MiS Preprint Repository

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, Kohn, Müller, Otto, Schäfer 2001, that is a variational model for a 2-d in-plane magnetization m on the cross section $\omega$. The modification consists of two parts:
1.) An unphysical but computationally convenient selection criterion 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 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, Ignat, Otto 2012, and then fed into a diffuse interface approximation for the selection criterion
1.) This retains some of the low complexity of the original model. Modification
2.) allows to model hysteresis as observed in experiments by van den Berg, Vatvani 1982; preliminary numerical simulations reveal good qualitative agreement.