SPIN-HALL EFFECT a new adventure in condensed matter physics San Houston State University, January 22 th 2008 JAIRO SINOVA Research fueled by: NERC

SPIN-HALL EFFECT SPIN-HALL EFFECT a new adventure in condensed matter physicsa new adventure in condensed matter physics

San Houston State University, January 22th 2008

JAIRO SINOVA

Research fueled by:

NERC

Branislav NikolicU. of DelawareAllan MacDonald

U of Texas

Tomas JungwirthInst. of Phys. ASCR

U. of Nottingham

Joerg WunderlichCambridge-Hitachi

Laurens MolenkampWuerzburg

Kentaro NomuraU. Of Texas

Ewelina HankiewiczU. of MissouriTexas A&M U.

Mario BorundaTexas A&M U.

Nikolai SinitsynTexas A&M U.

U. of Texas

Other collaborators: Bernd Kästner, Satofumi Souma, Liviu Zarbo, Dimitri Culcer , Qian Niu, S-Q Shen, Brian

Gallagher, Tom Fox, Richard Campton, Winfried Teizer, Artem Abanov

Sergio RodriguezTexas A&M U.

Xin LiuTexas A&M U.

Alexey KovalevTexas A&M U.

OUTLINEOUTLINE From electronics to spintronics:From electronics to spintronics:

Electron multipersonality: using the charge and using the Electron multipersonality: using the charge and using the spinspin

Success stories of metal based spintronicsSuccess stories of metal based spintronics Why semiconductor spintronics may be betterWhy semiconductor spintronics may be better Spin-orbit coupling: the necessary evilSpin-orbit coupling: the necessary evil The usual example: Das-Datta transistorThe usual example: Das-Datta transistor

Spin-Hall effect: Spin-Hall effect: Normal and anomalous Hall effect and Spin Hall effect Normal and anomalous Hall effect and Spin Hall effect

Three contributions to the AHEThree contributions to the AHE Turbulent history of the AHETurbulent history of the AHE Recent focus on the intrinsic AHERecent focus on the intrinsic AHE Application to the SHEApplication to the SHE Short but turbulent history of the SHEShort but turbulent history of the SHE

SHE experimentsSHE experiments Resolution of some of the controversyResolution of some of the controversy Spin Hall spin accumulationSpin Hall spin accumulation Theory challengesTheory challenges Experimental challengesExperimental challenges

ELECTRONICSELECTRONICS

UP TO NOW: all electronics are mostly basedon the manipulation of the charge of the electron so perhaps we should say “charge electronics”

Mr. Electron Two parts to hispersonality !

CHARGE

SPIN

SPINTRONICS: manipulate spin SPINTRONICS: manipulate spin and charge simultaneouslyand charge simultaneously

What is What is spintronics?spintronics?

Using the chargeUsing the charge

substrate

semiconductor

insulatorS Dgate

Vg

thin free charge carrierchannel induced by

electric field from gate

- - - - - -

>0

High mobility 2DEG: IQHE, FQHE, MIT, etc.

ALL computers have thesetransistors in one form or another

HIGH tunablity of electronic transportproperties the key to FET success in processing technology

the field effect transistor:the field effect transistor: work horse of information work horse of information processingprocessing

Using the spinUsing the spin

ferromagnetism:ferromagnetism: work horse of information work horse of information storingstoring

1st generation spintronic devices based on ferromagnetic metals: GMR– already in every computer

GMR allowed read-out heads in hard drives to be MUCH smaller

Magnetic tunneling junction (MTJ) or “spin valve” Nonvolatile MRAM: “Microchips that never forget ”

Compatibility with Si and GaAs next phase: semiconductor spintronics, a marriage of convenience!!!

A brighter future with semiconductor spintronicsA brighter future with semiconductor spintronics

MORE KNOBS = MORE PHYSICS

Can do what metals doCan do what metals do- GMR, TMR in diluted magnetic semi-cond., spin transfer,

etc.

Easy integration with semiconductor devicesEasy integration with semiconductor devices- possible way around impedance mismatch for spin

injection.

