers: transport with SO-coupling

intrinsic vs. extrinsic

Microscopic origin

Source Drain

GateVG

VDQ

Q

0

2

D'

D'

C2

QUC/QV&)Q(VdQU

TkC2

eB

2

Coulomb blockadeCoulomb blockade

• VVgg = 0 = 0

• VVgg 0 0

GG0

20 VCQ&

C2

)QQ(U

Q=ne - Q=ne - discretediscreteQQ00=C=CggVVgg - continuous - continuous

QQ00=-ne=-ne blocked blocked

QQ00=-(n+1/2)e=-(n+1/2)e open open

n-1 n n+1 n+2n-1 n n+1 n+2

EC

QQindind = = nnee

QQindind = (= (n+1/2)n+1/2)eeQ0

Q0

e2/2C

Wafer 1

0 -50 -100 -150-2

-1

0

1

2

Wafer 2

Int

[a.u.]

E [eV]

E [

eV]

0

2

4

6

8

10

1.48 1.49 1.50 1.51 1.520

2

4

6

8

10

p-AlGaAs

n-AlGaAs

GaAs/AlGaAs superlatticeGaAs substrate

etched

2DEG2DHG

i-GaAs

y

z GaAsp-AlGaAs

n-AlGaAs

GaAs/AlGaAs superlatticeGaAs substrate

etched

2DEG2DHG

i-GaAs

y

z GaAs

z [nm]

I

X

I

X

A

A

A

A

B

B

B

B

C

C

PLEL

p-AlGaAs

GaAs

Sub GaAs gap spectra analysis: PL vs EL

X : bulk GaAs excitons

I : recombinationwith impurity states

BB ( (A,CA,C): ): 3D electron – 3D electron – 2D hole 2D hole recombinationrecombination

Bias dependent emission wavelength for 3D electron – 2D hole Bias dependent emission wavelength for 3D electron – 2D hole recombination recombination [A. Y. Silov et al., APL 85, 5929 (2004)][A. Y. Silov et al., APL 85, 5929 (2004)]

++--

NO perp.-to-plane component of polarization at B=0NO perp.-to-plane component of polarization at B=0

BB≠0 behavior consistent with SO-split HH subband≠0 behavior consistent with SO-split HH subband

In-plane

detection angle

Perp.-to plane

detection angle

Circularly polarized EL

Light polarization due to recombination with SOLight polarization due to recombination with SO--split split holehole--subbandsubband in a in a pp--nn LED under forward biasLED under forward bias

spin operators of holes: j=3s

-0.2 0.0 0.2-0.50

-0.25

0.00

0.25

0.50

<sx>HH+

<sx>HH-

<sz>HH--

<<sszz>>HHHH++

<S

>

ky [nm-1]

spin-polarization of HH+ and HH- subbands

-0.2 0.0 0.2-0.50

-0.25

0.00

0.25

0.50

-0.2 0.0 0.2-0.50

-0.25

0.00

0.25

0.50

<sx>HH+

<sx>HH-

<sz>HH--

<<sszz>>HHHH++

<S

>

ky [nm-1]

spin-polarization of HH+ and HH- subbands

inin--planeplane polarization

0

20

E [

meV

]

a

HH+

HH-LH

- +

-20

0

20

ky [nm-1]

3D electron-2D hole Recombination

-0.2 0.0 0,2

0

20

E [

meV

]

a

HH+

HH-LH

- +

-20

0

20

ky [nm-1]

3D electron-2D hole Recombination

0

20

E [

meV

]

a

HH+

HH-LH

- +

-20

0

20

ky [nm-1]

0

20

E [

meV

]

a

HH+

HH-LH

- +

-20

0

20

0

20

E [

meV

]

a

HH+

HH-LH

- +

-20

0

20

0

20

E [

meV

]

a

HH+

HH-LH

- +

-20

0

20

ky [nm-1]

3D electron-2D hole Recombination

-0.2 0.0 0,2

s=1/2 electrons to j=3/2 holes plus selection rules

circular polarization of emitted light

Microscopic band-structure calculations of the 2DHG:

Pauli exclusion principle & Coulomb repulsionPauli exclusion principle & Coulomb repulsion FerromagnetismFerromagnetism

total wf antisymmetric = orbital wf antisymmetric * spin wf symmetric (aligned)

FEROFERO MAGMAG NETNET

ee--

• RobustRobust (can be as strong as bonding in solids)(can be as strong as bonding in solids)

• Strong coupling to magnetic fieldStrong coupling to magnetic field (weak fields = anisotropy fields needed (weak fields = anisotropy fields needed only to reorient macroscopic moment)only to reorient macroscopic moment)

Non-relativistic many-body1. Introduction

AMRAMR (anisotropic magnetoresistance)

Band structure depends on Band structure depends on MM

Ferromagnetism: sensitivity to magnetic field

SO-coupling: anisotropies in Ohmic transport characteristics

M || <100>

M ||

<01

0>

GaMnAs

ky

kx

spinspin-valve-valve

TMR (tunneling magnetoresistance)

