Stretched-exponential relaxation in two-dimensional easy-plane ferromagnets

A classical ferromagnet is described in a continuum approximation and at the microscopic level by the Landau-Lifshitz equation. In two spatial dimensions, vortices are the topological solutions of the model in the presence of easy-plane anisotropy. We argue that a system of vortices has an energy landscape whose gross features can be well described. We investigate numerically the effect of the complex energy landscape on the relaxation dynamics, namely a characteristic stretched-exponential decrease in the energy and the number of vortices present in the system as the system relaxes toward the ground state.