More tunable systemsMore tunable systems

- transport propertiestransport properties: carrier concentration is tuned by gates and chemical doping

- ferromagnetic state affected by carrier concentration (DMS) - optical control of non-equilibrium populations

Possibility of new physical regimes/effectsPossibility of new physical regimes/effects- TAMR - tunable spin-orbit couplingspin-orbit coupling

Necessities in performing Necessities in performing spintronics in semiconductorsspintronics in semiconductors

Spin-generation: “spin battery”Spin-generation: “spin battery” - injection (conventional)- optical, via selection rules (excitation with circular polarized light)- via SO coupling (e.g., occupation-asymmetry in k-space, Spin Hall

effect)Spin-manipulation- external magnetic field- via SO coupling (e.g. Datta Das Spin-transistor)

Spin-detection: “spin meter”- Magnetoresistive measurement (conventional) - optical, via selection rules (Spin LED)- via SO coupling (e.g., anomalous Hall effect)

Spin-orbit coupling interactionSpin-orbit coupling interaction

(one of the few echoes of relativistic physics in the solid state)(one of the few echoes of relativistic physics in the solid state)

Ingredients: -“Impurity” potential V(r)

- Motion of an electron

)(1

rVe

E

Producesan electric field

In the rest frame of an electronthe electric field generates and effective magnetic field

Ecm

kBeff

This gives an effective interaction with the electron’s magnetic moment

LSdr

rdV

err

mc

k

mc

SeBeffH SO

)(1

CONSEQUENCES•If part of the full Hamiltonian quantization axis of the spin now

depends on the momentum of the electron !! •If treated as scattering the electron gets scattered to the left or to

the right depending on its spin!!

Using SO: Datta-Das spin FET

V

- vBeff

- vBeff

-v

Beff

V/2

Datta-Das spin FET: the Datta-Das spin FET: the moviemovie

Movie created by Mario Borunda







SPIN HALL EFFECTSPIN HALL EFFECTA NEW TWIST ON AN OLD HATA NEW TWIST ON AN OLD HAT

References:N. A. Sinitsyn, J.E. Hill, Hongki Ming, Jairo Sinova, and A. H. MacDonald, Phys. Rev. Lett. 97, 106804 (2006)

Jairo Sinova, Shuichi Murakami, S.-Q. Shen, Mahn-Soo Choi, Solid State Comm. 138, 214 (2006).K. Nomura, J. Wunderlich, Jairo Sinova, B. Kaestner, A.H. MacDonald, T. Jungwirth, Phys. Rev. B 96, 076804 (2006).

B. Kaestner, J. Wunderlich, Jairo Sinova, T. Jungwirth, Appl. Phys. Lett. 88, 091106 (2006).K. Nomura, Jairo Sinova, N.A. Sinitsyn, and A. H. MacDonald, Phys. Rev. B. 72, 165316 (2005).

E. M. Hankiewicz, Tomas Jungwirth, Qian Niu, Shun-Qing Shen, and Jairo Sinova, Phys. Rev. B.72, 155305 (2005).N.A. Sinitsyn, Qian Niu, Jairo Sinova, K. Nomura, Phys. Rev. B 72, 045346 (2005).

Branislav K. Nikolic, Satofumi Souma, Liviu P. Zarbo, Jairo Sinova, Phys. Rev. Lett. 95, 046601 (2005). Joerg Wunderlich, Bernd Kaestner, Jairo Sinova, Tomas Jungwirth, Phys. Rev. Lett. 94, 047204 (2005).K. Nomura, Jairo Sinova, T. Jungwirth, Q. Niu, A. H. MacDonald, Phys. Rev. B 71, 041304(R) (2005).E. M. Hankiewicz, L.W. Molenkamp, T. Jungwirth, and Jairo Sinova, Phys. Rev. B 70, 241301 (2004)N. A. Sinitsyn, E. H. Hankiewicz, Winfried Teizer, Jairo Sinova, Phys. Rev. B 70, 081212 (R), (2004).

D. Culcer, Jairo Sinova, N. A. Sinitsyn, T. Jungwirth, A.H. MacDonald, Qian Niu, Phys. Rev. Lett 93, 046602 (2004). Jairo Sinova, Dimitrie Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, A.H. MacDonald, Phys. Rev. Lett. 92, 126603 (2004).

Anomalous Hall effect: where things Anomalous Hall effect: where things started, the unresolved problemstarted, the unresolved problem

MπRBR sH 40

Simple electrical measurement Simple electrical measurement of magnetizationof magnetization

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

I

_ FSO

FSO

_ __

majority

minority

VInMnAs

controversial theoretically: three contributions to the AHE (intrinsic deflection, skew scattering, side jump scattering)

Intrinsic Intrinsic deflectiondeflection

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.


