Spin transport in spin-orbit coupled bands

1
Spin transport in spin-orbit coupled bands

• Intrinsic contributions

Qian Niu University of Texas at Austin
2
Acknowledgements

• Collaborators
• D. Culcer, A. Dudarev,Yugui Yao, N. Sinitsyn,
• J. Sinova, T. Jungwirth, A. H. MacDonald

References by our team Culcer et al
(PRL,93,046602,2004) Sinova et al
(PRL,92,126603,2004) Dudarev et al
(PRL92,153005,2004)

Other references Murakami et al Science 301,
1248 (2003) Murakami et al cond-mat/0310005
Hu et al cond-mat/0310093
Schliemann et al cond-mat/0310108 Shen
cond-mat/0310368
Rashba cond-mat/0311110 Bernevig et al
cond-mat/0311024 Inoue et al
cond-mat/0402442 Xiong et al cond-mat/0403083
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Outline

• Motivation
• Boltzmann-wavepacket transport
• Spin dipole, torque dipole
• Equation of continuity current source
• Intrinsic extrinsic parts
• Spin current several attributions
• Spin Hall Effect
• Rashba model,
• Four band model
• HgSe, HgTe
• GaAs, Si, Ge
• Spin accumulation the role of torque dipole
• Conclusions

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Magneto-Electronics
1st generation spintronic devices based on
ferromagnetic metals already in commercial use
GMR ? read-out heads in hard drives
Magnetic tunneling junction (MTJ) or spin valve
? Nonvolatile MRAM Instant on


Compatibility with Si and GaAs ? next phase
semiconductor spintronics
S. Parkin (1990)
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A brighter future with semiconductor spintronics

• Can do what metals do
• GMR, spin transfer, ..., using ferromagnetic
  semiconductors
• Readily integrated with semiconductor devices
• possible way around impedance mismatch in spin
  injection.
• Tunable
• transport, magnetic and optical properties can be
  readily controlled by doping, gating, and
  pumping.
• Spin-orbit
• strong in semiconductors, may lead to novel
  effects such as electric generation and
  manipulation of spins

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Boltzmann-wavepacket transport

• Spin-orbit built into the bandstructure
• not a perturbation.
• Carrier of charge and spin
• represented by wave packets.
• Effects of external fields
• mixing of bands and drifting.
• Impurity effects
• scattering and relaxation.

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Effect of external fields

• Mixing
• Drifting

where
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Observable and wavepacket

• Charge

• Spin

(rc, kc)
(rc, kc)
(rs, ks)
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Macroscopic densities

• Spin density
• Torque density
• Spin current density

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Equation of continuity
intrinsic
extrinsic
Torque density
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Electric field induced source

• In the Rashba model
• Generally nonzero in inversion asymmetric
  crystals

L. S. Levitov et al., Sov. Phys. JETP 61, 133
(1985) P. R. Hammar and M. Johnson, Phys. Rev.
Lett. 88, 066806 (2002) Y. Kato et al,
Cond-mat/0403407 (2004).
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Spin current contributions

• Homogeneous systems ? ignore gradient terms.
• Spin current can be decomposed into
• Spin Hall agrees with the Kubo formula.

Convective term
Torque dipole
d/dt (Spin dipole)
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Spin Current intrinsic extrinsic

• Distribution equilibrium part shift
• Extrinsic spin current
• Intrinsic spin current

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Spin Current Rashba model

• Rashba Hamiltonian
• Spin current per carrier
• Spin-Hall conductivity

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Optical Lattice
6Li
(PRL 70, 2249 (1993)).
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Bands Spin Hall
like Rashba coupling!
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Spin Current four-band model

• Luttinger Hamiltonian
• The intrinsic spin current
• Spin-Hall conductivity

Energy
k
Heavy holes
Light holes
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Spin accumulation

• equation of continuity
• spin accumulation

sample
Js
S
x
lsspin diffusion length
30 ps
20000 V/cm
2.5x1017 spins x v/E
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Zero-gap semiconductors

• HgSe
• HgTe

0.0031 e / a
0.0023 e / a
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Insulators

• 1 strained HgSe and HgTe
• energy gap 40 meV
• Spin Hall conductivity unchanged.
• GaAs
• Ge
• Si

0.001 e / a
Symmetry js s E
0.0015 e / a
Covariant under time reversal and spatial
inversion
0.00017 e / a
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The torque dipole and spin accumulation

• Source term (no bulk spin generation)
• The equation of continuity
• Justifies the definition of the spin transport
  current
• In insulators, Jst believed to be zero (in
  progress).

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Spin transport current

• Without the torque dipole, the spin-Hall
  conductivity for the four band model is
• Similar magnitude to the original, but differs by
  a sign.

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Conclusions

• Boltzmann-wavepacket transport
• Intuitive, rigorous, local
• intrinsic contributions to spin source current
• Berry phase and much more.
• Intrinsic spin current
• convective term, a spin dipole and a torque
  dipole.
• Intrinsic spin Hall agrees with Kubo formula.
• Rashba, four-band, zero-gap, insulators
• Spin Accumulation
• cancellation of torque dipole terms