  We study static 180 degree domain walls in thin infinite magnetic films. We
establish the scaling of the minimal energy by {\Gamma}-convergence and the
energy minimizer pro-file, 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.
