Another approach to the thin-film Gamma-limit of the micromagnetic free energy in the regime of small samples

TL;DR

This paper investigates the asymptotic behavior of micromagnetic free energy in thin ferromagnetic films, using a novel PDE constraint approach that captures the magnetic field without solving magnetostatic equations, leading to a new Gamma-limit characterization.

Contribution

It introduces a new method treating Maxwell's equations as a PDE constraint, enabling analysis of the Gamma-limit without explicitly solving magnetostatic equations.

Findings

Recovered convergence results of minimizers by Gioia and James

Characterized the Gamma-limit of the micromagnetic energy

Provided a new approach to analyze thin-film micromagnetics

Abstract

The asymptotic behavior of the micromagnetic free energy governing a ferromagnetic film is studied as its thickness gets smaller and smaller compared to its cross section. Here the static Maxwell equations are treated as a Murat's constant-rank PDE constraint on the energy functional. In contrast to previous work this approach allows to keep track of the induced magnetic field without solving the magnetostatic equations. In particular, the mathematical results of Gioia and James [Proc. R. Soc. Lond. A 453 (1997), pp. 213-223] regarding convergence of minimizers are recovered by giving a characterization of the corresponding Gamma-limit.