  We report our theoretical results on the emergence of rectangular- and
square-shaped magnetic skyrmion crystals on a centrosymmetric square lattice
with magnetic anisotropy. By performing the simulated annealing for a
frustrated spin model with an easy-axis single-ion anisotropy on a square
lattice, we find that a competition of the interactions in momentum space gives
rise to the formation of two skyrmion crystals, where the skyrmion cores are
aligned in a rectangle- or square-lattice way. Especially, the interactions at
the higher harmonic wave vectors play an important role in stabilizing the
square/rectangular skyrmion crystals. Our results provide a reference to
explore further skyrmion-hosting materials in centrosymmetric tetragonal
systems.
