Reduced theory of symmetric and antisymmetric exchange interactions in nanowires

2024/07/22 by Di Fratta, Giovanni, Rybakov, Filipp N., Slastikov, Valeriy
#35C20 #35Q51 #49S05 #82D40 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Mathematical Physics (math-ph) #Pattern Formation and Solitons (nlin.PS)

paper · doi:10.48550/arxiv.2407.15430

Abstract

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 \mathbbS²-valued functions. The perturbation K is represented by a matrix-valued function defined on \mathbbS² with values in ℝ^{3 × 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.

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