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

TL;DR

This paper analyzes the micromagnetic energy with Dzyaloshinskii-Moriya interaction in thin films, proving Gamma-convergence to a 2D model relevant for boundary vortices and establishing uniqueness of local minimizers.

Contribution

It establishes the Gamma-convergence of the 3D micromagnetic energy to a 2D limit and analyzes local minimizers, providing new insights into boundary vortex configurations.

Findings

Gamma-convergence of energy to 2D model

Characterization of boundary vortices

Uniqueness of local minimizers in certain settings

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.