Existence and Uniqueness of Domain Walls for Notched Ferromagnetic Nanowires
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915057081778176 |
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| author | Côte, Raphaël Courtès, Clémentine Ferriere, Guillaume Godard-Cadillac, Ludovic Privat, Yannick |
| author_facet | Côte, Raphaël Courtès, Clémentine Ferriere, Guillaume Godard-Cadillac, Ludovic Privat, Yannick |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07357 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence and Uniqueness of Domain Walls for Notched Ferromagnetic Nanowires Côte, Raphaël Courtès, Clémentine Ferriere, Guillaume Godard-Cadillac, Ludovic Privat, Yannick Analysis of PDEs Classical Analysis and ODEs Optimization and Control 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. |
| title | Existence and Uniqueness of Domain Walls for Notched Ferromagnetic Nanowires |
| topic | Analysis of PDEs Classical Analysis and ODEs Optimization and Control |
| url | https://arxiv.org/abs/2412.07357 |