Thermally Assisted Spin Hall Effect

TL;DR

This paper presents a theoretical analysis of the thermally driven spin Hall effect using a relativistic stochastic approach, deriving an exact conductivity expression and identifying key correction contributions.

Contribution

It introduces a relativistic correction to the damping in Kramers' equation and derives an exact formula for spin Hall conductivity considering crystal potential effects.

Findings

Relativistic correction enhances spin Hall conductivity.

Crystal potential significantly influences conductivity.

Exact expression for electrical conductivity derived.

Abstract

The spin polarized charge transport is systematically analyzed as a thermally driven stochastic process. The approach is based on Kramers' equation describing the semiclassical motion under the inclusion of stochastic and damping forces. Due to the relativistic spin-orbit coupling the damping experiences a relativistic correction leading to an additional contribution within the spin Hall conductivity. A further contribution to the conductivity is originated from the averaged underlying crystal potential, the mean value of which depends significantly on the electric field. We derive an exact expression for the electrical conductivity. All corrections are estimated in lowest order of a relativistic approach and in the linear response regime.