Skyrmion crystals: Dynamics and phase transition

We study a crystal of skyrmions generated on a square lattice using a ferromagnetic exchange interaction and a Dzyaloshinskii-Moriya interaction between nearest-neighbors under an external magnetic field. The skyrmion crystal has a hexagonal structure which is shown to be stable up to a temperature Tc where a transition to the paramagnetic phase occur. We will show that the dynamics of the skyrmions at T < Tc follows a stretched exponential law.