Two-dimensional modelling of soft ferromagnetic films

We examine the response of a soft ferromagnetic film to an in-plane applied magnetic field by means of both theory and experiment. In the thin-film limit, we uncover a separation of scales in the rough energy landscape of micromagnetics: leading-order terms generate constraints which eliminate degrees of freedom, terms of second order in the film thickness lead to a (new) reduced variational model, higher-order terms are related to wall, vortex and anisotropy energies. We propose a new strategy to compute low-energy domain patterns, which proceeds in two steps: we determine first the magnetic charge density by solving a convex variational problem, then we construct an associated magnetization field using a robust numerical method. Experimental results show good agreement with the theory. Our analysis is consistent with prior work by van den Berg and by Bryant and Suhl, but it goes much further; in particular it applies even for large fields which penetrate the sample.