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  1. 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

  2. SHE - Theory( • 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

  3. 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

  4. 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.

  5. SHE - Experiment( • 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.

  6. 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]

  7. 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

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

  9. _ _ _ 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

  10. 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

  11. 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

  12. SO-coupling from host atoms (Intrinsic SHE/AHE) l=0 for electrons  weak SO l=1 for holes  strong SO Enhanced in asymmetric QW

  13. 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

  14. 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]

  15. 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: 

  16. Spin Hall conductivity

  17. Classical and Kubo formula give the same spin-Hall conductivity Color plot of spin-Hall conductivity: yellow=e/8π and red=0

  18. Disorder effects: finite lifetime (Born approximation) for Rashba 2DEG  intrinsic SHE

  19. 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:

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

  21. 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,..)

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

  23. - 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

  24. 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

  25. 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

  26. A dissipationless remark ...

  27. 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]

  28. 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)

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