Micromagnetics of thin films in the presence of Dzyaloshinskii–Moriya interaction

Author:

Davoli Elisa1,Di Fratta Giovanni1,Praetorius Dirk1,Ruggeri Michele2

Affiliation:

1. TU Wien, Institute of Analysis and Scientific Computing, Wiedner Hauptstraße 8–10, 1040 Vienna, Austria

2. University of Strathclyde, Department of Mathematics and Statistics, 26 Richmond Street, Glasgow G1 1XH, United Kingdom

Abstract

In this paper, we study the thin-film limit of the micromagnetic energy functional in the presence of bulk Dzyaloshinskii–Moriya interaction (DMI). Our analysis includes both a stationary [Formula: see text]-convergence result for the micromagnetic energy, as well as the identification of the asymptotic behavior of the associated Landau–Lifshitz–Gilbert equation. In particular, we prove that, in the limiting model, part of the DMI term behaves like the projection of the magnetic moment onto the normal to the film, contributing this way to an increase in the shape anisotropy arising from the magnetostatic self-energy. Finally, we discuss a convergent finite element approach for the approximation of the time-dependent case and use it to numerically compare the original three-dimensional (3D) model with the 2D thin-film limit.

Funder

Austrian Science Fund

FWF

Large Strain Challenges in Materials Science

Tunable materials: Geometry, Nonlocality, Chirality

Austrian Federal Ministry of Education, Science and Research (BMBWF) through the OeAD-WTZ

GDF

EPSRC

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Modeling and Simulation

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