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arXiv · 2412.07357

Existence and Uniqueness of Domain Walls for Notched Ferromagnetic Nanowires

Raphaël Côte·Clémentine Courtès·Guillaume Ferriere·Ludovic Godard-Cadillac·Yannick Privat
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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.

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Raphaël Côte, Clémentine Courtès, Guillaume Ferriere, Ludovic Godard-Cadillac, Yannick Privat. 2024-12-10. Existence and Uniqueness of Domain Walls for Notched Ferromagnetic Nanowires. https://arxiv.org/abs/2412.07357

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