Unified Description of the Intrinsic Spin-Hall Effects

Abstract

The intrinsic spin-Hall effects (SHE) in $p$-doped semiconductors [S. Murakami et al., Science 301, 1348 (2003)] and two-dimensional electron gases with Rashba spin-orbit coupling [J. Sinova et al., Phys. Rev. Lett. 92, 126603 (2004)] have been the subject of many theoretical studies, but their driving mechanisms have yet to be described in a unified manner. The former effect arises from the adiabatic topological curvature of momentum space, from which holes acquire a spin-dependent anomalous velocity. The SHE in the Rashba system, on the other hand, results from the momentum-dependent spin dynamics in the presence of an external electric field. The two effects clearly appear to originate from distinct mechanisms. Our motivation for this article is to address this apparent disparity and, in particular, to seek a unifying description of the effects. In this endeavor, we consider the explicit time-dependence of SHE systems starting with a general spin-orbit model. We find that by performing a gauge transformation of the general model with respect to time, a well-defined gauge field appears in time space which has the physical significance of an effective magnetic field. This magnetic field is shown to precisely account for the SHE in the Rashba system in the adiabatic limit. Remarkably, by carefully analyzing the equation of motion of the general model, this field component is also found to be the origin of the anomalous velocity due to the momentum space curvature. Our study therefore unifies the two seemingly disparate intrinsic SHEs under a common adiabatic framework.

20 pages, 1 figure

References in corpus (27)

• Dissipationless Quantum Spin Current at Room Temperature
• Intrinsic vs. extrinsic anomalous Hall effect in ferromagnets
• Spin current and polarization in impure 2D electron systems with spin-orbit coupling
• Microscopic approach to current-driven domain wall dynamics
• Suppression of the Persistent Spin Hall Current by Defect Scattering
• Semiclassical theories of the anomalous Hall effect
• SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors
• Spin-Hall effect in a disordered 2D electron-system
• Spin Hall effect and Berry phase in two dimensional electron gas
• Spin Transfer Torque for Continuously Variable Magnetization
• Spin-Hall conductivity due to Rashba spin-orbit interaction in disordered systems
• Absence of vertex correction for the spin Hall effect in p-type semiconductors
• Nonexistence of intrinsic spin currents
• Vertex Corrections on the Anomalous Hall Effect in Spin-polarized Two-dimensional Electron Gases with Rashba Spin-orbit Interaction
• Intrinsic Spin Hall Edges
• Spin Gauge Fields: from Berry Phase to Topological Spin Transport and Hall Effects
• Conserved Spin and Orbital Angular Momentum Hall Current in a Two-Dimensional Electron System with Rashba and Dresselhaus Spin-orbit Coupling
• Study of intrinsic spin and orbital Hall effects in Pt based on a (6s, 6p, 5d) tight-binding model
• The effect of in-plane magnetic field on the spin Hall effect in Rashba-Dresselhaus system
• Strain-Induced Coupling of Spin Current to Nanomechanical Oscillations
• Control of spin coherence in $n$-type GaAs quantum wells using strain
• Spin Hall utilizing U(1) and SU(2) gauge fields
• Nature of Spin Hall Effect in a finite Ballistic Two-Dimensional System with Rashba and Dresselhaus spin-orbit interaction
• Resonant intrinsic spin Hall effect in p-type GaAs quantum well structure
• Side jump contribution to spin-orbit mediated Hall effects and Berry curvature
• Coriolis force, geometric phase, and spin-electric coupling in semiconductors
• Spin Hall effect in infinitely large and finite-size diffusive Rashba two-dimensional electron systems: A helicity-basis nonequilibrium Green's function approach

Cited by in corpus (17)

• Inertial spin Hall effect in noncommutative space
• Inertial effect on spin orbit coupling and spin transport
• Effect of cosmic string on spin dynamics
• Gauge Physics of Spin Hall Effect
• Effect of surface state hybridization on current-induced spin-orbit torque in thin topological insulator films
• Spin force and the generation of sustained spin current in time-dependent Rashba and Dresselhauss systems
• Topological-Berry-phase-induced spin torque current in a two-dimensional system with generic $k$-linear spin-orbit interaction
• The geometric phase and the geometrodynamics of relativistic electron vortex beams
• Spin force and intrinsic spin Hall effect in spintronics systems
• Sustainable spin current in the time-dependent Rashba system
• Dynamical precession of spin in the two-dimensional spin-orbit coupled systems
• Curvature induced out of plane spin accumulation
• Adiabatic approximation for a uniform DC electric field
• Spin accumulation in disordered topological insulator thin films
• Understanding spin Hall effect in two-dimensional fermionic systems with generic spin-orbit interaction
• Spin Hall effect originated from fractal surface
• Effect of non-uniform exchange field in ferromagnetic graphene