Extrinsic spin Hall effect in inhomogeneous systems

TL;DR

This paper theoretically investigates how inhomogeneities in systems influence charge-to-spin conversion, revealing that electron flow vorticity induces spin accumulation via side-jump and skew-scattering, with implications for spin diffusion and Coulomb interactions.

Contribution

It introduces a generalized spin diffusion framework incorporating a spin source term from the divergence of the spin Hall current in inhomogeneous systems.

Findings

Spin accumulation is driven by electron flow vorticity.

The spin source term reduces to spin-vorticity coupling under certain conditions.

Long-range Coulomb interactions significantly affect charge inhomogeneity and spin dynamics.

Abstract

Charge-to-spin conversion in inhomogeneous systems is studied theoretically. We consider free electrons subject to impurities with spin-orbit interaction and with spatially modulated distribution, and calculate spin accumulation and spin current induced by an external electric field. It is found that the spin accumulation is induced by the vorticity of electron flow through the side-jump and skew-scattering processes, and the differences of the two processes are discussed. The results can be put in a form of generalized spin diffusion equation with a spin source term given by the divergence of the spin Hall current. This spin source term reduces to the form of spin-vorticity coupling when the spin Hall angle is independent of impurity concentration. We also study the effects of long-range Coulomb interaction, which is indispensable when the process involves charge inhomogeneity and accumulation as in the present problem.