Existence of higher degree minimizers in the magnetic skyrmion problem

Autor:	Muratov, Cyrill B., Simon, Theresa M., Slastikov, Valeriy V.
Rok vydání:	2024
Předmět:	Mathematics - Analysis of PDEs Condensed Matter - Mesoscale and Nanoscale Physics Mathematical Physics Nonlinear Sciences - Pattern Formation and Solitons 58E15 49S05 35J57 35Q99
Druh dokumentu:	Working Paper
Popis:	We demonstrate existence of topologically nontrivial energy minimizing maps of a given positive degree from bounded domains in the plane to $\mathbb S^2$ in a variational model describing magnetizations in ultrathin ferromagnetic films with Dzyaloshinskii-Moriya interaction. Our strategy is to insert tiny truncated Belavin-Polyakov profiles in carefully chosen locations of lower degree objects such that the total energy increase lies strictly below the expected Dirichlet energy contribution, ruling out loss of degree in the limits of minimizing sequences. The argument requires that the domain be either sufficiently large or sufficiently slender to accommodate a prescribed degree. We also show that these higher degree minimizers concentrate on point-like skyrmionic configurations in a suitable parameter regime. Comment: 29 pages, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2409.07205 Zobrazit plný text záznamu View this record from Arxiv