One-dimensional Neel walls under applied external fields

TL;DR

This paper provides a rigorous mathematical analysis of one-dimensional Ne9el walls in thin ferromagnetic films under external in-plane magnetic fields, establishing existence, uniqueness, and detailed properties of the wall profiles.

Contribution

It introduces a non-local variational framework for Ne9el walls and proves key properties of the minimizers, including their asymptotic behavior.

Findings

Existence and uniqueness of Ne9el wall profiles.

Regularity and strict monotonicity of solutions.

Asymptotic decay rates of the minimizers.

Abstract

We present a detailed analysis of one-dimensional N\'eel walls in thin uniaxial ferromagnetic films in the presence of an in-plane applied external field in the direction normal to the easy axis. Within the reduced one-dimensional thin film model, we formulate a non-local variational problem whose minimizers are given by one-dimensional N\'eel wall profiles. We prove existence, uniqueness (up to translations and reflections), regularity, strict monotonicity and the precise asymptotics of the decay of the minimizers in the considered variational problem.