Topological defects, pattern evolution, and hysteresis in thin magnetic   films
  Nature of the magnetic hysteresis for thin films is studied by the Monte-Carlo simulations. It is shown that a reconstruction of the magnetization pattern with external field occurs via the creation of vortex-antivortex pairs of a special kind at the boundaries of stripe domains. It is demonstrated that the symmetry of order parameter is of primary importance for this problem, in particular, the in-plane magnetic anisotropy is necessary for the hysteresis. 
P. A. Prudkovskii, A. N. Rubtsov and M. I. Katsnelson