  We report Monte-Carlo studies of the orientational order and melting of a 2D
skyrmion lattice containing more than one million spins. Two models have been
investigated, a microscopic model of lattice spins with Dzyaloshinskii-Moryia
interaction that possesses skyrmions, and the model in which skyrmions are
treated as point particles with repulsive interaction derived from a spin
model. They produce similar results. The skyrmion lattice exhibits a sharp
one-step transition between solid and liquid phases on temperature and the
magnetic field. This solid-liquid transition is characterized by the kink in
the magnetization. The field-temperature phase diagram is computed. We show
that the application of the field gradient to a 2D system of skyrmions produces
a solid-liquid interface that must be possible to observe in experiments.
