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 not by injection but by applying an electric field to a structure of a certain geometry Collaborators: Allan MacDonald, Dimitri Culcer, Ewelina Hankeiwc, Qian Niu, Kentaro Nomura, Nikolai Sinitsyn, Laurens Molenkamp, Winfried Teizer

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

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

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.

preprint cond-mat/0410295: on-line 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.

- Comments on experiments OUTLINE: - Theory remarks - Comments on experiments Kerr microscope Co-planar spin LED SHE in a 2D hole gas SHE in a bulk semiconductor [Wunderlich et. al., Phys. Rev. Lett. 94, 047204] [Kato et. al., Science 306, 1910]

Ordinary and quantum Hall effects B V I _ + + + + + + + + + + + + + _ _ _ _ _ _ _ _ _ _ FL Lorentz force deflect like-charge particles Quantum Resistance standard; fractional-charge carriers Ordinary: Sign and density of carriers; holes in SC

Anomalous Hall effect I V Simple electrical measurement Spin-orbit coupling “force” deflects like-spin particles I _ FSO majority minority V InMnAs Simple electrical measurement of magnetization

Spin-orbit coupling “force” deflects like-spin particles Spin Hall effect Spin-orbit coupling “force” deflects like-spin particles I _ FSO V=0 non-magnetic Spin-current generation in non-magnetic systems without applying external magnetic fields Spin accumulation without charge accumulation excludes simple electrical detection

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 Since I am the first talk and the topic of spin-orbit coupling will come up often let me introduce its basic notion. The spin orbit coupling interactions is nothing but an effective magnetic field interaction felt by a moving charge due to a changing electric field due to its relative motion in a potential generating such an electric field. Maxwell’s equations show us that this relative motion of the charge and the electric field induces an effective magnetic field proportional to the orbital momentum of the quasiparticle. As illustrated in the equation shown the spin quantization axis for such a E Beff k

Skew scattering off impurity potential (Extrinsic SHE/AHE) If only this SO effect then much too weak to give a sizable SHE/AHE

SO-coupling from host atoms (Intrinsic SHE/AHE) l=0 for electrons  weak SO l=1 for holes  strong SO Enhanced in asymmetric QW Since I am the first talk and the topic of spin-orbit coupling will come up often let me introduce its basic notion. The spin orbit coupling interactions is nothing but an effective magnetic field interaction felt by a moving charge due to a changing electric field due to its relative motion in a potential generating such an electric field. Maxwell’s equations show us that this relative motion of the charge and the electric field induces an effective magnetic field proportional to the orbital momentum of the quasiparticle. As illustrated in the equation shown the spin quantization axis for such a

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

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 MENTION OTHER WORKS HERE, EMPHASIZE THE COLLABORATIVE EFFORTS OF THE TEXAS, STANFORD, AND JAPAN GROUPS [Bychkov and Rashba 84]

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: 

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: finite lifetime (Born approximation) for Rashba 2DEG  intrinsic SHE

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 Talk about Inoue et al calculation. Mentioning the ommision of sigma_II. Ladder sum vertex correction:

Extrinsic  too weak to give any sizable effect Spin Hall effect ? Extrinsic  too weak to give any sizable effect Intrinsic  cancelled by vertex corrections for infinitely weak disorder

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)  vertex corrections vanish in all other studied SO-systems (bulk, 2DHG,..) [Bernevig, Zhang, cond-mat/0411457, cond-mat/0412550

- Look at transport in mesoscopic systems instead of conductivity in the thermodynamic limit [Hankiewicz et al., PRB 04] [Nikolic et al., cond-mat/0412595]

- 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

Experiment “A” a Experiment “B” +Ip -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 +Ip E [eV] a LED 1 -Ip CP [%] Experiment “A” Experiment “B” LED 2 Co-planar spin LED in GaAs 2D hole gas: ~1% polarization

+ a - 3D electron-2D hole Recombination E [meV] ky [nm-1] Self-consistent LDA & 6-band calculations for the [001] QW E [meV] a HH+ HH- LH - + ky [nm-1] 3D electron-2D hole Recombination -0.2 0.0 0,2 10 20 30 1 p2D [1011 cm-2] η [meV] 2.5 1.5 0.5 5 9 S [e/8] Modulation doping  weak disorder p-type asymmetric QW  strong SO Close to the intrinsic SHE regime

A dissipationless remark ...

Dissipative spin-polarized currents in non-magnetic systems at B=0 Spin-current is along the applied electric field  proportional to non-equilibrium distribution function asymmetric scattering involving spin-flip [Ganichev et al., cond-mat/0403641, Silov et al. APL 04]

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). anomalous velocity normal group velocity Berry curvature: M.V. Berry, Proc. Royal Soc. London (1984)

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