Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2506.11955 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913892515446784 |
|---|---|
| author | Deng, Bin Ignat, Radu Lamy, Xavier |
| author_facet | Deng, Bin Ignat, Radu Lamy, Xavier |
| contents | We study minimizers $\boldsymbol{m}\colon \mathbb R^2\to\mathbb S^2$ of the energy functional \begin{align*} E_σ(\boldsymbol{m}) = \int_{\mathbb R^2} \bigg(\frac 12 |\nabla\boldsymbol{m}|^2 +σ^2 \boldsymbol{ m} \cdot \nabla \times\boldsymbol{m} +σ^2 m_3^2
\bigg)\, dx\,, \end{align*} for $0<σ\ll 1$, with prescribed topological degree \begin{align*} Q(\boldsymbol{m})=\frac{1}{4π} \int_{\mathbb R^2}\boldsymbol{m} \cdot \partial_1 \boldsymbol{m}\times\partial_2\boldsymbol{m}\, dx =\pm 1\,. \end{align*} This model arises in thin ferromagnetic films with Dzyaloshinskii-Moriya interaction and easy-plane anisotropy, where these minimizers represent bimeron configurations. We prove their existence, and describe them precisely as perturbations of specific Möbius maps: we establish in particular that they are localized at scale of order $1/|\ln(σ^2)|$. The proof follows a strategy introduced by Bernand-Mantel, Muratov and Simon (Arch. Ration. Mech. Anal., 2021) for a similar model with easy-axis anisotropy, but requires several adaptations to deal with the less coercive easy-plane anisotropy and different symmetry properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11955 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The conformal limit for bimerons in easy-plane chiral magnets Deng, Bin Ignat, Radu Lamy, Xavier Analysis of PDEs We study minimizers $\boldsymbol{m}\colon \mathbb R^2\to\mathbb S^2$ of the energy functional \begin{align*} E_σ(\boldsymbol{m}) = \int_{\mathbb R^2} \bigg(\frac 12 |\nabla\boldsymbol{m}|^2 +σ^2 \boldsymbol{ m} \cdot \nabla \times\boldsymbol{m} +σ^2 m_3^2 \bigg)\, dx\,, \end{align*} for $0<σ\ll 1$, with prescribed topological degree \begin{align*} Q(\boldsymbol{m})=\frac{1}{4π} \int_{\mathbb R^2}\boldsymbol{m} \cdot \partial_1 \boldsymbol{m}\times\partial_2\boldsymbol{m}\, dx =\pm 1\,. \end{align*} This model arises in thin ferromagnetic films with Dzyaloshinskii-Moriya interaction and easy-plane anisotropy, where these minimizers represent bimeron configurations. We prove their existence, and describe them precisely as perturbations of specific Möbius maps: we establish in particular that they are localized at scale of order $1/|\ln(σ^2)|$. The proof follows a strategy introduced by Bernand-Mantel, Muratov and Simon (Arch. Ration. Mech. Anal., 2021) for a similar model with easy-axis anisotropy, but requires several adaptations to deal with the less coercive easy-plane anisotropy and different symmetry properties. |
| title | The conformal limit for bimerons in easy-plane chiral magnets |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2506.11955 |