Helicity locking of square skyrmion crystal in a centrosymmetric lattice system without vertical mirror symmetry

TL;DR

This paper theoretically demonstrates that square skyrmion crystals with locked helicity can be stabilized in centrosymmetric tetragonal lattices through anisotropic interactions arising from broken vertical mirror symmetry, independent of Dzyaloshinskii-Moriya interactions.

Contribution

It reveals a new mechanism for stabilizing and controlling skyrmion helicity in centrosymmetric magnets via anisotropic interactions without relying on Dzyaloshinskii-Moriya interaction.

Findings

Square skyrmion crystals with definite helicity are stabilized by off-diagonal interactions.

Helicity is determined by competition between anisotropic interactions.

Helicity-dependent phenomena like Edelstein effect are discussed.

Abstract

We theoretically investigate the stability of a square skyrmion crystal (SkX) in a centrosymmetric tetragonal lattice structure with the emphasis on the role of the magnetic anisotropy arising from the absence of vertical mirror symmetry. Our analysis is based on an effective bilinear and biquadratic model in momentum space, which is a canonical model for itinerant magnets in a weak-coupling regime. By performing the simulated annealing for the model on the two-dimensional square lattice, we find that the off-diagonal spin component in the interaction, which becomes nonzero when the vertical mirror symmetry is broken, gives rise to the square SkX with a definite helicity in an external magnetic field. We show that the helicity of the centrosymmetric SkXs is determined by the competition between the off-diagonal and diagonal anisotropic interactions, the latter of which appears in the discrete fourfold-rotational lattice structure. Furthermore, we discuss helicity-dependent physical phenomena by introducing odd-parity multipoles, where electric (magnetic) and electric (magnetic) toroidal multipoles are sources of an antisymmetric spin polarization and an Edelstein effect (a magnetoelectric effect). We also discuss the stability of the SkXs with different helicities in a magnetic field rotation. Our results provide a way of engineering the helicity-locked SkXs by the symmetric anisotropic interaction in centrosymmetric magnets, which is distinct from that by the antisymmetric Dzyaloshinskii-Moriya interaction in noncentrosymmetric magnets.