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

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.