The contribution of spin torque to spin Hall coefficient and spin motive force in spin-orbit coupling system

TL;DR

This paper rigorously derives the relativistic angular momentum conservation in quantum electrodynamics and investigates nonrelativistic spin currents and torques in spin-orbit systems, revealing a comprehensive spin Hall coefficient and a new spin motive force.

Contribution

It introduces a precise derivation of spin currents and torques up to order 1/c^4 in spin-orbit coupling systems, including a novel spin motive force analogous to Lorentz force.

Findings

A complete spin Hall coefficient including spin torque dipole contributions.

Discovery of a new spin motive force similar to Lorentz force.

Exact analysis of relativistic angular momentum conservation in quantum electrodynamics.

Abstract

We derive rigorously the relativistic angular momentum conservation equation by means of quantum electrodynamics. The novel nonrelativistic spin current and torque in the spin-orbit coupling system, up to the order of $1/c^{4}$, are exactly investigated by using Foldy-Wouthuysen transformation. We find a perfect spin Hall coefficient including the contribution of spin torque dipole. A novel spin motive force, analogue to the Lorentz force, is also obtained for understanding of the spin Hall effect.