Joule heating in spin Hall geometry

TL;DR

This paper derives a general formula for entropy production due to spin currents in spin Hall systems, revealing dissipation contributions related to the spin Hall angle, applicable across various spin current sources.

Contribution

It introduces a universal theoretical framework for entropy production in spin Hall geometry, extending previous dissipation formulas to include diverse spin current sources.

Findings

Dissipation in spin Hall systems includes a term proportional to the square of the spin Hall angle.

The derived formula applies regardless of the spin current source, such as electric fields or temperature gradients.

Reproduces previous results under the relaxation time approximation.

Abstract

The theoretical formula for the entropy production rate in the presence of spin current is derived using the spin-dependent transport equation and thermodynamics. This theory is applicable regardless of the source of the spin current, for example, an electric field, a temperature gradient, or the Hall effect. It reproduces the result in a previous work on the dissipation formula when the relaxation time approximation is applied to the spin relaxation rate. By using the developed theory, it is found that the dissipation in spin Hall geometry has a contribution proportional to the square of the spin Hall angle.