(1) Hitachi Cambridge Laboratory, UK

(2) National Physical Laboratory, UK

(3) Texas A&M University, USA

(4) Institute of Physics ASCR, Czech Republic

(5) University of Nottingham, UK

J. Wunderlich(1), B. Kästner(1,2), J. Sinova (3), T. Jungwirth (4,5)

Spin Hall effectSpin Hall effect

Collaborators: Allan MacDonald, Dimitri Culcer, Ewelina Hankeiwc, Qian Niu, Kentaro Nomura, Nikolai Sinitsyn, Laurens Molenkamp, Winfried

Teizer

Entin-Wohlman:2005_a O. Entin-Wohlman, A. Aharony, Y. M. Galperin, V. I. Kozub, and V. Vinokur, "Orbital ac spin-Hall effect in the hopping regime", (2005), preprint cond-mat/0502478: on-line

Liu:2005_a S. Y. Liu and X. L. Lei, "Vanishing of the Dissipationless Spin Hall Effect in a Diffusive Two-Dimensional Electron Gas with Spin-Orbit Coupling", (2005), preprint cond-mat/0502392: on-line

Yao:2005_a Y. Yao, and Z. Fang, "Intrinsic Spin Hall Effect in Semiconductors and Simple Metals: First-Principles Calculations", (2005), preprint cond-mat/0502351: on-line

Bernevig:2005_a B. Andrei Bernevig, Taylor L. Hughes, Shou-Cheng Zhang, "Orbitronics: the Intrinsic Orbital Hall Effect in p-Doped Silicon", (2005), preprint cond-mat/0502345: on-line

Li:2005_a Jian Li, Liangbin Hu, and Shun-Qing Shen, "Spin resolved Hall effect driven by spin-orbit couplin", (2005), preprint cond-mat/0502102: on-line

Hu:2005_a Jiangping Hu, "Spin Polarization and Dichroism Effects by Electric Field", (2005), preprint cond-mat/0502005: on-line

Lou:2005_a Ping Lou and Tao Xiang, "Spin Hall current and two-dimensional magnetic monopole in a Corbino disk", (2005), preprint cond-mat/0501307: on-line

Nikolic:2004_b Nikolic et al., "Non-Equilibrium Spin Accumulation due to the Spin Hall Effect in Mesoscopic Two-Probe Ballistic Spin-Orbit ", (2004), preprint cond-mat/0412595: on-line

Bernevig:2004_e B. Andrei Bernevig and Shou-Cheng Zhang, "Intrinsic Spin-Hall Effect in n-Doped Bulk GaAs", (2004), preprint cond-mat/0412550: on-line

Kou:2004_a Su-Peng Kou, Xiao-Liang Qi, and Zheng-Yu Weng, "Conserved Dissipationless Spin Currents in a Doped Mott Insulator", (2004), preprint cond-mat/0412146: on-line

Mele:2004_a C.L. Kane and E.J. Mele, "Quantum Spin Hall Effect in Graphene", (2004), preprint cond-mat/0411737: on-line

Bernevig:2004_d B. Andrei Bernevig, Xiaowei Yu, Shou-Cheng Zhang, "Maxwell Equation for the Coupled Spin-Charge Wave Propagation", (2004), preprint cond-mat/0411276: on-line

Sun:2004_a Qing-feng Sun, Jian Wang, Hong Guo, "Quantum transport theory for nanostructures with Rashba spin-orbital interaction", (2004), preprint cond-mat/0411469: on-line

Shekhter:2004_a A. Shekhter, et al., "Chiral spin resonance and spin-Hall conductivity in the presence of the electron-electron interactions", (2004), preprint cond-mat/0411239: on-line

Serebrennikov:2004_a Yuri A. Serebrennikov, "Gometric spin dephasing of carriers with strong spin-orbit coupling", (2004), preprint cond-mat/0411683: on-line

Chang:2004_a Ming-Che Chang, "The effect of in-plane magnetic field on the spin Hall effect in Rashba-Dresselhaus system", (2004), preprint cond-mat/cond-mat/0411697: on-line

Liu:2004_d S. Y. Liu, X. L. Lei, "Spin Hall Effect in a Diffusive Rashba Two-dimensional Electron Gas", (2004), preprint cond-mat/0411629: on-line

Bernevig:2004_c B. Andrei Bernevig and Shou-Cheng Zhang, "Intrinsic Spin Hall Effect in the Two Dimensional Hole Gas", (2004), preprint cond-mat/0411457: on-line

