Reduced theory of symmetric and antisymmetric exchange interactions in nanowires
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908443621720064 |
|---|---|
| author | Di Fratta, Giovanni Rybakov, Filipp N. Slastikov, Valeriy |
| author_facet | Di Fratta, Giovanni Rybakov, Filipp N. Slastikov, Valeriy |
| contents | We investigate the behavior of minimizers of perturbed Dirichlet energies supported on a wire generated by a regular simple curve $γ$ and defined in the space of $\mathbb{S}^2$-valued functions. The perturbation $K$ is represented by a matrix-valued function defined on $\mathbb{S}^2$ with values in $\mathbb{R}^{3 \times 3}$. Under natural regularity conditions on $K$, we show that the family of perturbed Dirichlet energies converges, in the sense of $Γ$-convergence, to a simplified energy functional on $γ$. The reduced energy unveils how part of the antisymmetric exchange interactions contribute to an anisotropic term whose specific shape depends on the curvature of $γ$.
We also discuss the significant implications of our results for studies of ferromagnetic nanowires when Dzyaloshinskii-Moriya interaction (DMI) is present. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15430 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reduced theory of symmetric and antisymmetric exchange interactions in nanowires Di Fratta, Giovanni Rybakov, Filipp N. Slastikov, Valeriy Analysis of PDEs Materials Science Mathematical Physics Pattern Formation and Solitons 49S05, 35C20, 35Q51, 82D40 We investigate the behavior of minimizers of perturbed Dirichlet energies supported on a wire generated by a regular simple curve $γ$ and defined in the space of $\mathbb{S}^2$-valued functions. The perturbation $K$ is represented by a matrix-valued function defined on $\mathbb{S}^2$ with values in $\mathbb{R}^{3 \times 3}$. Under natural regularity conditions on $K$, we show that the family of perturbed Dirichlet energies converges, in the sense of $Γ$-convergence, to a simplified energy functional on $γ$. The reduced energy unveils how part of the antisymmetric exchange interactions contribute to an anisotropic term whose specific shape depends on the curvature of $γ$. We also discuss the significant implications of our results for studies of ferromagnetic nanowires when Dzyaloshinskii-Moriya interaction (DMI) is present. |
| title | Reduced theory of symmetric and antisymmetric exchange interactions in nanowires |
| topic | Analysis of PDEs Materials Science Mathematical Physics Pattern Formation and Solitons 49S05, 35C20, 35Q51, 82D40 |
| url | https://arxiv.org/abs/2407.15430 |