Existence and Uniqueness of Domain Walls for Notched Ferromagnetic Nanowires
Abstract
In this article, we investigate a simple model of notched ferromagnetic nanowires using tools from calculus of variations and critical point theory. Specifically, we focus on the case of a single unimodal notch and establish the existence and uniqueness of the critical point of the energy. This is achieved through a lifting argument, which reduces the problem to a generalized Sturm-Liouville equation. Uniqueness is demonstrated via a Mountain-Pass argument, where the assumption of two distinct critical points leads to a contradiction. Additionally, we show that the solution corresponds to a system of magnetic spins characterized by a single domain wall localized in the vicinity of the notch. We further analyze the asymptotic decay of the solution at infinity and explore the symmetric case using rearrangement techniques.
Keywords
Cite
@article{arxiv.2412.07357,
title = {Existence and Uniqueness of Domain Walls for Notched Ferromagnetic Nanowires},
author = {Raphaël Côte and Clémentine Courtès and Guillaume Ferriere and Ludovic Godard-Cadillac and Yannick Privat},
journal= {arXiv preprint arXiv:2412.07357},
year = {2024}
}