A simple analytical description for the cross-tie domain wall structure

A closed form analytical expression for the magnetization vector distribution within the cross-tie domain wall in an isotropic ferromagnetic thin film is given. The expression minimizes the exchange energy functional exactly, and the magnetostatic energy by means of an adjustable parameter (wall width). The equilibrium value of the wall width and the film thickness corresponding to the transition between the N{\'e}el and the cross-tie walls are calculated. The results are compared with the recent experiments and are in good qualitative agreement.