Scaling laws and the rate of convergence in thin magnetic films

We study static 180 degree domain walls in thin infinite magnetic films. We establish the scaling of the minimal energy by Γ-convergence and the energy minimizer profile, which turns out to be the so-called transverse wall as predicted in earlier numerical and experimental work. Surprisingly, the minimal energy decays faster than the area of the film cross section at an infinitesimal cross section diameter. We establish a rate of convergence of the rescaled energies as well.