Nonlinear Stability of Static N\'eel Walls in Ferromagnetic Thin Films

TL;DR

This paper proves the nonlinear stability of static 180° Néel walls in ferromagnetic thin films under a specific wave-type dynamic model, showing small disturbances lead to convergence towards a translated static wall.

Contribution

It establishes the nonlinear orbital stability of static Néel walls within a reduced wave-type dynamic framework, extending understanding of magnetic domain wall stability.

Findings

Spectrum of the linearized operator is in the stable complex half plane.

Small perturbations converge to a translated static Néel wall.

Provides mathematical proof of stability in a specific dynamic model.

Abstract

In this paper, the nonlinear (orbital) stability of static 180^\circ N\'eel walls in ferromagnetic films, under the reduced wave-type dynamics for the in-plane magnetization proposed by Capella, Melcher and Otto [CMO07], is established. It is proved that the spectrum of the linearized operator around the static N\'eel wall lies in the stable complex half plane with non-positive real part. This information is used to show that small perturbations of the static N\'eel wall converge to a translated orbit belonging to the manifold generated by the static wall.