Phase transition thresholds and chiral magnetic fields of general degree
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911347583746048 |
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| author | Ibrahim, Slim Miura, Tatsuya Román, Carlos Shimizu, Ikkei |
| author_facet | Ibrahim, Slim Miura, Tatsuya Román, Carlos Shimizu, Ikkei |
| contents | We study a variational problem for the Landau--Lifshitz energy with Dzyaloshinskii--Moriya interactions arising in 2D micromagnetics, focusing on the Bogomol'nyi regime. We first determine the minimal energy for arbitrary topological degree, thereby revealing two types of phase transitions consistent with physical observations. In addition, we prove the uniqueness of the energy minimizer in degrees $0$ and $-1$, and nonexistence of minimizers for all other degrees. Finally, we show that the homogeneous state remains stable even beyond the threshold at which the skyrmion loses stability, and we uncover a new stability transition driven by the Zeeman energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24598 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Phase transition thresholds and chiral magnetic fields of general degree Ibrahim, Slim Miura, Tatsuya Román, Carlos Shimizu, Ikkei Analysis of PDEs 35Q60, 82D40, 82B26 We study a variational problem for the Landau--Lifshitz energy with Dzyaloshinskii--Moriya interactions arising in 2D micromagnetics, focusing on the Bogomol'nyi regime. We first determine the minimal energy for arbitrary topological degree, thereby revealing two types of phase transitions consistent with physical observations. In addition, we prove the uniqueness of the energy minimizer in degrees $0$ and $-1$, and nonexistence of minimizers for all other degrees. Finally, we show that the homogeneous state remains stable even beyond the threshold at which the skyrmion loses stability, and we uncover a new stability transition driven by the Zeeman energy. |
| title | Phase transition thresholds and chiral magnetic fields of general degree |
| topic | Analysis of PDEs 35Q60, 82D40, 82B26 |
| url | https://arxiv.org/abs/2512.24598 |