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

TL;DR

This paper studies the stability and core displacement of N"eel skyrmions in polar magnets with uniaxial anisotropy under tilted magnetic fields, revealing how anisotropy and crystal symmetry influence skyrmion robustness.

Contribution

It provides a detailed analysis of skyrmion stability in polar magnets with axial symmetry, highlighting the effects of anisotropy and magnetic field orientation on skyrmion core displacement and robustness.

Findings

Moderate easy-plane anisotropy extends skyrmion stability range.

Easy-axis anisotropy enhances robustness against tilted fields.

Skyrmion core displacement depends on crystal symmetry and magnetic field direction.

Abstract

We investigate the stability of N\'eel 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 N\'eel 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 N\'eel 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 chiral magnets with D$_{2d}$ symmetry, depends on the in-plane orientation of the magnetic field and can be parallel, anti-parallel, 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, GaV$_4$S$_8$ and GaV$_4$Se$_8$.