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We investigate the instability toward a skyrmion crystal under an in-planemagnetic field in centrosymmetric tetragonal magnets. By performing thesimulated annealing for a spin model on the square lattice, we find that theinterplay among the easy-plane two-spin anisotropic interaction, positivebiquadratic interaction, and high-harmonic wave-vector interaction plays animportant role in stabilizing the skyrmion crystal in the in-plane externalmagnetic field. The obtained skyrmion crystal consists of a pair of vortex andantivortex with opposite polarization in terms of the out-of-plane spincomponent. We also show that various multiple-$Q$ states emerge depending onthe model parameters. Our results indicate the possibility of topological spintextures in centrosymmetric tetragonal magnets with easy-plane magneticanisotropy when the ground-state spin configuration at zero field ischaracterized by a single-$Q$ in-plane cycloidal spiral state.

Anisotropic skyrmion crystal on a centrosymmetric square lattice under an in-plane magnetic field