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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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J. Wunderlich(1), B. Kästner(1,2), J. Sinova (3), T. Jungwirth (4,5)
Collaborators: Allan MacDonald, Dimitri Culcer,Ewelina Hankeiwc,Qian Niu, Kentaro Nomura,Nikolai Sinitsyn, Laurens Molenkamp, Winfried Teizer
SHE  Theory(http://unix12.fzu.cz/msnew)
Covered by T.J.
SHE  Experiment(http://unix12.fzu.cz/msnew)
Covered by J.W.
 Theory remarks
 Comments on experiments
Kerr microscope
Coplanar 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]
_ _ _ _ _ _ _ _ _ _
_
FL
+ + + + + + + + + + + + +
I
V
Ordinary and quantum Hall effects
Lorentz force deflect likecharge particles
Quantum
Resistance standard;
fractionalcharge carriers
Ordinary:
Sign and density of
carriers; holes in SC
_
_
_
FSO
_
FSO
I
minority
V
Anomalous Hall effect
Spinorbit coupling “force” deflects likespin particles
InMnAs
Simple electrical measurement
of magnetization
_
_
FSO
_
nonmagnetic
FSO
I
V=0
Spin Hall effect
Spinorbit coupling “force” deflects likespinparticles
Spincurrent generation in nonmagnetic systems
without applying external magnetic fields
Spin accumulation without charge accumulation
excludes simple electrical detection
E
Beff
Spinorbit 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
scattering
Skew scattering off impurity potential (Extrinsic SHE/AHE)
If only this SO effect then much too weak to give a sizable SHE/AHE
SOcoupling from host atoms (Intrinsic SHE/AHE)
l=0 for electrons weak SO
l=1 for holes strong SO
Enhanced in asymmetric QW
Experiment
sAH 1000 (W cm)1
Theroy
sAH 750 (W cm)1
Let’s start with a simple model: Rashba SO coupling in a 2DEGs
Inversion symmetry
no RSO
Broken inversion symmetry
RSO
[Bychkov and Rashba 84]
Heuristic argument: zcomponent of spin due to precession in effective "Zeeman" field
Classical dynamics in kdependent (Rashba) field:
LLG equations for small drift adiabatic solution:
Color plot of spinHall conductivity:
yellow=e/8π and red=0
Disorder effects: finite lifetime (Born approximation) for Rashba 2DEG
intrinsic SHE
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, condmat/0408136
Loss et al, condmat/0407342 v2
Inoue, Bauer, Molenkamp PRB 04
Ladder sum vertex correction:
Intrinsic cancelled by vertex
corrections for infinitely weak
disorder
Extrinsic too weak to give
any sizable effect
Ways to solve (go around) the controversy:
 Skew scattering in SOcoupled bands not done yet
 Intrinsic SHE in RashbaSO systems beyond
perturbation theory by solving Kubo formula exactly
inconclusive (finitesize effects)
[Nomura et al. PRB '05]
 Other than RashbaSO systems (intrinsic AHE explains experiments here)
[Bernevig, Zhang, condmat/0411457,
condmat/0412550
vertex corrections vanish in all
other studied SOsystems (bulk, 2DHG,..)
 Look at transport in mesoscopic systems instead
of conductivity in the thermodynamic limit
[Nikolic et al., condmat/0412595]
[Hankiewicz et al., PRB 04]
Kato, Myars, Gossard, Awschalom, [Science 306, 1910]
"Observation of the spin Hall effect
in semiconductors"
Local Kerr effect in ntype GaAs and InGaAs:
~0.03% polarization
Bulk semiconductor stronger disorder
ntype material weaker SOcoupling
Not in the intrinsic SHE regime
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 spinHall effect in a two dimensional
spinorbit coupled semiconductor system
Coplanar spin LED in GaAs 2D hole gas: ~1% polarization
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 cm2]
0.2 0.0 0,2
ky [nm1]
Selfconsistent LDA & 6band
calculations for the [001] QW
Modulation doping weak disorder
ptype asymmetric QW strong SO
Close to the intrinsic SHE regime
Dissipative spinpolarized currents
in nonmagnetic systems at B=0
Spincurrent is along the applied electric field proportional to
nonequilibriumdistribution function
asymmetric scattering involving spinflip
[Ganichev et al.,condmat/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, 13481351 (2003).
normal group velocity
anomalous 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