A classical S2 spin system with discrete out-of-plane anisotropy: Variational analysis at surface and vortex scalings. (June 2023)

• Record Type: Journal Article
• Authors: Cicalese, Marco; Orlando, Gianluca; Ruf, Matthias
• Is Part Of: Nonlinear analysis. Volume 231(2023)
• Publication Date: 2023-06
• Subjects: 49J45 -- 49M25 -- 82B20 -- 82D40; Γ-convergence -- Interface energy -- Topological singularities; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.112929
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider a classical Heisenberg system of S 2 spins on a square lattice of spacing ɛ . We introduce a magnetic anisotropy by constraining the out-of-plane component of each spin to take only finitely many values. Computing the Γ -limit of a suitable scaling of the energy functional as ɛ → 0 we prove that, in the continuum description, the system concentrates energy at the boundary of sets in which the out-of-plane component of the spin is constant. In a second step we analyze a different scaling of the energy and we prove that, in each of such phases, the energy can further concentrate on finitely many points corresponding to vortex-like singularities of the in-plane components of the spins.