The micromagnetic energy with Dzyaloshinskii-Moriya interaction in a thin-film regime relevant for boundary vortices

Abstract

We consider the three-dimensional micromagnetic model with Dzyaloshinskii-Moriya interaction in a thin-film regime. We prove the $ \Gamma $-convergence of the micromagnetic energy in the considered regime, for which the $ \Gamma $-limit energy is two-dimensional and relevant for boundary vortices. We then study local minimizers of the $ \Gamma $-limit energy and prove a uniqueness result in a certain setting.