  We study theoretically, via Monte Carlo simulations on lattices containing up
to 1000 x 1000 spins, thermal creation of skyrmion lattices in a 2D
ferromagnetic film with perpendicular magnetic anisotropy and
Dzyaloshinskii-Moriya interaction. At zero temperature, skyrmions only appear
in the magnetization process in the presence of static disorder. Thermal
fluctuations violate conservation of the topological charge and reduce the
effective magnetic anisotropy that tends to suppress skyrmions. In accordance
with recent experiments, we find that elevated temperatures assist the
formation of skyrmion structures. Once such a structure is formed, it can be
frozen into a regular skyrmion lattice by reducing the temperature. We
investigate topological properties of skyrmion structures and find the average
skyrmion size. Energies of domain and skyrmion states are computed. It is shown
that skyrmion lattices have lower energy than labyrinth domains within a narrow
field range.
