Unified theory of spin and charge in a ferromagnet

TL;DR

This paper develops a comprehensive theoretical framework linking spin and charge dynamics in ferromagnets, revealing the nature of various forces and extending the collective coordinate approach to include electric charge.

Contribution

It introduces a unified theory that incorporates both spin and charge degrees of freedom, expanding the collective coordinate method to account for electric charge.

Findings

Adiabatic spin-transfer torque is a gyroscopic force.

Nonadiabatic spin emf is a dissipative force.

Equations of motion balance conservative, gyroscopic, and dissipative forces.

Abstract

We derive a unified theory of spin and charge degrees of freedom in a ferromagnet. The spin-transfer torque and spin electromotive force are examined from the coarse-grained perspective of collective coordinates. The resulting equations of motion reflect a balance of conservative, gyroscopic (Berry-phase), and dissipative forces. We then expand the space of collective coordinates by adding the electric charge. The adiabatic spin-transfer torque and spin emf turn out to be a gyroscopic force; their nonadiabatic counterparts are a dissipative force.