Spin-injection Hall effectSpin-injection Hall effect:  A new member of the spintronic Hall

family

Institute of Physics of the Academy of Science of the Czech Republic, Prague, November 18th,

2008

JAIRO SINOVATexas A&M University

Institute of Physics ASCR

Research fueled by: 1

Hitachi CambridgeJorg Wunderlich, A.

Irvine, et al

Institute of Physics ASCRTomas Jungwirth,, Vít Novák, et

al

Texas A&MA. Kovalev, M. Borunda,

A. Kovalev, et al

2

Anomalous Hall transport: lots to think about

Taguchi et al Fang et al

Wunderlich et al

Kato et al

Valenzuela et al

SHE Inverse SHE

SHEIntrinsic AHE(magnetic monopoles?)

AHE

AHE in complex spin textures

Brune et al

The family of spintronic Hall effectsThe family of spintronic Hall effects

3

AHEB=0

polarized charge current

gives charge-spin

current

Electrical detection

jqs––– – –– – –– – –

+ + + + + + + + + +AHE

Ferromagnetic(polarized charge current)

SHEB=0

charge current gives

spin current

Optical detection

jq

SHE

nonmagnetic(unpolarizedcharge current)

SHE-1

B=0spin current

gives charge current

Electrical detection

js–––––––––––

+ + + + + + + + + +iSHE

4

Towards a spin-based non-magnetic FET device:Towards a spin-based non-magnetic FET device: can we electrically measure the spin-polarization?

ISHE is now routinely used to detect other effects related to the generated spin-currents (Sitho et al Nature 2008)

Can we achieve direct spin polarization detection through an electrical measurement in an all paramagnetic semiconductor system?

Long standing paradigm: Datta-Das FET

Unfortunately it has not worked: •no reliable detection of spin-polarization in a diagonal transport configuration •No long spin-coherence in a Rashba SO coupled system

Alternative:Alternative: utilize technology developed to detect SHE in 2DHG and measure polarization via Hall

probes

J. Wunderlich, B. Kaestner, J. Sinova andT. Jungwirth, Phys. Rev. Lett. 94 047204 (2005)

Spin-Hall Effect

5

B. Kaestner, et al, JPL 02; B. Kaestner, et al Microelec. J. 03; Xiulai Xu, et al APL 04, Wunderlich et al PRL 05

Proposed experiment/device: Coplanar photocell in reverse bias with Hall probes along the 2DEG channelBorunda, Wunderlich, Jungwirth, Sinova et al PRL 07

Device schematic - materialmaterial

6

i pn

2DHG

-

2DHGi p

n

7

Device schematic - trenchtrench

i

p

n2DHG

2DEG

8

Device schematic – n-etchn-etch

Vd

VH

2DHG

2DEG

Vs

9

Device schematic – Hall Hall measurementmeasurement

2DHG

2DEG

e

h

ee

ee

e

hh

h

h h

Vs

Vd

VH

10

Device schematic – SIHE SIHE measurementmeasurement

0 30 60 90 120 150

-50

-40

-30

-20

-10

0

10

20

30

40

50

0

2

4

6

8

10

12

14

16

18

20

22

24R

H [

]

tm [s]

RL [k

]

0 30 60 90 120 150

-50

-40

-30

-20

-10

0

10

20

30

40

50

0

2

4

6

8

10

12

14

16

18

20

22

24R

H [

]

tm [s]

RL [k

]

0 30 60 90 120 150

-50

-40

-30

-20

-10

0

10

20

30

40

50

0

2

4

6

8

10

12

14

16

18

20

22

24R

H [

]

tm [s]

RL [k

]

0 30 60 90 120 150

-50

-40

-30

-20

-10

0

10

20

30

40

50

0

2

4

6

8

10

12

14

16

18

20

22

24R

H [

]

tm [s]

RL [k

]

0 30 60 90 120 1500

2

4

6

8

10

12

14

16

18

20

22

24

tm [s]

RL [k

]5m

Reverse- or zero-biased: Photovoltaic Photovoltaic CellCell

trans. signaltrans. signal

Red-shift of confined 2D hole free electron trans.due to built in field and reverse biaslight excitation with = 850nm

(well below bulk band-gap energy)

σσooσσ++σσ-- σσoo

VL

0.95

1.00

1.05

0.95

1.00

1.05

0 30 60 90 120 150

0.95

1.00

1.05

tm [s]

P/Pav.