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)

Skew Skew scatteringscattering


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.

Side-jump Side-jump scatteringscattering


Related to the intrinsic effect: analogy to refraction from an imbedded medium

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.

(thanks to P. Bruno– CESAM talk)

A history of controversy

THE THREE CONTRIBUTIONS TO THE AHE: THE THREE CONTRIBUTIONS TO THE AHE: MICROSCOPIC KUBO APPROACHMICROSCOPIC KUBO APPROACH

Skew scattering

Side-jump scattering

Intrinsic AHE: accelerating between scatterings

SkewσH

Skew (skew)-1 2~σ0 S where

S = Q(k,p)/Q(p,k) – 1~

V0 Im[<k|q><q|p><p|k>]

Vertex Corrections σIntrinsic

Intrinsicσ0 /εF

n, q

n, q m, p

m, pn’, k

n, q

n’n, q

FOCUS ON INTRINSIC AHE: semiclassical and KuboFOCUS ON INTRINSIC AHE: semiclassical and Kubo

K. Ohgushi, et al PRB 62, R6065 (2000); T. Jungwirth et al PRL 88, 7208 (2002);T. Jungwirth et al. Appl. Phys. Lett. 83, 320 (2003); M. Onoda et al J. Phys. Soc. Jpn. 71, 19 (2002); Z. Fang, et al, Science 302, 92 (2003).

'

2

'

'

2

)(

'ˆˆ'Im]Re[

nnk knkn

yx

nkknxy EE

knvknknvknff

V

e

nk

nknxy kfV

e

)(]Re[ '

2

Semiclassical approach in the “clean limit”

Kubo:

n, q

n’n, q

STRATEGY: compute this contribution in strongly SO coupled ferromagnets and compare to experimental results, does it work?

Success of intrinsic AHE approach in Success of intrinsic AHE approach in comparing to experiment: comparing to experiment: phenomenological “proof”phenomenological “proof”• DMS systems (Jungwirth et al PRL 2002, APL 03)

• Fe (Yao et al PRL 04)• layered 2D ferromagnets such as SrRuO3 and

pyrochlore ferromagnets [Onoda and Nagaosa, J. Phys. Soc. Jap. 71, 19 (2001),Taguchi et al., Science 291, 2573 (2001), Fang et al Science 302, 92 (2003), Shindou and Nagaosa, Phys. Rev. Lett. 87, 116801 (2001)]

• colossal magnetoresistance of manganites, Ye et~al Phys. Rev. Lett. 83, 3737 (1999).

• CuCrSeBr compounts, Lee et al, Science 303, 1647 (2004)

Berry’s phase based AHE effect is quantitative-successful in many instances BUT still not a theory that treats systematically intrinsic and extrinsic contribution in an equal footing AND supposedly equivalent theories

give different results when disorder is incorporated.

Experiment AH 1000

(cm)-1

TheroyAH 750 (cm)-1

Spin Hall effectSpin Hall effect

Take now a PARAMAGNET instead of a FERROMAGNET: 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 accumulationSpin accumulation without charge accumulationexcludes simple electrical detectionexcludes simple electrical detection

Carriers with same charge but opposite spin are deflected by the spin-orbit coupling to opposite sides.

Spin Hall Effect(Dyaknov and Perel)

InterbandCoherent Response

(EF) 0

Occupation # Response

`Skew Scattering‘(e2/h) kF (EF )1

X `Skewness’

[Hirsch, S.F. Zhang] Intrinsic

`Berry Phase’(e2/h) kF

[Murakami et al,

Sinova et al]

Influence of Disorder`Side Jump’’

[Inoue et al, Misckenko et al, Chalaev et al…] Paramagnets

INTRINSIC SPIN-HALL EFFECT: INTRINSIC SPIN-HALL EFFECT: Murakami et al Science 2003 (cond-mat/0308167)

Sinova et al PRL 2004 (cont-mat/0307663)

as there is an intrinsic AHE (e.g. Diluted magnetic semiconductors), there should be an intrinsic spin-Hall

effect!!!

