Convergent tangent plane integrators for the simulation of chiral magnetic skyrmion dynamics

Hrkac, Gino and Pfeiler, Carl-Martin and Praetorius, Dirk and Ruggeri, Michele and Segatti, Antonio and Stiftner, Bernhard (2019) Convergent tangent plane integrators for the simulation of chiral magnetic skyrmion dynamics. Advances in Computational Mathematics, 45 (3). pp. 1329-1368. ISSN 1019-7168 (https://doi.org/10.1007/s10444-019-09667-z)

[thumbnail of Hrkac-etal-ACM-2019-Convergent-tangent-plane-integrators]
Preview
 Text. Filename: Hrkac_etal_ACM_2019_Convergent_tangent_plane_integrators.pdf
Final Published Version
License: Creative Commons Attribution 4.0 logo
Download (3MB)| Preview

Abstract

We consider the numerical approximation of the Landau–Lifshitz–Gilbert equation, which describes the dynamics of the magnetization in ferromagnetic materials. In addition to the classical micromagnetic contributions, the energy comprises the Dzyaloshinskii–Moriya interaction, which is the most important ingredient for the enucleation and the stabilization of chiral magnetic skyrmions. We propose and analyze three tangent plane integrators, for which we prove (unconditional) convergence of the finite element solutions towards a weak solution of the problem. The analysis is constructive and also establishes existence of weak solutions. Numerical experiments demonstrate the applicability of the methods for the simulation of practically relevant problem sizes.

CORE (COnnecting REpositories)