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Spin Hall effect. J. Wunderlich (1) , B. Kästner (1,2) , J. Sinova (3) , T. Jungwirth (4,5). Hitachi Cambridge Laboratory, UK National Physical Laboratory, UK Texas A&M University, USA Institute of Physics ASCR, Czech Republic University of Nottingham, UK.

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slide1

Spin Hall effect

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

  • Hitachi Cambridge Laboratory, UK
  • National Physical Laboratory, UK
  • Texas A&M University, USA
  • Institute of Physics ASCR, Czech Republic
  • University of Nottingham, UK

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

slide2

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

  • 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
slide3

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-line
  • Zhang: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-line
  • Nomura: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-line
  • Schliemann: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-line
  • Hankiewicz: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-line
  • Bernevig:2004_a
    • B. A. Bernevig, "On the nature of spin currents", Phys. Rev. B 71, 073201 (2004): on-line, preprint cond-mat/0406153: on-line
  • Murakami: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
slide4

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

slide5

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

  • 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

Covered by J.W.

slide6

OUTLINE:

- Theory remarks

- Comments on experiments

Kerr microscope

Co-planar spin LED

SHE in a bulk

semiconductor

SHE in a 2D

hole gas

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

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

slide7

B

_ _ _ _ _ _ _ _ _ _

_

FL

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

I

V

Ordinary and quantum Hall effects

Lorentz force deflect like-charge particles

Quantum

Resistance standard;

fractional-charge carriers

Ordinary:

Sign and density of

carriers; holes in SC

slide8

majority

_

_

_

FSO

_

FSO

I

minority

V

Anomalous Hall effect

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

InMnAs

Simple electrical measurement

of magnetization

slide9

_

_

_

FSO

_

non-magnetic

FSO

I

V=0

Spin Hall effect

Spin-orbit coupling “force” deflects like-spinparticles

Spin-current generation in non-magnetic systems

without applying external magnetic fields

Spin accumulation without charge accumulation

excludes simple electrical detection

slide10

k

E

Beff

Spin-orbit coupling (relativistic effect)

Produces

an electric field

Ingredients: - potential V(r)

- motion of an electron

E

In the rest frame of an electron

the electric field generates and

effective magnetic field

- gives an effective interaction with the electron’s

magnetic moment

slide11

skew

scattering

Skew scattering off impurity potential (Extrinsic SHE/AHE)

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

slide12

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

l=0 for electrons  weak SO

l=1 for holes  strong SO

Enhanced in asymmetric QW

intrinsic ahe approach explains many experiments
Intrinsic 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

sAH  1000 (W cm)-1

Theroy

sAH  750 (W cm)-1

slide14
INTRINSIC SPIN-HALL EFFECT:[Murakami et al Science 2003 (cond-mat/0308167)Sinova et al PRL 2004 (cont-mat/0307663)]

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

Inversion symmetry

 no R-SO

Broken inversion symmetry

 R-SO

[Bychkov and Rashba 84]

slide15

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

Classical dynamics in k-dependent (Rashba) field:

LLG equations for small drift adiabatic solution:

classical and kubo formula give the same spin hall conductivity
Classical and Kubo formula give the same spin-Hall conductivity

Color plot of spin-Hall conductivity:

yellow=e/8π and red=0

disorder effects beyond the born approximation for rashba 2deg
Disorder effects: beyond the Born approximation for Rashba 2DEG

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

Mal'shukov et al, PRL 04

Raimondi et al, PRB 04

Khaetskii, cond-mat/0408136

Loss et al, cond-mat/0407342 v2

Inoue, Bauer, Molenkamp PRB 04

Ladder sum vertex correction:

slide20

Spin Hall effect ?

Intrinsic cancelled by vertex

corrections for infinitely weak

disorder

Extrinsic too weak to give

any sizable effect

slide21

Ways to solve (go around) the controversy:

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

- Intrinsic SHE in Rashba-SO systems beyond

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)

[Bernevig, Zhang, cond-mat/0411457,

cond-mat/0412550

 vertex corrections vanish in all

other studied SO-systems (bulk, 2DHG,..)

slide22

- Look at transport in mesoscopic systems instead

of conductivity in the thermodynamic limit

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

[Hankiewicz et al., PRB 04]

slide23

- 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 disorder

n-type material  weaker SO-coupling

Not in the intrinsic SHE regime

slide24

Experiment “A”

LED 1

a

+Ip

CP [%]

-Ip

Experiment “B”

+Ip

LED 1

CP [%]

LED 2

E [eV]

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

slide25

3D electron-2D hole

Recombination

9

2.5

a

η [meV]

1.5

S [e/8]

5

+

-

E [meV]

HH+

0.5

1

HH-

10 20 30

LH

p2D [1011 cm-2]

-0.2 0.0 0,2

ky [nm-1]

Self-consistent LDA & 6-band

calculations for the [001] QW

Modulation doping  weak disorder

p-type asymmetric QW  strong SO

Close to the intrinsic SHE regime

slide27

Dissipative spin-polarized currents

in non-magnetic systems at B=0

Spin-current is along the applied electric field  proportional to

non-equilibriumdistribution function

asymmetric scattering involving spin-flip

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

slide28

Dissipationless intrinsic spin Hall effect

● Heuristic argument: transverse spin current generated between scattering events

Sinova, Culcer, Niu, Sinitsyn, Jungwirth,

MacDonald, PRL 92, 126603 (2004)

● Boltzman equation for current: transverse anomalous velocity in the equilibrium

band structure due to combined E and SO effects

Jungwirth, Niu, MacDonald, Phys. Rev. Lett. (2002)

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

normal group velocity

anomalous velocity

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

slide29

Caution: the dissipationless transverse intrinsic SHE is accompanied

by a dissipative longitudinal response to the electric field