Stability of Higher-Order Skyrmion Crystals Under Competing Magnetic Anisotropies in D3d Systems

We investigate the stability of higher-order skyrmion crystals with large topological charges in the presence of crystal-dependent magnetic anisotropies. Focusing on the competition between two types of bond-dependent anisotropy allowed by D3d crystalline symmetry on a two-dimensional triangular lattice, we systematically construct a low-temperature magnetic phase diagram using simulated annealing. Our analysis reveals that the stability of the higher-order skyrmion crystal with skyrmion number of two is strongly controlled by the relative sign of the bond-dependent anisotropy to the D3d-type anisotropy: a positive anisotropy, which favors spin oscillations perpendicular to the ordering wave vector, enhances its stability, whereas a negative anisotropy, favoring oscillations parallel to the ordering wave vector, suppresses it and instead stabilizes a topologically trivial double-Q state. We further examine the field evolution of these phases under an out-of-plane magnetic field and show that distinct types of skyrmion crystals with the skyrmion number of one emerge in the intermediate-field regime. These results highlight that the competition between different magnetic anisotropies in crystalline systems is a key factor governing the stability of both zero-field and field-induced skyrmion crystals.