Melting and freezing of a skyrmion lattice.

We report comprehensive Monte-Carlo studies of the melting of skyrmion lattices (SkL) in systems of small, medium, and large sizes with the number of skyrmions ranging from 10 3 to over 10 5 . Large systems exhibit hysteresis similar to that observed in real experiments on the melting of SkLs. For sufficiently small systems which achieve thermal equilibrium, a fully reversible sharp solid-liquid transition on temperature with no intermediate hexatic phase is observed. A similar behavior is found on changing the magnetic field that provides the control of pressure in the SkL. We find that on heating the melting transition occurs via a formation of grains with different orientations of hexagonal axes. On cooling, the fluctuating grains coalesce into larger clusters until a uniform orientation of hexagonal axes is slowly established. The observed scenario is caused by collective effects involving defects and is more complex than a simple picture of a transition driven by the unbinding and annihilation of dislocation and disclination pairs.