Skyrmion crystals in layered systems with a fourfold screw axis

We study magnetic phase transitions and skyrmion crystal formation in a layered square-lattice spin system with a fourfold screw axis under a magnetic field.The screw symmetry induces layer-dependent anisotropic interactions, leading to competing wave vectors and multiple-$Q$ magnetism.Using simulated annealing, we obtain the phase diagram as a function of field and anisotropy.A square skyrmion crystal with finite scalar spin chirality and skyrmion number $-1$ per layer is stabilized over a wide intermediate-field region.In the isotropic limit, the system shows a sequence of a single-$Q$, skyrmion crystal, and fully polarized state.Increasing anisotropy modifies the single-$Q$ state, induces a layer-dependent single-$Q$ phase at high fields, and enhances skyrmion crystal stability.In the strongly anisotropic regime, a trivial double-$Q$ phase appears at low fields, while the skyrmion crystal remains the only topologically nontrivial phase.These results show that nonsymmorphic screw symmetry stabilizes skyrmion crystals in layered magnetic systems.