Skyrmion robustness in noncentrosymmetric magnets with axial symmetry: The role of anisotropy and tilted magnetic fields

We investigate the stability of Nel skyrmions against tilted magnetic fields in polar magnets with uniaxial anisotropy ranging from easy-plane to easy-axis type. We construct the corresponding phase diagrams and investigate the internal structure of skewed skyrmions with displaced cores. We find that moderate easy-plane anisotropy increases the stability range of Neel skyrmions for fields along the symmetry axis, while moderate easy-axis anisotropy enhances their robustness against tilted magnetic fields. We stress that the direction along which the skyrmion cores are shifted depends on the symmetry of the underlying crystal lattice. The cores of Neel skyrmions, realized in polar magnets with C-nv symmetry, are displaced either along or opposite to the off-axis (in-plane) component of the magnetic field depending on the rotation sense of the magnetization, dictated by the sign of the Dzyaloshinskii constant. The core shift of antiskyrmions, present in noncentrosymmetric magnets with D-2d symmetry, depends on the in-plane orientation of the magnetic field and can be parallel, antiparallel, or perpendicular to it. We argue that the role of anisotropy in magnets with axially symmetric crystal structure is different from that in cubic helimagnets. Our results can be applied to address recent experiments on polar magnets with C-3v symmetry, GaV4S8 and GaV4Se8, and Mn1.4Pt0.9Pd0.1Sn with D-2d symmetry.