Spin Hall effect
J. Wunderlich(1), B. Kästner(1,2), J. Sinova (3), T. Jungwirth (4,5)
(1)
(2)
(3)
(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
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-lin
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-lin
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.
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.
OUTLINE:
- Theory remarks
- Comments on experiments
Kerr microscope
Co-planar spin LED
10 µm
p n
SHE in a 2D
hole gas
[Wunderlich et. al., Phys. Rev. Lett. 94, 047204]
SHE in a bulk
semiconductor
[Kato et. al., Science 306, 1910]
Ordinary and quantum Hall effects
B Lorentz force deflect like-charge particles
_ _ _ _ _ _ _ _ _ _
_
Ordinary:
+++++++++++++
Sign and density of
carriers; holes in SC
V
Quantum
FL
I
Resistance standard;
fractional-charge carriers
Anomalous Hall effect
Spin-orbit coupling “force” deflects like-spin particles
majority
__ FSO
_
FSO
I
 H  R0 B  4πRs M
minority
V
InMnAs
Simple electrical measurement
of magnetization
Spin Hall effect
Spin-orbit coupling “force” deflects like-spin particles
_
FSO
__
FSO
non-magnetic
I
V=0
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)
E


- motion of an electron
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
k
E
H SO
Beff

1
E   V (r )
e
 
  μ  Beff


 k  
 E
Beff  

cm


Skew scattering off impurity potential (Extrinsic SHE/AHE)
H SO

 2s   
  2 2   k  Vimp(r)
m c 



skew
scattering
If only this SO effect then much too weak to give a sizable SHE/AHE
SO-coupling from host atoms (Intrinsic SHE/AHE)
H SO

E






 
 es   k  1 dV (r ) 
    Beff  
 r
   s  l
 mc   mc  er dr 
l=0 for electrons  weak SO
l=1 for holes  strong SO

E
Enhanced in asymmetric QW

v
Intrinsic AHE approach explains many experiments
• (Ga,Mn)As systems [Jungwirth et al PRL 02, APL 03]
• Fe [Yao et al PRL 04]
Experiment
sAH  1000 (W cm)-1
Theroy
sAH  750 (W cm)-1
• 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]
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
  
2k 2
2k 2
Hk 
 ( k xsy  k ys x ) 
 s  ( z  k )
2m
2m
[Bychkov and Rashba 84]
Heuristic argument: z-component of spin due to precession in effective "Zeeman" field
 dk

Classical dynamics in k-dependent (Rashba) field:    ( z  k ), x  eE
x
dt

LLG equations for small drift  adiabatic solution:
 dy
x nz  

dt
x dt
dn y

nz  

x
2
eEx
y ( t )
ny ( t ) 
x
Spin Hall conductivity
js ,y ~  d p( nz , p p y )
2
s sH   js , y / E x  e / 8
Classical and Kubo formula give the same spin-Hall conductivity
s xysH
Color plot of spin-Hall conductivity:
yellow=e/8π and red=0
 e
m 2 2
*
for n2 D  n2 D 

4
8




e n2 D
*

for
n

n
2D
2D
 8 n*2 D
Disorder effects: finite lifetime (Born approximation) for
Rashba 2DEG
ε F /(/τ)
 F  (  /  )
SO  k F   / 
 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?
Inoue, Bauer, Molenkamp PRB 04
Ladder sum vertex correction:
Mal'shukov et al, PRL 04
Raimondi et al, PRB 04
Khaetskii, cond-mat/0408136
Loss et al, cond-mat/0407342 v2
~
  0
s xysH  0
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)
[Bernevig, Zhang, cond-mat/0411457,
 vertex corrections vanish in all
other studied SO-systems (bulk, 2DHG,..) 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
SO   / 
Not in the intrinsic SHE regime
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
Experiment “A”
LED 1
a
IP
-Ip
LED 1
p n
n
z
LED 2
0
LED 1
y
-Ip
Experiment “B”
+Ip
x
Ip
x
-1
LED 1
1
0
z ILED 1
ILED 2
y
LED 2
1.505
1.510
1.515
-1
1.520
E [eV]
Co-planar spin LED in GaAs 2D hole gas: ~1% polarization
CP [%]
1.5m
channel
zI
x
y
1
CP [%]
Ip
+Ip
y
z
Self-consistent LDA & 6-band
calculations for the [001] QW
etched
GaAs
p-AlGaAs
2DHG
2DEG
i-GaAs
n-AlGaAs
E [meV]
20
a
0
s+
s20
HH+
9
2.5
5
1.5
1
0.
5
10
20
30
p2D [1011 cm-2]
0
HH-
LH
-20
-0.2
0.0
Modulation doping  weak disorder
p-type asymmetric QW  strong SO
0,2
ky [nm-1]
SO   / 
Close to the intrinsic SHE regime
sS [e/8]
3D electron-2D hole
Recombination
 / η [meV]
GaAs/AlGaAs superlattice
GaAs substrate
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
Berry curvature: M.V. Berry, Proc. Royal Soc. London (1984)
normal group velocity
Caution: the dissipationless transverse intrinsic SHE is accompanied
by a dissipative longitudinal response to the electric field