Based on ferromagnetism only

no (few) spin-up DOS available at EF large spin-up DOS available at EF

Gould, Ruster, Jungwirth, et al., PRL '04, '05

[100]

[010]

[100]

[010]

[100]

[010]

(Ga,Mn)As(Ga,Mn)As

AuAu

- no exchange-bias needed

- spin-valve with ritcher phenomenology than TMR

Tunneling AMR: anisotropic tunneling DOS due to SO-coupling

MRAMMRAM

[010]

Magnetization[110]

[100]

[110][010]

Current

Magnetisation in plane

y

x

jt

z

Wavevector dependent tunnelling probabilityT (ky, kz) in GaMnAs Red high T; blue low T.

xz

y

jt

constriction

Magnetization perp. to plane

Magnetization in-plane

Giddings, Khalid, Jungwirth, Wunderlich et al., PRL '05

thin film

TAMR in metals

Bolotin,Kemmeth, Ralph, cond-mat/0602251

Shick, Maca, Masek, Jungwirth, PRB '06

NiFe TAMR TMR

TMR ~TAMR >>AMR

ab-initio calculations

Viret et al., cond-mat/0602298 Fe, Co break junctions TAMR >TMR

EXPERIMENT

Spin Hall Effect

2DHG

2DEG VT

VD

Single Electron TransistorSingle Electron Transistor

Source Drain

GateVG

VDQ

Q

0

2

D'

D'

C2

QUC/QV&)Q(VdQU

TkC2

eB

2

Coulomb blockadeCoulomb blockade

• VVgg = 0 = 0

• VVgg 0 0

GG0

20 VCQ&

C2

)QQ(U

Q=ne - Q=ne - discretediscreteQQ00=C=CggVVgg - continuous - continuous

QQ00=-ne=-ne blocked blocked

QQ00=-(n+1/2)e=-(n+1/2)e open open

n-1 n n+1 n+2n-1 n n+1 n+2

EC

QQindind = = nnee

QQindind = (= (n+1/2)n+1/2)eeQ0

Q0

e2/2C

Coulomb blockade anisotropic magnetoresistanceCoulomb blockade anisotropic magnetoresistance

Band structure (group velocities, scattering rates, chemical potentialchemical potential) depend on M

Spin-orbit couplingSpin-orbit coupling

If lead and dot differentIf lead and dot different (different carrier concentrations in our (Ga,Mn)As SET)

Q

0

DL'

D' )M()M()M(&

e

)M(Q)Q(VdQU

GMMGG0

20

C

C

e

)M(V&)]M(VV[CQ&

C2

)QQ(U

electric && magneticmagnetic

control of Coulomb blockade oscillations

Wunderlich, Jungwirth, Kaestner, Shick, et al., preprint

• CBAMR if change of |CBAMR if change of |((MM)| ~ )| ~ ee22//22CC

• In our (Ga,Mn)As ~ meV (~ 10 Kelvin)In our (Ga,Mn)As ~ meV (~ 10 Kelvin)

• In room-T ferromagnet change of |In room-T ferromagnet change of |((MM)|~100K )|~100K

• Room-T conventional SET (e2/2C >300K) possible

-0.08 0.00 0.080

20

RC [

M

]

-BC1 -BC2BC2

BC1

B [ T ]

POWER“OFF”

Electrical operation mode

“READ”:measure RC

at VG = VG1

“1” (M1)

“0” (M0)

“WRITE”permanently

POWER “ON”

POWER“OFF”

Electrical operation mode

Electrical operation mode

“READ”:measure RC

at VG = VG1

“1” (M1)

“0” (M0)

“WRITE”permanently

POWER “ON”

M1 -M1

M0 M0

VG = VG1 = 1.04V

1.00 1.01 1.02 1.03 1.046

8

10

12

14

16

18

20

VG0VG1

RC [

M

]

VG [ V ]

electric modeelectric mode

magneticmagneticnonnon--volatilevolatile

modemode

0.6 0.8 1.00

25

50

RC [

M

]

VG [ V ]

““00””

““11””

MM00(a)

(b)

(c)

MM11

Magnetic non-volatile mode

VG = VG1 : M0 (“0”) M1 (“1”)

[[InverseInverse:: VG = VG0 : M0 (“1”) M1 (“0”)]

M0 : B B0 0 BC1 < B0 < BC2

M1 : B B1 0 B1 < -BC2

Electric modeM = M1 : VG0 (“0”) VG1 (“1”)

[[InverseInverse:: M = M0 : VG0 (“1”) VG1 (“0”)]

(d)

Magnetic non-volatile mode

VG = VG1 : M0 (“0”) M1 (“1”)

[[InverseInverse:: VG = VG0 : M0 (“1”) M1 (“0”)]

M0 : B B0 0 BC1 < B0 < BC2

M1 : B B1 0 B1 < -BC2

Electric modeM = M1 : VG0 (“0”) VG1 (“1”)

[[InverseInverse:: M = M0 : VG0 (“1”) VG1 (“0”)]

(d)

