Spin Hall effects in diffusive normal metals

TL;DR

This paper derives diffusion equations for spin and charge transport in normal metals considering spin-orbit interactions and impurity scattering, and evaluates the magnitude of spin Hall effects in realistic geometries.

Contribution

It introduces a comprehensive theoretical framework for spin and charge flow in metals, incorporating multiple scattering mechanisms and providing quantitative predictions for spin Hall effects.

Findings

Quantitative estimates of spin Hall effects in various geometries

Identification of dominant scattering mechanisms under different conditions

Derivation of diffusion equations including skew, side-jump, and anomalous velocities

Abstract

We consider spin and charge flow in normal metals. We employ the Keldysh formalism to find transport equations in the presence of spin-orbit interaction, interaction with magnetic impurities, and non-magnetic impurity scattering. Using the quasiclassical approximation, we derive diffusion equations which include contributions from skew scattering, side-jump scattering and the anomalous spin-orbit induced velocity. We compute the magnitude of various spin Hall effects in experimental relevant geometries and discuss when the different scattering mechanisms are important.