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

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