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
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

2. 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/ : 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/ : 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/ : 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/ : 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/ : on-line
Hu:2005_a
Jiangping Hu, "Spin Polarization and Dichroism Effects by Electric Field", (2005), preprint cond-mat/ : 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/ : 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/ : 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/ : 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/ : on-line
Mele:2004_a
C.L. Kane and E.J. Mele, "Quantum Spin Hall Effect in Graphene", (2004), preprint cond-mat/ : 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/ : 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/ : 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/ : on-line
Serebrennikov:2004_a
Yuri A. Serebrennikov, "Gometric spin dephasing of carriers with strong spin-orbit coupling", (2004), preprint cond-mat/ : 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/ : 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/ : 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/ : 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/ : 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/ : 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/ : 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/ : 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/ : 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/ : on-line
Khaetskii:2004_a
Alexander Khaetskii, "Nonexistence of intrinsic spin currents", (2004), preprint cond-mat/ : on-line
Rashba:2004_c
Emmanuel I. Rashba, "Spin Dynamics and Spin Transport", (2004), preprint cond-mat/ : 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/ : 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/ : 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/ : on-line
Schmeltzer:2004_a
D. Schmeltzer, "Topological spin current", (2004), preprint cond-mat/ : 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/ : 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/ : on-line
Murakami:2004_a
Shuichi Murakami, "Spin Hall Effect in p-type Semiconductors", (2004), preprint cond-mat/ : on-line
Xiong:2004_a
Ye Xiong and X.C. Xie, "Spin Hall Conductance in Disordered Two-Dimensional Electron Systems", (2004), preprint cond-mat/ : on-line
Dyakonov:2004_a
M. I. Dyakonov, "Spintronics?", (2004), preprint cond-mat/ : on-line
 2005 
Raimondi:2004_a
Roberto Raimondi and Peter Schwab, "Spin-Hall effect in a disordered 2D electron-system", Phys. Rev. B 71, (2005): on-line, preprint cond-mat/ : on-line
Zhang:2004_b
S. Zhang and Z. Yang, "Intrinsic Spin and Orbital-Angular-Momentum Hall Effect", Phys. Rev. Lett. 94, (2005): on-line, preprint cond-mat/ : on-line
Nomura:2004_a
K. Nomura, et al., "Non-vanishing spin Hall currents in disordered spin-orbit coupling systems", Phys. Rev. B 71, (2005): on-line, preprint cond-mat/ : 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, (2005): on-line, preprint cond-mat/ : on-line
 2004 
Rashba:2004_d
Emmanuel I. Rashba, "Sum rules for spin-Hall conductivity cancelation", Physica B 70, (R) (2004): on-line, preprint cond-mat/ : 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, (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, (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, (2004): on-line, preprint cond-mat/ : on-line
Bernevig:2004_a
B. A. Bernevig, "On the nature of spin currents", Phys. Rev. B 71, (2004): on-line, preprint cond-mat/ : on-line
Murakami:2004_b
Shuichi Murakami, Naoto Nagaosa, Shou-Cheng Zhang, "Spin Hall Insulator", Phys. Rev. Lett. 93, (2004): on-line, preprint cond-mat/ : 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/ : 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/ : on-line
Murakam:2004_a
Shuichi Murakami, "Absence of vertex correction for the spin Hall effect in p-type semiconductors", Phys. Rev. B 69, (2004): on-line, preprint cond-mat/ : on-line
Rashba:2004_b
Emmanuel I. Rashba, "Spin currents, spin populations, and dielectric function", Phys. Rev. B 70, (2004): on-line, preprint cond-mat/ : 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, (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, (2004): on-line, preprint cond-mat/ : 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, (2004): on-line,
Bernevig:2003_a
Bogdan et al., "Dissipationless spin current in anisotropic p-doped semiconductors", Phys. Rev. B 70, (2004): on-line, preprint cond-mat/ : on-line
Shen:2003_a
Shun-Qing Shen, "Spin Hall effect and Berry phase in two dimensional electron gas", Phys. Rev. B 70, (2004): on-line, preprint cond-mat/ : 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, (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, (2004): on-line, preprint cond-mat/ : on-line
Culcer:2004_a
Dimitrie Culcer, et al., "Semiclassical theory of spin transport in spin-orbit coupled systems", Phys. Rev. Lett. 93, (2004): on-line, preprint cond-mat/ : on-line
 2003 
Rashba:2003_a
Emmanuel I. Rashba, "Spin currents in thermodynamic equilibrium: The challenge of discerning transport currents", Phys. Rev. B 68, (2003): on-line
Culcer:2003_a
Dimitrie Culcer, Allan MacDonald, Qian Niu, "Anomalous Hall effect in paramagnetic two dimensional systems", Phys. Rev. B 68, (2003): on-line, preprint cond-mat/ : 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/ : 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, (2003): on-line, preprint cond-mat/ : on-line
Sinova:2004_a
Jairo Sinova, et al., "Universal Intrinsic Spin-Hall Effect", Phys. Rev. Lett. 92, (2004): on-line, preprint cond-mat/ : 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/ : on-line
Covered by T.J.

5. preprint cond-mat/0410295: on-line
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, (2005):
preprint cond-mat/ : 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. - 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, ]
[Kato et. al., Science 306, 1910]

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

8. 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

9. 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

10. 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

11. 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
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

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

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/
Loss et al, cond-mat/ v2
Inoue, Bauer, Molenkamp PRB 04
Talk about Inoue et al calculation. Mentioning the ommision of sigma_II.
Ladder sum vertex correction:

20. 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

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

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

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” a Experiment “B” +Ip -Ip LED 1 CP [%] LED 2 E [eV]
Wunderlich, Kästner, Sinova, Jungwirth, [Phys. Rev. Lett. 94, ]
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

25. + 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 ,2 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

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-equilibrium distribution function
asymmetric scattering involving spin-flip
[Ganichev et al., cond-mat/ , 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, (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, (2003).
anomalous velocity
normal group 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