km

kkk

m

kH xyyxk

0

22

0

22

2)(

2

Inversion symmetry no R-SO

Broken inversion symmetry R-SO

Bychkov and Rashba (1984)

(differences: spin is a non-conserved quantity, define spin current as the gradient term of the continuity equation. Spin-Hall conductivity: linear response of this operator)

n, q

n’n, q

‘‘Universal’ spin-Hall conductivityUniversal’ spin-Hall conductivity

*22*

2

2

4

22*22

sH

for8

for8

DDD

D

DD

xy

nnn

ne

mnn

e

Color plot of spin-Hall conductivity:yellow=e/8π and red=0

n, q

n’n, q

SHE conductivity: all contributions– Kubo formalism perturbation theory

Skewσ0 S

Vertex Corrections σIntrinsic

Intrinsicσ0 /εF

n, q

n’n, q

= j = -e v

= jz = {v,sz}

Disorder effects: beyond the finite Disorder effects: beyond the finite lifetime approximation for Rashba lifetime approximation for Rashba

2DEG2DEGQuestion: Are there any other major effects beyond

the finite life time broadening? Does side jump contribute significantly?

Ladder partial sum vertex correction:

Inoue et al PRB 04Raimondi et al PRB 04Mishchenko et al PRL 04Loss et al, PRB 05

~

the vertex corrections are zero for 3D hole systems (Murakami 04) and 2DHG (Bernevig and Zhang 05)

n, q

n’n, q

+ +…=0

For the Rashba example the side jump contribution cancels the intrinsic contribution!!

k1 Rashba: g=constant α = 1 k3 Rashba: g=constant α = 3

Nomura et al. PRB 06

2DEG+Rahsba

2DHG+Rahsba

For these models one can do the exact calculations numerically: testing the perturbation theory

4.6

k^3 Rashba model k^1 Rashba model

Numerical results for SHE conductivities Numerical results for SHE conductivities in 2D electrons and in 2D holesin 2D electrons and in 2D holes

iEE

njnnjn

EE

EfEf

V

i

nnnn

nn

nn

''

'

',

||''||)()(

2D electron+Rashba 2D holes+Rashba

Prediction: one should observe strong intrinsic SHE in 2D hole systems

Nomura et al PRB 05







First experimentalFirst experimental observations at the end of 2004observations at the end of 2004

Wunderlich, Kästner, Sinova, Jungwirth, cond-mat/0410295PRL 05

Experimental observation of the spin-Hall effect in a two dimensional spin-orbit coupled semiconductor system

Co-planar spin LED in GaAs 2D hole gas: ~1% polarization Co-planar spin LED in GaAs 2D hole gas: ~1% polarization

-1

0

1

CP

[%]

Light frequency (eV)1.505 1.52

Kato, Myars, Gossard, Awschalom, Science Nov 04

Observation of the spin Hall effect bulk in semiconductors

Local Kerr effect in n-type GaAs and InGaAs: Local Kerr effect in n-type GaAs and InGaAs: ~0.03% polarization ~0.03% polarization (weaker SO-coupling, stronger disorder)(weaker SO-coupling, stronger disorder)

p -AlG a As

i-G a As

n- -d o p e d AlG a As

e tc he d

QW

I

Top Emission

Side Emission

Electrode

Spin polarization detected through circular polarization of emitted lightSpin polarization detected through circular polarization of emitted light

ConventionalConventional vertical spin-LEDvertical spin-LED Novel dual Novel dual co-planar spin-LEDco-planar spin-LED

Y. Ohno: Nature 402, 790 (1999) R. Fiederling: Nature 402, 787 (1999)

● SHE in 2DHG with strong and tunable SO● SHE detected directly in the 2DHG● Light emission near edge of the 2DHG● No hetero-interface along the LED current

2DHG2DHG

2DEG2DEG

How our experiment worked: creating a spin-meter at edges

1 .5 mc h a n n e l

n

n

py

xz

L E D 1

L E D 2

I P+Ip

E [eV]

a

-1

0

1

LED 1

-Ip

CP

[%]

a

Opposite perpendicular polarization for opposite Opposite perpendicular polarization for opposite IIpp currents currents

or opposite edges or opposite edges SPIN HALL EFFECT SPIN HALL EFFECT

xy

zIp

-Ip

ILED 1

Experiment “A”

xy

zIpILED 1

ILED 2

Experiment “B”

1.505 1.510 1.515 1.520

-1

0

1

+Ip LED 1

LED 2b

CP

[%]

OTHER RECENT EXPERIMENTS

“demonstrate that the observed spin accumulation is due to a transverse bulk electron spin current”

Sih et al, Nature 05, PRL 05

Valenzuela and Tinkham cond-mat/0605423, Nature 06

Transport observation of the SHE by spin injection!!

