Asymmetric domain walls of small angle in soft ferromagnetic films

TL;DR

This paper rigorously analyzes the structure and energy of asymmetric domain walls in soft ferromagnetic films as the angle between domains approaches zero, revealing a bifurcation from symmetric to asymmetric configurations.

Contribution

It provides the first rigorous derivation of the asymptotic structure and energy of asymmetric domain walls in the Landau-Lifshitz model for small angles.

Findings

Asymmetric domain walls emerge as the energy-minimizing configuration for small angles.

A supercritical bifurcation causes the transition from symmetric to asymmetric walls.

The asymptotic structure of these walls is characterized as the angle approaches zero.

Abstract

We focus on a special type of domain walls appearing in the Landau-Lifshitz theory for soft ferromagnetic films. These domain walls are divergence-free $S^2$-valued transition layers that connect two directions in $S^2$ (differing by an angle $2\theta$) and minimize the Dirichlet energy. Our main result is the rigorous derivation of the asymptotic structure and energy of such "asymmetric" domain walls in the limit $\theta \to 0$. As an application, we deduce that a supercritical bifurcation causes the transition from symmetric to asymmetric walls in the full micromagnetic model.