Magnetic domain wall dynamics associated with the dynamic phase transition

We studied the interaction between two magnetic domain walls in a one- dimensional anisotropic XY-spin system in an oscillating magnetic field using the time-dependent Ginzburg-Landau (TDGL) equation. There are two types of magnetic domain walls, Néel and Bloch walls, in this system. The interaction between two Néel walls is attractive. For two Bloch walls, the interaction depends on the chiralities of the walls. The interaction is attractive when two neighboring Bloch walls have different chiralities, and it is repulsive when two Bloch walls have the same chiralities. The distance between two walls shows logarithmic time dependence for all cases. The numerical results are analytically explained by making use of the Fourier-expansion approximation.