2024/01/31 by Radu Ignat, Ignat, Radu, François L’Official +1 · 2 citations
Engineering · Physics and Astronomy · #35B25 #49J45 #82D40 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Thin Films #Magnetic properties of thin films #Mathematical Physics (math-ph) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2401.17830
openalex publication_date 2024/01/31 · openalex created_date 2024/02/02 · openalex updated_date 2026/07/28
We consider a three-dimensional micromagnetic model with Dzyaloshinskii-Moriya interaction in a thin-film regime for boundary vortices. In this regime, we prove a dimension reduction result: the nonlocal three-dimensional model reduces to a local two-dimensional Ginzburg-Landau type model in terms of the averaged magnetization in the thickness of the film. This reduced model captures the interaction between boundary vortices (so-called renormalised energy), that we determine by a Γ-convergence result at the second order and then we analyse its minimisers. They nucleate two boundary vortices whose position depends on the Dzyaloshinskii-Moriya interaction.