Anisotropic magnetic interactions in hexagonal AB-stacked kagome lattice structures: Applications to $\mathrm{Mn}_3\mathrm{X}$ ($\mathrm{X}$ = $\mathrm{Ge}$, $\mathrm{Sn}$, $\mathrm{Ga}$) compounds

TL;DR

This paper develops a comprehensive symmetry-based model for Mn3X compounds with AB-stacked kagome lattices, revealing the role of interplane Dzyaloshinskii-Moriya interactions and anisotropic exchanges in their magnetic properties.

Contribution

It introduces a new interplane Dzyaloshinskii-Moriya interaction term and analyzes anisotropic exchanges, advancing understanding of magnetic Hamiltonians in Mn3X kagome compounds.

Findings

Identified the significance of interplane Dzyaloshinskii-Moriya interactions.

Showed competition between anisotropic exchange and single-ion anisotropy.

Predicted neutron scattering intensities to guide experimental verification.

Abstract

$\mathrm{Mn}_3\mathrm{X}$ compounds in which the magnetic $\mathrm{Mn}$ atoms form AB-stacked kagome lattices have received a tremendous amount of attention since the observation of the anomalous Hall effect in $\mathrm{Mn}_3\mathrm{Ge}$ and $\mathrm{Mn}_3\mathrm{Sn}$. Although the magnetic ground state has been known for some time to be an inverse triangular structure with an induced in-plane magnetic moment, there have been several controversies about the minimal magnetic Hamiltonian. We present a general symmetry-based model for these compounds that includes a previously unreported interplane Dzyaloshinskii-Moriya interaction, as well as anisotropic exchange interactions. The latter are shown to compete with the single-ion anisotropy which strongly affects the ground state configurations and elementary spin-wave excitations. Finally, we present the calculated elastic and inelastic neutron scattering intensities and point to experimental assessment of the types of magnetic anisotropy in these compounds that may be important.