Non-Abelian gauge field effects and its relevance to spinning particle dynamics in the technology of spintronics

TL;DR

This paper explores how non-Abelian gauge fields influence spin dynamics in condensed matter systems, providing a formal framework that links spin precession, gauge fields, and spintronic phenomena.

Contribution

It introduces a formal description of spin precession as a local SU(2) transformation, establishing conditions for gauge field effects on spin motion in spintronics.

Findings

Spin gauge fields affect spin particle motion in both classical and quantum regimes.

A 'no-precession' condition is identified as necessary for gauge field influence.

The framework explains phenomena like anomalous Hall and spin Hall effects.

Abstract

We describe formally the precession of spin vector about the k-space effective magnetic field in condensed matter system with spin orbital effects as constituting a local transformation of the electron wavefunction which necessarily invokes the SU(2) transformation rule to ensure covariance. We showed a "no-precession" condition as pre-requisite for the spin gauge field to exert its influence on spin particle motion. The effects of the spin gauge field on spin particle motion were shown to be consistent in both classical and quantum pictures, which hence should underpin theoretical explanations for important effects in anomalous Hall, spin Hall, spin torque, optical Magnus, geometric quantum computation.