Mal'shukov:2004_a A.G. Mal'shukov and K.A. Chao, "Spin-Hall conductivity of a disordered 2D electron gas with Dresselhaus spin-orbit interaction", (2004), preprint cond-mat/0410607: on-line

Souma:2004_a Satofumi Souma and Branislav K. Nikolic, "Spin Hall Current Driven by Quantum Interferences in Mesoscopic Rashba Rings", (2004), preprint cond-mat/0410716: on-line

Shen:2004_b Shun-Qing Shen, et al., "Resonant spin Hall conductance in quantum Hall systems lacking bulk and structural inversion symmetry", (2004), preprint cond-mat/0410169: on-line

Sheng:2004_a L. Sheng, D. N. Sheng, and C. S. Ting, "Spin-Hall Effect in Two-Dimensional Electron Systems with Rashba Spin-Orbit Coupling and Disorder", (2004), preprint cond-mat/0409038: on-line

Nikolic:2004_a Branislav K. Nikolic, Liviu P. Zarbo, and Satofumi Souma, "Mesoscopic Spin Hall Effect in Multiprobe Semiconductor Bridges", (2004), preprint cond-mat/0408693: on-line

SHE - TheorySHE - Theory (http://unix12.fzu.cz/msnew)

Bernevig:2004_b B. Andrei Bernevig and Shou-Cheng Zhang, "Spin Splitting and Spin Current in Strained Bulk Semiconductors", (2004), preprint cond-mat/0408442: on-line

Khaetskii:2004_a Alexander Khaetskii, "Nonexistence of intrinsic spin currents", (2004), preprint cond-mat/0408136: on-line

Rashba:2004_c Emmanuel I. Rashba, "Spin Dynamics and Spin Transport", (2004), preprint cond-mat/0408119: on-line

Wang:2004_b Xindong Wang and X.-G. Zhang, "Spin symmetry and spin current of helicity eigenstates of the Luttinger Hamiltonian", (2004), preprint cond-mat/0407699: on-line

Dimitrova:2004_b Ol'ga V. Dimitrova, "Spin-Hall Conductivity and Pauli Susceptibility in the Presence of Electron-Electron Interactions", (2004), preprint cond-mat/0407612: on-line

Chalaev:2004_a Oleg Chalaev, Daniel Loss, "Spin-Hall conductivity due to Rashba spin-orbit interaction in disordered systems", (2004), preprint cond-mat/0407342: on-line

Schmeltzer:2004_a D. Schmeltzer, "Topological spin current", (2004), preprint cond-mat/0406565: on-line

Zhang:2004_a Ping Zhang and Qian Niu, "Charge-Hall effect driven by spin force: reciprocal of the spin-Hall effect", (2004), preprint cond-mat/0406436: on-line

Dimitrova:2004_a Ol'ga V. Dimitrova, "Universal value of Spin-Hall Conductivity of 2D Rashba metal with impurities", (2004), preprint cond-mat/0405339: on-line

Murakami:2004_a Shuichi Murakami, "Spin Hall Effect in p-type Semiconductors", (2004), preprint cond-mat/0405003: on-line

Xiong:2004_a Ye Xiong and X.C. Xie, "Spin Hall Conductance in Disordered Two-Dimensional Electron Systems", (2004), preprint cond-mat/0403083: on-line

Dyakonov:2004_a M. I. Dyakonov, "Spintronics?", (2004), preprint cond-mat/0401369: on-line

-------- 2005 --------Raimondi:2004_a

Roberto Raimondi and Peter Schwab, "Spin-Hall effect in a disordered 2D electron-system", Phys. Rev. B 71, 033311 (2005): on-line, preprint cond-mat/0408233: on-lineZhang:2004_b

S. Zhang and Z. Yang, "Intrinsic Spin and Orbital-Angular-Momentum Hall Effect", Phys. Rev. Lett. 94, 066602 (2005): on-line, preprint cond-mat/0407704: on-lineNomura:2004_a

K. Nomura, et al., "Non-vanishing spin Hall currents in disordered spin-orbit coupling systems", Phys. Rev. B 71, 041304 (2005): on-line, preprint cond-mat/0407279: on-lineSchliemann:2004_a

John Schliemann, Daniel Loss, "Spin-Hall transport of heavy holes in III-V semiconductor quantum wells", Phys. Rev. B 71, 085308 (2005): on-line, preprint cond-mat/0405436: on-line-------- 2004 --------Rashba:2004_d

