Transverse spin diffusion in ferromagnets

TL;DR

This paper explores the transverse spin diffusion in ferromagnets, linking phenomenological models with microscopic theories, and highlights its physical origin from itinerant-electron spin flows and spin pumping effects.

Contribution

It introduces a comprehensive phenomenological and microscopic framework for understanding transverse spin diffusion in ferromagnets, including disorder and electron-electron interactions.

Findings

Identification of the spin diffusion in terms of transverse spin conductivity

Development of a microscopic theory for Stoner and s-d models

Connection between spin pumping and enhanced Gilbert damping

Abstract

We discuss the dissipative diffusion-type term of the form $\mathbf{m}\times\nabla^2\partial_t\mathbf{m}$ in the phenomenological Landau-Lifshitz equation of ferromagnetic precession, which describes enhanced Gilbert damping of finite-momentum spin waves. This term arises physically from itinerant-electron spin flows through a perturbed ferromagnetic configuration and can be understood to originate in the ferromagnetic spin pumping in the continuum limit. We develop a general phenomenology as well as provide microscopic theory for the Stoner and s-d models of ferromagnetism, taking into account disorder and electron-electron scattering. The latter is manifested in our problem through the Coulomb drag between the spin bands. The spin diffusion is identified in terms of the transverse spin conductivity, in analogy with the Einstein relation in the kinetic theory.