Time-periodic N\'eel wall motions

TL;DR

This paper constructs time-periodic motions of Neel walls in thin ferromagnetic films by perturbing static profiles, under specific conditions on external magnetic fields, advancing understanding of dynamic magnetic domain behaviors.

Contribution

It introduces a method to generate time-periodic Neel wall motions from static profiles using perturbation techniques within a controlled parameter regime.

Findings

Successful construction of time-periodic Neel wall solutions

Applicable under small external magnetic field amplitudes

Provides insights into dynamic behaviors of magnetic domain walls

Abstract

In thin ferromagnetic films, the predominance of the magnetic shape anisotropy leads to in-plane magnetizations. The simplest domain wall in this geometry is the one-dimensional Neel wall that connects two magnetizations of opposite sign by a planar 180 degree rotation. In this paper, we perturb the static Neel wall profile in order to construct time-periodic Neel wall motions governed by to the Landau-Lifshitz-Gilbert equation. Our construction works within a certain parameter regime and requires the restriction to external magnetic fields with small amplitudes and suitable time averages.