Phenomenological description of the nonlocal magnetization relaxation in magnonics, spintronics, and domain-wall dynamics

TL;DR

This paper introduces and analyzes the Landau-Lifshitz-Baryakhtar (LLBar) equation, a phenomenological model incorporating nonlocal damping effects in magnetization dynamics, revealing significant impacts on magnon and domain wall behaviors.

Contribution

The paper derives the LLBar equation linking nonlocal damping to spin current pumping and investigates its effects on spin wave decay and domain wall motion.

Findings

Nonlocal damping reduces magnon lifetime and propagation length.

Nonlocal damping significantly affects domain wall mobility.

Walker breakdown field is strongly influenced by nonlocal damping.

Abstract

A phenomenological equation called Landau-Lifshitz-Baryakhtar (LLBar) equation, which could be viewed as the combination of Landau-Lifshitz (LL) equation and an extra "exchange damping" term, was derived by Baryakhtar using Onsager's relations. We interpret the origin of this "exchange damping" as nonlocal damping by linking it to the spin current pumping. The LLBar equation is investigated numerically and analytically for the spin wave decay and domain wall motion. Our results show that the lifetime and propagation length of short-wavelength magnons in the presence of nonlocal damping could be much smaller than those given by LL equation. Furthermore, we find that both the domain wall mobility and the Walker breakdown field are strongly influenced by the nonlocal damping.