I/Iav.

V/Vav.

Vav. = 9.4mV

Iav. = 525nA

(a)

(b)

(c)

11

-1/2

-1/2 +1/2

+1/2 +3/2-3/2

bulk

Transitions allowed for ħω>EgTransitions allowed for ħω<Eg

-1/2

-1/2 +1/2

+1/2+3/2-3/2

Band bending: stark effect

Transitions allowed for ħω<Eg

5m

-4 -2 0 2 4-100

-50

0

50

100

tm [s]

RH [

]

n2

+ -

Spin injection Hall effect: Spin injection Hall effect: experimental observation

-4 -2 0 2 4-100

-50

0

50

100

tm [s]

RH [

]

n1 (4)

n2

-4 -2 0 2 4-100

-50

0

50

100

tm [s]

RH [

]

n1 (4)

n2

n3 (4)

Local Hall voltage changes sign and magnitude along the stripe12

Spin injection Hall effect Anomalous Hall effect

-1.0 -0.5 0.0 0.5 1.0-2

-1

0

1

2

H [

10-3 ]

( ) / (

)

n1

-1.0 -0.5 0.0 0.5 1.0

-10

-5

0

5

10

H [

10-3 ]

( ) / (

)

n2

-1.0 -0.5 0.0 0.5 1.0

-0.5

0.0

0.5

H [

10-3 ]

( ) / (

)

p

-1.0 -0.5 0.0 0.5 1.0

-0.5

0.0

0.5

H [

10-3 ]

( ) / (

)

p

13

and high temperature operation

Zero bias-

-6 -3 0 3 6

-5

0

5

tm [s]

H [

10-3

]

n1 (10)

n3 (50)

n2 VB = 0V

T = 4K

+-

-6 -3 0 3 6

-1

0

1

tm [s]

H [

10-3

]

n1 (2)

n3

n2 (2)

T = 230K

VB = -10V

A

+-

Persistent Spin injection Hall effectPersistent Spin injection Hall effect

14

THEORY CONSIDERATIONSTHEORY CONSIDERATIONSSpin transport in a 2DEG with Rashba+Dresselhaus

SO

))(V(2 dis

*22

rkkkkkm

kH yyxxyxxy

2DEG

15

, AeV 0

02.0

AeV 03.001.00

)AeV/ (for0

03.001.0 ZE

For our 2DEG system:

067.0 emm

The 2DEG is well described by the effective Hamiltonian:

Hence

GaAs, for A 2o

3.5)(

11

3 22

2*

sogg EE

P GaAs, for AeV with 30

102 BkB z zE*

16

• spin along the [110] direction is conserved

• long lived precessing spin wave for spin perpendicular to [110]

What is special about ?

))((2

22

yxxy kkm

kH

2DEG ))(V( dis

* rk

Ignoring the term

for now

k k Q

• The nesting property of the Fermi surface:

2

4

m

Q

The long lived spin-excitation: “spin-helix”

0, , zQ Qk k Q k Q k k k k kk k k

S c c S c c S c c c c

0 0, 2 , ,z zQ Q Q QS S S S S S

ReD , 0k Q k k Q k

H c c k Q k c c

An exact SU(2) symmetry

Only Sz, zero wavevector U(1) symmetry previously known:

J. Schliemann, J. C. Egues, and D. Loss, Phys. Rev. Lett. 90, 146801 (2003).

K. C. Hall et. al., Appl. Phys. Lett 83, 2937 (2003).

• Finite wave-vector spin components

• Shifting property essential

17

• Spin configurations do not depend on the particle initial momenta.

• For the same x+ distance traveled, the spin precesses by exactly the same angle.

• After a length xP=h/4mα all the spins return exactly to the original configuration.

