Asymptotic stability of 2-domain walls for the Landau-Lifshitz-Gilbert equation in a nanowire with Dzyaloshinskii-Moriya interaction

TL;DR

This paper proves the asymptotic stability of two well-separated magnetic domain walls in a nanowire with Dzyaloshinskii-Moriya interaction under the Landau-Lifshitz-Gilbert flow, extending previous localized analysis methods.

Contribution

It establishes the asymptotic stability of two opposite-speed domain walls in a nanowire considering Dzyaloshinskii-Moriya interaction, using a localized analytical framework.

Findings

Stable configurations when two walls have opposite speeds

Analysis based on localized framework from prior work

Results extend understanding of magnetic domain wall dynamics

Abstract

We consider a ferromagnetic nanowire, with an energy functional E with easy-axis in the direction $e_1$, and which takes into account the Dzyaloshinskii-Moriya interaction. We consider configurations of the magnetization which are perturbations of two well separated domain wall, and study their evolution under the Landau-Lifshitz-Gilbert flow associated to E. Our main result is that, if the two walls have opposite speed, these configurations are asymptotically stable, up to gauges intrinsic to the invariances of the energy E. Our analysis builds on the framework developed in [4], taking advantage that it is amenable to space localisation.