Emmanuel I. Rashba, "Sum rules for spin-Hall conductivity cancelation", Physica B 70, 201309(R) (2004): on-line, preprint cond-mat/0409476: on-lineHankiewicz:2004_b

E. M. Hankiewicz, et al., "Manifestation of the spin-Hall effect through transport measurements in the mesoscopic regime", Phys. Rev. B 70, 241301(R) (2004): on-line, Ma:2004_a

Xiaohua Ma, et al., "Influences of spin accumulation on the intrinsic spin Hall effect in two dimensional electron gases with Rashba spin-orbit coupling", Phys. Rev. B 70, 195343 (2004): on-line, Mishchenko:2004_a

E.G. Mishchenko, et al., "Spin current and polarization in impure 2D electron systems with spin-orbit coupling", Phys. Rev. Lett. 93, 226602 (2004): on-line, preprint cond-mat/0406730: on-lineBernevig:2004_a

B. A. Bernevig, "On the nature of spin currents", Phys. Rev. B 71, 073201 (2004): on-line, preprint cond-mat/0406153: on-lineMurakami:2004_b

Shuichi Murakami, Naoto Nagaosa, Shou-Cheng Zhang, "Spin Hall Insulator", Phys. Rev. Lett. 93, 156804 (2004): on-line, preprint cond-mat/0406001: on-line

Lee:2004_a Wei-Li Lee, et al., "Dissipationless Anomalous Hall Current in the Ferromagnetic Spinel CuCr2Se4-xBrx", Science 303, 1647 (2004): on-line, preprint cond-mat/0405584: on-line

Zutic:2004_a Igor Zutic, Jaroslav Fabian and S. Das Sarma, "Spintronics: Fundamentals and applications", Rev. Mod. Phys. 76, 323 (2004): on-line, preprint cond-mat/0405528: on-line

Murakam:2004_a Shuichi Murakami, "Absence of vertex correction for the spin Hall effect in p-type semiconductors", Phys. Rev. B 69, 241202 (2004): on-line, preprint cond-mat/0405001: on-line

Rashba:2004_b Emmanuel I. Rashba, "Spin currents, spin populations, and dielectric function", Phys. Rev. B 70, 161201 (2004): on-line, preprint cond-mat/0404723: on-line

Shen:2004_a Shun-Qing Shen, et al., "Resonant Spin Hall Conductance in Two-Dimensional Electron Systems with Rashba Interaction in a Magnetic Field", Phys. Rev. Lett 92, 256603 (2004): on-line,

Inoue:2004_a Jun-ichiro Inoue, et al., "Suppression of the Persistent Spin Hall Current by Defect Scattering", Phys. Rev. B 70, 041303 (2004): on-line, preprint cond-mat/0402442: on-line

Hu:2004_a Liangbin Hu, et al., "Effects of spin imbalance on the electric-field-driven quantum dissipationless spin current in p-doped semiconductors", Phys. Rev. B 70, 235323 (2004): on-line,

Bernevig:2003_a Bogdan et al., "Dissipationless spin current in anisotropic p-doped semiconductors", Phys. Rev. B 70, 113301 (2004): on-line, preprint cond-mat/0311024: on-line

Shen:2003_a Shun-Qing Shen, "Spin Hall effect and Berry phase in two dimensional electron gas", Phys. Rev. B 70, 081311 (2004): on-line, preprint cond-mat/0310368: on-line

Sinitsyn:2003_a N. A. Sinitsyn, et al., "Spin-Hall and spin-diagonal conductivity in the presence of Rashba and Dresselhaus spin-orbit coupling", Phys. Rev. B 70, 081312(R) (2004): on-line,

Schliemann:2004_b John Schliemann and Daniel Loss, "Dissipation effects in spin-Hall transport of electrons and holes", Phys. Rev. B 69, 165315 (2004): on-line, preprint cond-mat/0310108: on-line

Culcer:2004_a Dimitrie Culcer, et al., "Semiclassical theory of spin transport in spin-orbit coupled systems", Phys. Rev. Lett. 93, 046602 (2004): on-line, preprint cond-mat/0309475: on-line

-------- 2003 --------Rashba:2003_a

Emmanuel I. Rashba, "Spin currents in thermodynamic equilibrium: The challenge of discerning transport currents", Phys. Rev. B 68, 241315 (2003): on-lineCulcer:2003_a