Physical Picture: Persistent Spin Helix

Thanks to SC Zhang, Stanford University

18

19

Persistent state spin helix verified by pump-probe experiments

Similar wafer parameters to ours

The Spin-Charge Drift-Diffusion Transport Equations

For arbitrary α,β spin-charge transport equation is obtained for diffusive regime

For propagation on [1-10], the equations decouple in two blocks. Focus on the one coupling Sx+ and Sz:

For Dresselhauss = 0, the equations reduce to Burkov, Nunez and MacDonald, PRB 70, 155308 (2004);

Mishchenko, Shytov, Halperin, PRL 93, 226602 (2004)

STTSCSC SDS

STSCnB SDS

STSCnB SDS

SBSBn Dn

zxxxxzzt

xzxxxxt

xzxxxxt

xxxxt

)( 21222

2212

1122

212

20

k

mTkB F

F 2

22

2/1222

2/1 )(2

,)()(2

DTCvD F 2/12

2/12 4,2/ and

STTSC SDS

STSC SDS

zxxzzt

xzxxxt

)( 2122

222

2~~

4~~~

arctan,)~~~

(||,)exp(|| 21

22

41

22

21

21414

22

22

1LL

LLLLLLqiqq

]exp[)( ]011[0/]011[/ xqSxS xzxz Steady state solution for the spin-polarization

component if propagating along the [1-10] orientation

22/1 ||2

~ mL

21

Steady state spin transport in diffusive regime

Spatial variation scale consistent with the one observed in SIHE

MRBR sH 40

Understanding the Hall signal of the SIHE: Anomalous Hall effect

Simple electrical measurement of out of plane magnetization

Spin dependent “force” deflects like-spin particles

I

_ FSO

FSO

_ __

majority

minority

V

InMnAs

sRR 0

22

y

x

xxxy

xyxx

y

x

E

E

j

j

xxxyxx

xxxx

122

22

222 xxxxxxxyxx

xy

xyxx

xyxy BA

xxxy AB

23

2xxxxxy BA xxxy AB

Anomalous Hall effect (scaling with ρ)

Dyck et al PRB 2005

Kotzler and Gil PRB 2005

Co films

Edmonds et al APL 2003

GaMnAs Strong SO coupled regime

Weak SO coupled regime

Intrinsic deflection

Side jump scattering

24

Electrons have an “anomalous” velocity perpendicular to the electric field related to their Berry’s phase curvature which is nonzero when they have spin-orbit coupling.

~τ0 or independent of impurity density

Electrons deflect first to one side due to the field created by the impurity and deflect back when they leave the impurity since the field is opposite resulting in a side step. They however come out in a different band so this gives rise to an anomalous velocity through scattering rates times side jump.

independent of impurity density

Skew scattering

Asymmetric scattering due to the spin-orbit coupling of the electron or the impurity. This is also known as Mott scattering used to polarize beams of particles in accelerators.

~1/ni

STRONG SPIN-ORBIT COUPLED REGIME (Δso>ħ/τ)

Vimp(r)

Vimp(r)

Electrons deflect to the right or to the left as they are accelerated by an electric field ONLY because of the spin-orbit coupling in the periodic potential (electronics structure)

E

SO coupled quasiparticles

25

WEAK SPIN-ORBIT COUPLED REGIME (Δso<ħ/τ)

Side jump scattering from SO disorder

Electrons deflect first to one side due to the field created by the impurity and deflect back when they leave the impurity since the field is opposite resulting in a side step. They however come out in a different band so this gives rise to an anomalous velocity through scattering rates times side jump.

independent of impurity density λ*Vimp(r)

Skew scattering from SO disorder

Asymmetric scattering due to the spin-orbit coupling of the electron or the impurity. This is also known as Mott scattering used to polarize beams of particles in accelerators.

~1/ni

λ*Vimp(r)

The terms/contributions dominant in the strong SO couple regime are strongly reduced (quasiparticles not well defined due to strong disorder broadening). Other terms, originating from the interaction of the quasiparticles with the SO-coupled part of the disorder potential dominate.

