Calculus of Variations and Geometric Measure Theory

G. Di Fratta

Micromagnetics of curved thin films

created by difratta on 01 Jun 2020
modified on 14 Jun 2023


Published Paper

Inserted: 1 jun 2020
Last Updated: 14 jun 2023

Journal: Zeitschrift fuer Angewandte Mathematik und Physik (ZAMP)
Year: 2020


In this paper, we aim at a reduced 2d-model describing the observable states of the magnetization in curved thin films. Under some technical assumptions on the geometry of the thin-film, it is well-known that the demagnetizing field behaves like the projection of the magnetization on the normal to the thin film. We remove these assumptions and show that the result holds for a broader class of surfaces; in particular, for compact surfaces. We treat both the stationary case, governed by the micromagnetic energy functional and the time-dependent case driven by the Landau-Lifshitz-Gilbert equation.

Keywords: Micromagnetics, Curved thin films, Γ-convergence, Landau-Lifshitz-Gilbert equation