Role of Single-Ion Anisotropy in Stabilizing Higher-Order Skyrmion Crystals in D_3d-Symmetric Magnets

We investigate the role of single-ion anisotropy in stabilizing higher-order skyrmion crystal phases in centrosymmetric magnets under D3d symmetry. Using a classical spin model that incorporates both single-ion and D3d-type magnetic anisotropies, we perform simulated annealing calculations to explore the ground-state spin configurations. We find that a skyrmion crystal with a skyrmion number of two is stabilized over a wide range of parameters of single-ion anisotropy and D3d-type anisotropy. We also show that the skyrmion core position shifts from an interstitial site to an on-site location as the magnitude of the easy-axis single-ion anisotropy increases. Furthermore, we demonstrate that the magnetic field drives a variety of topological phase transitions depending on the sign and magnitude of the single-ion and D3d-type anisotropies. These results provide a possible microscopic understanding of how complex topological spin textures can be stabilized in centrosymmetric D3d magnets, suggesting that multiple phases with topological spin textures could emerge even in the absence of the Dzyaloshinskii–Moriya interaction.