Better understood than the strongly SO couple regime

26

AHE contribution

zzi

H pxpnn

ex 3

]011[*

]011[ 101.1)(2)(

Type (i) contribution much smaller in the weak SO coupled regime where the SO-coupled bands are not resolved, dominant contribution from type (ii)

Crepieux et al PRB 01Nozier et al J. Phys. 79

Two types of contributions: i)S.O. from band structure interacting with the field (external and internal)ii)Bloch electrons interacting with S.O. part of the disorder

))(V(2 dis

*22

rkkkkkm

kH yyxxyxxy

2DEG

)(2

02

*2

nnnVe

xy

skew)(

2 *2

nne

xy

jump-side

4103.5 jump-sideH

Lower bound estimate of skew scatt. contribution

Spin injection Hall effect: Theoretical consideration

Local spin polarization calculation of the Hall signal Weak SO coupling regime extrinsic skew-scattering term is dominant

)(2)( ]011[*

]011[ xpnn

ex z

iH

27

Lower bound estimate

The family of spintronics Hall effects

SHE-1

B=0spin current

gives charge current

Electrical detection

AHEB=0

polarized charge current

gives charge-spin

current

Electrical detection

SHEB=0

charge current gives

spin currentOptical

detection

28

SIHEB=0

Optical injected polarized

current gives charge current

Electrical detection

29

SIHE: a new tool to explore spintronics

•nondestructive electric probing tool of spin propagation without magnetic elements

•all electrical spin-polarimeter in the optical range

•Gating (tunes α/β ratio) allows for FET type devices (high T operation)•New tool to explore the AHE in the strong SO coupled regime

Why is AHE difficult theoretically in the strong SO couple regime?

•AHE conductivity much smaller than σxx : many usual approximations fail

•Microscopic approaches: systematic but cumbersome; what do they mean; use non-gauge invariant quantities (final result gauge invariant)

•Multiband nature of band-structure (SO coupling) is VERY important; hard to see these effects in semi-classical description (where other bands are usually ignored).

•Simple semi-classical derivations give anomalous terms that are gauge dependent but are given physical meaning (dangerous and wrong)

•Usual “believes” on semi-classically defined terms do not match the full semi-classical theory (in agreement with microscopic theory)

•What happens near the scattering center does not stay near the scattering centers (not like Las Vegas)•T-matrix approximation (Kinetic energy conserved); no longer the case, adjustments have to be made to the collision integral term•Be VERY careful counting orders of contributions, easy mistakes can be made.

30

0)(

)(ˆ

ˆ ''

k

kHkv

k

Hv nn

nnk

• Boltzmann semiclassical approach: easy physical interpretation of different contributions (used to define them) but very easy to miss terms and make mistakes. MUST BE CONFIRMED MICROSCOPICALLY! How one understands but not necessarily computes the effect.

• Kubo approach: systematic formalism but not very transparent.

• Keldysh approach: also a systematic kinetic equation approach (equivalent to Kubo in the linear regime). In the quasi-particle limit it must yield Boltzmann semiclassical treatment.

Microscopic vs. SemiclassicalAHE in the strongly SO couple regime

31

32

Recent progress: full understanding of simple models in each approach

Semi-classical approach:Gauge invariant formulation; shown to match microscopic approach in 2DEG+Rashba,

GrapheneSinitsyn et al PRB 05, PRL 06, PRB 07 Borunda et al PRL 07, Nunner et al PRB 08Sinitsyn JP:C-M 08

Kubo microscopic approach:

Results in agreement with semiclassical calculations 2DEG+Rashba, Graphene

Sinitsyn et al PRL 06, PRB 07, Nunner PRB 08, Inoue PRL 06, Dugaev PRB 05

NEGF/Keldysh microscopic approach:

Numerical/analytical results in agreement in the metallic regime with

semiclassical calculations 2DEG+Rashba, Graphene

Kovalev et al PRB 08, Onoda PRL 06, PRB 08

– – – – – – – – – – – + + + + + + + + + +

jqsnonmagneticSpin-polarizer

current injected optically

Spin injection Hall effect (SIHE)Spin injection Hall effect (SIHE)

Up to now no 2DEG+R ferromagnetis: SIHE offers this possibility

33

CONCLUSIONS

Spin-injection Hall effect observed in a conventional

2DEG

- nondestructive electrical probing tool of spin propagation

- indication of precession of spin-polarization

- observations in qualitative agreement with theoretical

expectations

- optical spin-injection in a reverse biased coplanar pn-

junction: large and persistent Hall signal (applications

!!!)