Transverse domain walls in thin ferromagnetic strips

TL;DR

This paper analyzes the properties of transverse domain walls in thin ferromagnetic strips, establishing their existence, uniqueness, and symmetry, and connects these solutions to a limiting energy functional derived from micromagnetic theory.

Contribution

It provides a rigorous characterization of domain wall solutions as minimizers of a specific energy functional in thin ferromagnetic strips, including their existence and symmetry properties.

Findings

Existence and uniqueness of 180° and 360° domain walls.

Symmetry and monotonicity of magnetization profiles.

Derivation of the energy as a Gamma-limit of micromagnetic energy.

Abstract

We present a characterization of the domain wall solutions arising as minimizers of an energy functional obtained in a suitable asymptotic regime of micromagnetics for infinitely long thin film ferromagnetic strips in which the magnetization is forced to lie in the film plane. For the considered energy, we provide existence, uniqueness, monotonicity, and symmetry of the magnetization profiles in the form of 180$^\circ$ and 360$^\circ$ walls. We also demonstrate how this energy arises as a $\Gamma$-limit of the reduced two-dimensional thin film micromagnetic energy that captures the non-local effects associated with the stray field, and characterize its respective energy minimizers.