# One-dimensional in-plane edge domain walls in ultrathin ferromagnetic films

## TL;DR

This paper investigates the existence, properties, and numerical profiles of one-dimensional edge domain walls in ultrathin ferromagnetic films with in-plane anisotropy, revealing how magnetization transitions occur near film edges.

## Contribution

It proves the existence of edge domain walls as energy minimizers and provides a numerical analysis of their profiles in ultrathin ferromagnetic films.

## Key findings

- Existence of classical solutions for edge domain walls.
- Numerical profiles reveal transition layer characteristics.
- Edge domain walls minimize micromagnetic energy functional.

## Abstract

We study existence and properties of one-dimensional edge domain walls in ultrathin ferromagnetic films with uniaxial in-plane magnetic anisotropy. In these materials, the magnetization vector is constrained to lie entirely in the film plane, with the preferred directions dictated by the magnetocrystalline easy axis. We consider magnetization profiles in the vicinity of a straight film edge oriented at an arbitrary angle with respect to the easy axis. To minimize the micromagnetic energy, these profiles form transition layers in which the magnetization vector rotates away from the direction of the easy axis to align with the film edge. We prove existence of edge domain walls as minimizers of the appropriate one-dimensional micromagnetic energy functional and show that they are classical solutions of the associated Euler-Lagrange equation with Dirichlet boundary condition at the edge. We also perform a numerical study of these one-dimensional domain walls and uncover further properties of these domain wall profiles.