Perturbation theory of the dynamic inverse spin Hall effect with charge conservation

TL;DR

This paper develops a gauge-invariant theoretical framework for the dynamic inverse spin Hall effect in metals, emphasizing charge conservation and linking spin currents to induced charge currents, aligning with experimental observations.

Contribution

It introduces a gauge-invariant theory incorporating vertex corrections to ensure charge conservation in the dynamic inverse spin Hall effect.

Findings

Charge current is proportional to the spin current pumped by magnetization dynamics.

The theory aligns with recent experimental results.

Charge conservation is maintained through diagrammatic vertex corrections.

Abstract

We present gauge-invariant theory of the dynamic inverse spin Hall effect driven by the spin--orbit interaction in metallic systems. Charge conservation is imposed diagrammatically by including vertex corrections. We show the charge current is induced by an effective electric field that is proportional to the spin current pumped by the magnetization dynamics. The result is consistent with recent experiments.