Dimitrie Culcer, Allan MacDonald, Qian Niu, "Anomalous Hall effect in paramagnetic two dimensional systems", Phys. Rev. B 68, 045327 (2003): on-line, preprint cond-mat/0311147: on-lineHu:2003_a

Jiangping Hu, Bogdan A. Bernevig and Congjun Wu, "Spin current in spin-orbit coupling systems", Int. J. Mod. Phys. B 17, 5991 (2003), preprint cond-mat/0310093: on-lineMurakami:2003_b

Shuichi Murakami, et al., "SU(2) Non-Abelian holonomy and dissipationless spin current in semiconductors", Phys. Rev. B B 69, 235206 (2003): on-line, preprint cond-mat/0310005: on-lineSinova:2004_a

Jairo Sinova, et al., "Universal Intrinsic Spin-Hall Effect", Phys. Rev. Lett. 92, 126603 (2004): on-line, preprint cond-mat/0307663: on-lineMurakami:2003_a

Shuichi Murakami, Naoto Nagaosa, Shou-Cheng Zhang, "Dissipationless Quantum Spin Current at Room Temperature", Science 301, 1348 (2003): on-line, preprint cond-mat/0308167: on-line--------

Covered by T.J.

Wunderlich:2004_a J. Wunderlich, et al. "Experimental observation of the spin-Hall effect in a two dimensional spin-orbit coupled semiconductor system", Phys. Rev. Lett. 94, 047204 (2005):

preprint cond-mat/0410295: on-line

Kato:2004_d Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, "Observation of the Spin Hall Effect in Semiconductors", Science 306, 1910 (2004): on-line

SHE - ExperimentSHE - Experiment (http://unix12.fzu.cz/msnew)

Covered by J.W.

OUTLINE:OUTLINE:

- Theory remarks

- Comments on experiments

Kerr microscope

[Kato et. al., Science 306, 1910]

np10 µm

Co-planar spin LED

[Wunderlich et. al., Phys. Rev. Lett. 94, 047204]

SHE in a 2Dhole gas

SHE in a bulksemiconductor

Ordinary and quantum Hall effectsOrdinary and quantum Hall effects

Ordinary: Sign and density ofSign and density ofcarriers; holes in SCcarriers; holes in SC

Quantum Resistance standard;Resistance standard;fractional-charge carriersfractional-charge carriers

B

V

I

_

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

_ _ _ _ _ _ _ _ _ _ FL

Lorentz force deflect like-chargelike-charge particles

Anomalous Hall effectAnomalous Hall effect

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

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

Ingredients: - potential V(r)

- motion of an electron

Producesan electric field

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

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

E

E

Beff

k

Spin-orbit coupling Spin-orbit coupling (relativistic effect)

effSO BμH

)(1

rVe

E

Ecm

kBeff

(r)Vkcm

sH imp22

2

SO

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

skewscattering

If only this SO effect then much too weak to give a sizable SHE/AHE

lsdr

rdV

err

mc

k

mc

seBH effSO

)(1

l=0 for electrons weak SO

l=1 for holes strong SO

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

E

E

v

Enhanced in asymmetric QW

Intrinsic AHE approach explains many experimentsIntrinsic AHE approach explains many experiments

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

• Fe [Yao et al PRL 04]

• 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]

• Manganites, [Ye et al. PRL 99]

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

Experiment AH 1000 (cm)-1

TheroyAH 750 (cm)-1

Let’s start with a simple model: Rashba SO coupling in a 2DEGs

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

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

)kz(m2

k)kk(

m2

kH

22

xyyx

22

k

Inversion symmetry no R-SO

Broken inversion symmetry R-SO

[Bychkov and Rashba 84]

Classical dynamics in k-dependent (Rashba) field:

Heuristic argument: z-component of spin due to precession in effective "Zeeman" fieldHeuristic argument: z-component of spin due to precession in effective "Zeeman" field

xx eE

dt

dk),kz(

LLG equations for small drift adiabatic solution:

x

yy

)t()t(n

dt

d

dt

dnn y

x

yzx

x2

x

z eEn

Spin Hall conductivitySpin Hall conductivity

)pn(pd~j yp,z2

y,s

8/eE/j xy,ssH

Classical and Kubo formula give the same spin-Hall conductivityClassical and Kubo formula give the same spin-Hall conductivity

*D2D2*

D2

D2

4

22*

D2D2sHxy

nnforn

n

8

e

mnnfor

8

e

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

Disorder effects: finite lifetime (Born approximation) for Disorder effects: finite lifetime (Born approximation) for Rashba 2DEGRashba 2DEG

)/τ/(εF

/kFSO

)/(F intrinsic SHEintrinsic SHE

Disorder effects: Disorder effects: beyondbeyond the Born the Born approximation for Rashba 2DEGapproximation for Rashba 2DEG

Question: Are there any other major effects beyond the finite life time broadening? Can vertex corrections

be ignored?