Saitoh et al APL 06

Next: solving some of the SHE Next: solving some of the SHE controversycontroversy

• Does the SHE conductivity vanish due to scattering? Seems to be the case in 2DRG+Rashba,

does not for any other system studied

• Dissipationless vs. dissipative transport

• Is the SHE non-zero in the mesoscopic regime?

• What is the best definition of spin-current to relate spin-conductivity to spin accumulation

•……

APCTP Workshop on Semiconductor APCTP Workshop on Semiconductor Nano-Spintronics: Spin-Hall Effect and Related IssuesNano-Spintronics: Spin-Hall Effect and Related Issues

August 8-11, 2005 APCTP, Pohang, Korea August 8-11, 2005 APCTP, Pohang, Korea

http://faculty.physics.tamu.edu/sinova/SHE_workshop_APCTP_05.html

A COMMUNITY WILLING TO WORK TOGETHER

Semantics agreement:The intrinsic contribution to the spin Hall conductivity is the spin Hall conductivity in the

limit of strong spin orbit coupling and >>1. This is equivalent to the single bubble contribution to the Hall conductivity in the weakly scattering regime.

General agreement•The spin Hall conductivity in a 2DEG with Rashba coupling vanishes in the absence of a magnetic field and spin-dependent scattering. The intrinsic contribution to the spin Hall conductivity is identically cancelled by scattering (even weak scattering). This unique feature of this model can be traced back to the specific spin dynamics relating the rate of change of the spin and the spin current directly induced, forcing such a spin current to vanish in a steady non-equilibrium situation.

•The cancellation observed in the 2DEG Rashba model is particular to this model and in general the intrinsic and extrinsic contributions are non-zero in all the other models studied so far. In particular, the vertex corrections to the spin-Hall conductivity vanish for p-doped models.

The new challenge: understanding spin accumulation

Spin is not conserved; analogy with e-h system

Burkov et al. PRB 70 (2004)

Spin diffusion length

Quasi-equilibrium

Parallel conduction

Spin Accumulation – Weak SO

Spin Accumulation – Strong SO

Mean FreePath?

Spin Precession

Length

?

SPIN ACCUMULATION IN 2DHG: EXACT DIAGONALIZATION

STUDIES

so>>ħ/

Width>>mean free path

Nomura, Wundrelich et al PRB 06

Key length: spin precession length!!Independent of !!

-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

%

1.5mchannel

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

Theoretical achievements:

Theoretical challenges:GUT the bulk (beyond simple graphene)

intrinsic + extrinsic SHE+AHE+AMR

Obtain the same results for different equivalent approaches (Keldysh and Kubo must agree)

Othersmaterials and defectscoupling with the latticeeffects of interactions (spin Coulomb drag)spin accumulation -> SHE conductivity

Intrinsic SHEback to the beginning on a higher level

2003 2006Extrinsic SHE

approx microscopic modelingExtrinsic + intrinsic AHE in graphene:

two approaches with the same answer

WHERE WE ARE GOING (THEORY)

Experimental achievements

Experimental (and experiment modeling) challenges:

Photoluminescence cross sectionedge electric field vs. SHE induced spin accumulationfree vs. defect bound recombinationspin accumulation vs. repopulationangle-dependent luminescence (top vs. side emission)hot electron theory of extrinsic experiments

Optical detection of current-induced polarizationphotoluminescence (bulk and edge 2DHG)Kerr/Faraday rotation (3D bulk and edge, 2DEG)

Transport detection of the SHE

Generaledge electric field (Edelstein) vs. SHE induced spin accumulation

SHE detection at finite frequenciesdetection of the effect in the “clean” limit

WHERE WE ARE GOING (EXPERIMENTS)

Branislav NikolicU. of DelawareAllan MacDonald

U of Texas

Tomas JungwirthInst. of Phys. ASCR

U. of Nottingham

Joerg WunderlichCambridge-Hitachi

Laurens MolenkampWuerzburg

Kentaro NomuraU. Of Texas

Ewelina HankiewiczU. of MissouriTexas A&M U.

