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

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/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

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

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)

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:

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.

Effect of external fields Mixing Drifting where

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

Macroscopic densities Spin density Torque density Spin current density

Equation of continuity intrinsic extrinsic Torque density:

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).

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)

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

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

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

Bands & Spin Hall like Rashba coupling!

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

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]

Zero-gap semiconductors HgSe HgTe = 0.0031 e / a = 0.0023 e / a

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

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).

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.

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