A thin-film limit in the Landau-Lifshitz-Gilbert equation relevant for the formation of N\'eel walls

TL;DR

This paper investigates the behavior of thin ferromagnetic films, establishing the conditions for Ne9el wall formation, their uniqueness as energy minimizers, and their dynamical properties under the Landau-Lifshitz-Gilbert flow.

Contribution

It provides a rigorous analysis of Ne9el wall formation, uniqueness, and dynamics in thin-film ferromagnets within a specific asymptotic regime.

Findings

Compactness of magnetizations in the Ne9el wall regime

Ne9el walls are asymptotically the unique energy minimizers

Analysis of magnetization flow under Landau-Lifshitz-Gilbert dynamics

Abstract

We consider an asymptotic regime for two-dimensional ferromagnetic films that is consistent with the formation of transition layers (N\'eel walls). We first establish compactness of S2-valued magnetizations in the energetic regime of N\'eel walls and characterize the set of accumulation points. We then prove that N\'eel walls are asymptotically the unique energy minimizing configurations. We finally study the corresponding dynamical issues, namely the compactness properties of the magnetizations under the flow of the Landau-Lifshitz-Gilbert equation.