Skyrmion crystal and spiral phases in centrosymmetric bilayer magnets with staggered Dzyaloshinskii-Moriya interaction

We theoretically study a stabilization mechanism of the skyrmion crystal in centrosymmetric magnets with bilayer structure. show that interplay between layer-dependent staggered Dzyaloshinskii-Moriya interaction arises from absence local inversion symmetry and interlayer exchange gives rise to plethora multiple-$Q$ states including quantized topological number. By performing simulated annealing for triangular-lattice model under an external magnetic field, we demonstrate forms triangular-shaped crystals different helicities each layer owing interaction. Although relative positions core are depending on sign interactions, phases robustly appear both ferromagnetic antiferromagnetic interactions. also find another two triple-$Q$ uniform scalar chirality but without number low- high-field regions. Especially, low-field state exhibits opposite crystal, which is not found single-layer system. Our results indicate lack lattice structure key ingredient induce spin textures magnets.