Domain Configurations in Soft Ferromagnetic Films under External Field

This note is about the prediction of the domain and wall configuration formed by the magnetization m in a soft ferromagnetic film under an external field. We propose a modification of the reduced model introduced by DeSimone et al. (2001), that is a variational model for a 2-d in-plane magnetization m on the cross section ω. The modification consists of two parts:1.) An unphysical but computationally convenient selection criterion in DeSimone et al. (2001) is replaced by a selection criterion based on physical wall energy,2.) The set of admissible configurations is restricted by imposing an additional boundary condition at the boundary ∂ω of the cross section.The specific wall energy is computed off-line based on a 2-d reduction of the 3-d model from Döring et al. (2012b), and then fed into a diffuse interface approximation for the selection criterion 1.). This retains some of the low complexity of the original model DeSimone et al. (2001). Modification 2.) allows to model hysteresis as observed in experiments by van den Berg and Vatvani (1982); preliminary numerical simulations reveal good qualitative agreement.