Anisotropic spin model and multiple-$Q$ states in cubic systems

TL;DR

This paper classifies anisotropic exchange interactions in cubic systems and demonstrates their role in stabilizing multiple-$Q$ magnetic states, providing insights into complex magnetic structures in various materials.

Contribution

It constructs an effective spin model for cubic systems incorporating anisotropic interactions and shows how these interactions lead to multiple-$Q$ states through simulated annealing.

Findings

Anisotropic exchange interactions are key to multiple-$Q$ state formation.

Several multiple-$Q$ instabilities are identified in the ground state.

The model explains multiple-$Q$ states in materials like EuPtSi and SrFeO$_3$.

Abstract

Multiple-$Q$ states manifest themselves in a variety of noncollinear and noncoplanar magnetic structures depending on the magnetic interactions and lattice structures. In particular, cubic-lattice systems can host a plethora of multiple-$Q$ states, such as magnetic skyrmion and hedgehog lattices. We here classify momentum-dependent anisotropic exchange interactions in the cubic-lattice systems based on the magnetic representation analysis. We construct an effective spin model for centrosymmetric cubic space groups, $Pm\bar{3}m$ and $Pm\bar{3}$, and noncentrosymmetric ones, $P\bar{4}3m$, $P432$, and $P23$: The former include the symmetric anisotropic exchange interaction, while the latter additionally include the Dzyaloshinskii-Moriya interaction. We demonstrate that the anisotropic exchange interaction becomes the origin of the multiple-$Q$ states by applying the anisotropic spin model to the case under $Pm\bar{3}$. We show several multiple-$Q$ instabilities in the ground state by performing simulated annealing. Our results will be a reference for not only exploring unknown multiple-$Q$ states but also understanding the origin of the multiple-$Q$ states observed in both noncentrosymmetric and centrosymmetric magnets like EuPtSi and SrFeO$_3$.