Article Dans Une Revue ESAIM: Control, Optimisation and Calculus of Variations Année : 2025

Existence and uniqueness of domain walls for notched ferromagnetic nanowires

Résumé

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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Dates et versions

hal-05170804 , version 1 (09-12-2024)
hal-05170804 , version 2 (19-07-2025)

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Raphaël Côte, Clémentine Courtès, Guillaume Ferriere, Ludovic Godard-Cadillac, Yannick Privat. Existence and uniqueness of domain walls for notched ferromagnetic nanowires. ESAIM: Control, Optimisation and Calculus of Variations, 2025, 31, pp.60. ⟨10.1051/cocv/2025051⟩. ⟨hal-05170804v2⟩
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