1. Spin transport in spin-orbit coupled bands
Intrinsic contributions
Qian Niu
University of Texas at Austin

2. References by our team:
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/
Hu et al cond-mat/ Schliemann et al cond-mat/
Shen cond-mat/ Rashba cond-mat/
Bernevig et al cond-mat/ Inoue et al cond-mat/
Xiong et al cond-mat/

3. Outline Motivation Boltzmann-wavepacket transport Spin Hall Effect
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

4. 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 ”
Although the idea of utilizing the spin degree of freedom of the electron to
Compatibility with Si and GaAs  next phase: semiconductor spintronics
S. Parkin (1990)

5. 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
The broader possibilities of semiconductor spintronics:

6. 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.

7. Effect of external fields
Mixing
Drifting
where

8. Observable and wavepacket
Charge
Spin
(rc, kc)
(rc, kc)
(rs, ks)

9. Macroscopic densities
Spin density
Torque density
Spin current density

10. Equation of continuity
intrinsic
extrinsic
Torque density:

11. 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, (2002)
Y. Kato et al, Cond-mat/ (2004).

12. 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)

13. Spin Current: intrinsic & extrinsic
Distribution: equilibrium part + shift
Extrinsic spin current
Intrinsic spin current

14. Spin Current: Rashba model
Rashba Hamiltonian:
Spin current per carrier:
Spin-Hall conductivity:

15. Optical Lattice
6Li
(PRL 70, 2249 (1993)).

16. Bands & Spin Hall
like Rashba coupling!

17. Spin Current: four-band model
Luttinger Hamiltonian:
The intrinsic spin current:
Spin-Hall conductivity:
Energy k
Heavy holes
Light holes

18. Spin accumulation equation of continuity: spin accumulation: Js S x
sample Js S x
ls=spin diffusion length
30 ps
20000 V/cm
2.5x1017 spins x [v]/[E]

19. Zero-gap semiconductors
HgSe
HgTe
= e / a
= e / a

20. Insulators 1% strained HgSe and HgTe energy gap: ~ 40 meV
Spin Hall conductivity: unchanged.
GaAs Ge Si
= e / a
Symmetry:
js = s E
= e / a
Covariant under time reversal
and spatial inversion
= e / a

21. 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).

22. 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.

23. 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