Inoue, Bauer, Molenkamp PRB 04

Ladder sum vertex correction:

Mal'shukov et al, PRL 04Raimondi et al, PRB 04Khaetskii, cond-mat/0408136Loss et al, cond-mat/0407342 v2

0~

0sHxy

ExtrinsicExtrinsic too weak to give any sizable effect

IntrinsicIntrinsic cancelled by vertexcorrections for infinitely weakdisorder

Spin Hall effect ?Spin Hall effect ?

vertex corrections vanish in allvertex corrections vanish in all other studied SO-systems (bulk, 2DHG,..)other studied SO-systems (bulk, 2DHG,..)

- Skew scattering in SO-coupled bands - Skew scattering in SO-coupled bands not done yet

- Intrinsic SHE in Rashba-SO systems beyond - Intrinsic SHE in Rashba-SO systems beyond perturbation theory by solving Kubo formula exactly perturbation theory by solving Kubo formula exactly

inconclusive (finite-size effects) [Nomura et al. PRB '05]

- Other than Rashba-SO systems (intrinsic AHE explains experiments here)- Other than Rashba-SO systems (intrinsic AHE explains experiments here)

[Bernevig, Zhang, cond-mat/0411457,cond-mat/0412550

Ways to solve (go around) the controversy:Ways to solve (go around) the controversy:

- Look at transport in mesoscopic systems instead - Look at transport in mesoscopic systems instead of conductivity in the thermodynamic limit of conductivity in the thermodynamic limit

[Nikolic et al., cond-mat/0412595][Hankiewicz et al., PRB 04]

- Measure the effect- Measure the effect

Kato, Myars, Gossard, Awschalom, [Science 306, 1910]

"Observation of the spin Hall effect in semiconductors"

Local Kerr effect in n-type GaAs and InGaAs: ~0.03% polarization

Bulk semiconductor stronger disordern-type material weaker SO-coupling

/SO Not in the intrinsic SHE regimeNot in the intrinsic SHE regime

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

[%]

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 2

CP

[%]

Wunderlich, Kästner, Sinova, Jungwirth, [Phys. Rev. Lett. 94, 047204]

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

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

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

Self-consistent LDA & 6-band calculations for the [001] QW

Close to the intrinsic SHE regimeClose to the intrinsic SHE regime /SO

10 20 301

p2D [1011 cm-2]η

[m

eV]

2.5

1.5

0.5

5

9

S [e/8]/

Modulation doping weak disorder p-type asymmetric QW strong SO

A dissipationless remark ...A dissipationless remark ...

[Ganichev et al., cond-mat/0403641, Silov et al. APL 04]

Dissipative spin-polarized currents Dissipative spin-polarized currents in non-magnetic systems at B=0in non-magnetic systems at B=0

Spin-current is along the applied electric field proportional to

non-equilibriumnon-equilibrium distribution functiondistribution function

asymmetric scattering involving spin-flip

Dissipationless intrinsic spin Hall effectDissipationless intrinsic spin Hall effect

● ● Boltzman equation for current: transverse anomalous velocity in theBoltzman equation for current: transverse anomalous velocity in the equilibrium equilibrium band structure band structure due to combined due to combined EE and SO effects and SO effects Jungwirth, Niu, MacDonald, Phys. Rev. Lett. (2002)

Murakami, Nagaosa, Zhang, Science 301, 1348-1351 (2003).

Berry curvature: M.V. Berry, Proc. Royal Soc. London (1984)

anomalous velocity normal group velocity

● ● Heuristic argument: transverse spin current generatedHeuristic argument: transverse spin current generated between scattering events between scattering events

Sinova, Culcer, Niu, Sinitsyn, Jungwirth,

MacDonald, PRL 92, 126603 (2004)

CautionCaution: the dissipationless transverse intrinsic SHE is accompanied by a dissipative longitudinal responsedissipative longitudinal response to the electric field