Mario BorundaTexas A&M U.

Nikolai SinitsynTexas A&M U.

U. of Texas

Other collaborators: Bernd Kästner, Satofumi Souma, Liviu Zarbo, Dimitri Culcer , Qian Niu, S-Q Shen, Brian Gallagher, Tom Fox, Richard Campton, Winfried Teizer, Artem Abanov

Sergio RodriguezTexas A&M U.

Xin LiuTexas A&M U.

Alexey KovalevTexas A&M U.

NERC

2D spin-LED

2DHG 2DEG 2DHG

2DEG VT

VD

Light emitted comes from Type II recombination processes: 3D electrons with 2D holes. 3D electrons have an asymmetric momentum space population (e.g. ky>0)

Measurement of 2DHG Rashba

splitting

Spin-Hall effect measrement

Sub GaAs gap spectra analysis: EL vs PLSub GaAs gap spectra analysis: EL vs PL

X : bulk GaAs excitons

I : recombinationwith impurity states

1.48 1.49 1.50 1.51 1.520

2

4

6

8

10

0

2

4

6

8

10

Wafer 1

0 -50 -100 -150-2

-1

0

1

2

Wafer 2

Int [a.u

.]

E [eV]

E [

eV]

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]

a

b

c

d

I

X

I

X

A

A

A

A

B

B

B

B

C

C

PLEL

p-AlGaAs

GaAs

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

2D hole 2D hole recombinationrecombination

OUTLINEOUTLINE Metal and semiconductor based spintronicsMetal and semiconductor based spintronics Spin-orbit coupling in semiconducting systemsSpin-orbit coupling in semiconducting systems Hall effect, Anomalous Hall effect, and Spin Hall Hall effect, Anomalous Hall effect, and Spin Hall

effecteffect Ordinary and quantum Hall effectOrdinary and quantum Hall effect Anomalous Hall effect and spin Hall effect (SHE)Anomalous Hall effect and spin Hall effect (SHE) Intrinsic SHE in Rashba SO couple systems Intrinsic SHE in Rashba SO couple systems

Optical detection of the polarizationOptical detection of the polarization Our measuring technique: LED probe of Our measuring technique: LED probe of

polarizationpolarization Lateral 2DEG-2DHG junctionLateral 2DEG-2DHG junction Comparison of electro-luminescence and photo-Comparison of electro-luminescence and photo-

luminescenceluminescence Measurement of the SO splitting: in-plane Measurement of the SO splitting: in-plane

polarization through asymmetric recombinationpolarization through asymmetric recombination SHE measurementSHE measurement Conclusions and outlookConclusions and outlook

Light polarization due to recombination with SO-split Light polarization due to recombination with SO-split hole-subband in a p-n LED under hole-subband in a p-n LED under forwardforward bias 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--

<s<szz>>HHHH++

<S

>

ky [nm-1]

spin-polarization of HH+ and HH- subbands

in-planein-plane polarization

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

circular polarization of emitted light

Microscopic band-structure calculations of the 2DHG:

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

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

1.500 1.505-20

-10

0

10

20

Bz = +3T

Bz = -3T-10

-5

0

5

10

Bx = +3T

Bx = -3T

E [eV]-3 -2 -1 0 1 2 3

xy

z , B

xy

z , B

B [T]

x, By

z

x, By

z

x, By

α

x, By

z

x, By

z

x, By

x, By

z

x, By

z

x, By

z

x, By

α

CP

[%]

1.500 1.505-20

-10

0

10

20

Bz = +3T

Bz = -3T-10

-5

0

5

10

Bx = +3T

Bx = -3T

E [eV]-3 -2 -1 0 1 2 3

xy

z , B

xy

z , B

B [T]

x, By

z

x, By

z

x, By

α

x, By

z

x, By

z

x, By

x, By

z

x, By

z

x, By

z

x, By

α

CP

[%]

In-plane

detection angle/polarization

Perp.-to plane

detection angle/polarization

20m

n

p Jun

ction

y

xz

20m

n

p Jun

ction

y

xz

Documents

SPIN-HALL EFFECT a new adventure in condensed matter physics San Houston State University, January 22 th 2008 JAIRO SINOVA Research fueled by: NERC