1. Reduced theory of symmetric and antisymmetric exchange interactions in nanowires
- Author
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Di Fratta, Giovanni, Rybakov, Filipp N., and Slastikov, Valeriy
- Subjects
Mathematics - Analysis of PDEs ,Condensed Matter - Materials Science ,Mathematical Physics ,Nonlinear Sciences - Pattern Formation and Solitons ,49S05, 35C20, 35Q51, 82D40 - Abstract
We investigate the behavior of minimizers of perturbed Dirichlet energies supported on a wire generated by a regular simple curve $\gamma$ 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 $\Gamma$-convergence, to a simplified energy functional on $\gamma$. The reduced energy unveils how part of the antisymmetric exchange interactions contribute to an anisotropic term whose specific shape depends on the curvature of $\gamma$. We also discuss the significant implications of our results for studies of ferromagnetic nanowires when Dzyaloshinskii-Moriya interaction (DMI) is present.
- Published
- 2024