Square skyrmion crystal in centrosymmetric itinerant magnets

TL;DR

This paper theoretically explains the stabilization of square skyrmion crystals in centrosymmetric itinerant magnets, highlighting the role of multiple interactions and anisotropies, and relates findings to recent experimental observations in GdRu₂Si₂.

Contribution

It introduces a theoretical model showing how a square skyrmion crystal is stabilized by combined interactions, differing from triangular skyrmions, and explores various spin textures in such systems.

Findings

Square skyrmion crystal stabilized by multiple interactions.

Contrast with triangular skyrmions stabilized by a single interaction.

Diverse noncollinear and noncoplanar spin textures observed.

Abstract

We theoretically investigate the origin of the square-type skyrmion crystal in centrosymmetric itinerant magnets, motivated from the recent experimental finding in GdRu$_2$Si$_2$ [N. D. Khanh $\mathit{et}$ $\mathit{al.}$, Nat. Nanotech. $\mathbf{15}$, 444 (2020)]. By simulated annealing for an effective spin model derived from the Kondo lattice model on a square lattice, we find that a square skyrmion crystal composed of a superposition of two spin helices is stabilized in a magnetic field by synergy between the positive biquadratic, bond-dependent anisotropic, and easy-axis anisotropic interactions. This is in stark contrast to triangular skyrmion crystals which are stabilized by only one of the three, suggesting that the square skyrmion crystal is characteristic of itinerant magnets with magnetic anisotropy. We also show that a variety of noncollinear and noncoplanar spin textures appear depending on the model parameters as well as the applied magnetic field. The present systematic study will be useful not only for identifying the key ingredients in GdRu$_2$Si$_2$ but also for exploring further skyrmion-hosting materials in centrosymmetric itinerant magnets.