Antiferro skyrmion crystals consisting of skyrmions and anti-skyrmions on a bilayer square lattice

An antiferro-type skyrmion crystal consisting of skyrmions with a negative topological charge and antiskyrmions with a positive topological charge manifests itself in its peculiar topological magnetism. We theoretically investigate the emergence of such an antiferro-type skyrmion crystal, where the topological charge exists in each sublattice but vanishes in the whole system. By performing the simulated annealing for an effective spin model with competing exchange interactions and staggered Dzyaloshinskii-Moriya interaction in momentum space on a bilayer square lattice, we find that the synergy between the antiferromagnetic interlayer exchange interaction and high-harmonic wave-vector interaction in addition to the staggered Dzyaloshinskii-Moriya interaction results in the antiferro-type skyrmion crystal in an external magnetic field. We show that the antiferro-type skyrmion crystal turns into the ferro-type skyrmion crystal with the same topological charge for both layers when the magnitude of the external magnetic field is varied. We also demonstrate that the competing interactions between ordering wave-vector channels and their high-harmonic wave-vector channels are essential in stabilizing the antiferro-type skyrmion crystal. Our results provide important ingredients to realize the antiferro-type skyrmion crystal by the external magnetic field, which can be utilized for low-power and high-speed spintronic devices based on antiferromagnetic materials.