CBAMR CBAMR new device concepts new device concepts

Electrically generated spin polarization in normal semiconductors Electrically generated spin polarization in normal semiconductors SPIN HALL EFFECTSPIN HALL EFFECT

B

V

I

_

+ + + + + + + + + + + + +

_ _ _ _ _ _ _ _ _ _ FL

Lorentz force deflect chargedcharged--particles towards the edge

Ordinary Hall effectOrdinary Hall effect

Detected by measuring transverse voltage

Spin Hall effectSpin Hall effect

Spin-orbit coupling “force” deflects like-spinlike-spin particles

I

_ FSO

FSO

_ __

V=0

non-magnetic

Spin-current generation in non-magnetic systems Spin-current generation in non-magnetic systems without applying external magnetic fieldswithout applying external magnetic fields

Spin accumulation without charge accumulationexcludes simple electrical detection

Microscopic theory and some interpretationMicroscopic theory and some interpretation

- weak dependence on impurity scattering time

- SSzzedgeedge ~ j ~ jzz

bulkbulk / v / vFF

ttsoso=h/=h/soso : (intrinsic) spin-precession time

LLsoso=v=vFF t tsoso : spin-precession length

SSzzedgeedge L Lsoso ~ j ~ jzz

bulkbulk t tsoso

Nomura, Wunderlich, Sinova, Kaestner, MacDonald,Jungwirth, Phys. Rev. B '05

experimentally detected

non-conserving (ambiguous)theoretical quantity

spin * velocity

-1

0

1

Pol

ariz

atio

n in

%

1.505 1.510 1.515 1.520

-1

0

1

Energy in eV

Pol

ariz

atio

n in

%

1.5m

channel

n

n

py

xz

LED1

LED2

10m channel

SHE experiment in SHE experiment in GaAs/AlGaAs 2DHGGaAs/AlGaAs 2DHG

- shows the basic SHE symmetries

- edge polarizations can be separated over large distances with no significant effect on the magnitude

- 1-2% polarization over detection length of ~100nm consistent with theory prediction (8% over 10nm accumulation length)

Wunderlich, Kaestner, Sinova, Jungwirth, Phys. Rev. Lett. '05

Nomura, Wunderlich, Sinova, Kaestner, MacDonald,Jungwirth, Phys. Rev. B '05

1.5 mchannel

n

n

p yxz

Conventionally generated spin polarization in non-magnetic semiconductorsConventionally generated spin polarization in non-magnetic semiconductors: spin injection from ferromagnets, circular polarized light sources,

external magnetic fields

SHESHE: small electrical currents in simple semiconductor microchips

SHE microchip, 100A

high-field lab. equipment, 100 A

Spin and Anomalous Hall effectsSpin and Anomalous Hall effects

MπR4BR s0H

Simple electrical measurement Simple electrical measurement of magnetizationof magnetization

Spin-orbit coupling “force” deflects like-spinlike-spin particles

I

_ FSO

FSO

_ __

majority

minority

VInMnAs

(r)Vkcm

sH imp22

2

SO

Skew scattering off impurity potential Skew scattering off impurity potential (Extrinsic SHE/AHE)

skewscattering

lsdr

rdV

err

mc

k

mc

seBH effSO

)(1

bands from l=0 atomic orbitals weak SO(electrons in GaAs)

bands from l>0 atomic orbitals strong SO(holes in GaAs)

SO-coupling from host atoms SO-coupling from host atoms (Intrinsic SHE/AHE)

E

Intrinsic AHE approach explains many experimentsIntrinsic AHE approach explains many experiments

• (Ga,Mn)As systems [Jungwirth et al. PRL 02, APL 03]

• Fe [Yao, Kleinman, Macdonald, Sinova, Jungwirth et al PRL 04]

• Co [Kotzler and Gil PRB 05]

• Layered 2D ferromagnets such as SrRuO3 and pyrochlore ferromagnets [Onoda and Nagaosa, J. Phys. Soc. Jap. 01,Taguchi et al., Science 01, Fang et al Science 03, Shindou and Nagaosa, PRL 01]

• Ferromagnetic spinel CuCrSeBr [Lee et al. Science 04]

Experiment AH 1000 (cm)-1

TheroyAH 750 (cm)-1

Hall effects familyHall effects family

• OrdinaryOrdinary: carrier density and charge; magnetic field sensing

• QuantumQuantum: text-book example a strongly correlated many-electron system with e.g. fractionally charged quasiparticles; universal, material independent resistance

• Spin and AnomalousSpin and Anomalous: relativistic effects in solid state;

spin and magnetization generation and detection

Spin-orbit couplingSpin-orbit coupling Dirac eq. in external field V(r) & 2nd-order in v /c around non-relativistic limit

ee--

effSO BsH

p)V(cm2

1B

22eff

V

BBeffeff

pss

FM without SO-couplingGaAs valence band As p-orbitals large SO

BexBeff Bex + Beff

GaMnAs valence band FM & large SO

SpintronicsSpintronics

FerromagnetismFerromagnetism Coulomb repulsion & Pauli exclusion principle