Ordered ground states of kagome magnets with generic exchange anisotropy

TL;DR

This paper classifies the possible classical ground states in kagome magnets with generic exchange anisotropy, identifying five main phases and mapping their occurrence based on symmetry analysis and energy optimization.

Contribution

It provides a comprehensive symmetry-based classification of ground states in anisotropic kagome magnets with six exchange parameters, expanding understanding of their magnetic phases.

Findings

Identified five distinct classical ground state phases for generic exchange parameters.

Mapped the phase diagram showing the rarity of the ${ m E}$ noncoplanar$_{12}$ state.

Most kagome magnets are likely to exhibit four main ordered states.

Abstract

There is a growing family of rare-earth kagome materials with dominant nearest-neighbor interactions and strong spin orbit coupling. The low symmetry of these materials makes theoretical description complicated, with six distinct nearest-neighbor coupling parameters allowed. In this Article, we ask what kinds of classical, ordered, ground states can be expected to occur in these materials, assuming generic (i.e. non-fine-tuned) sets of exchange parameters. We use symmetry analysis to show that there are only five distinct classical ground state phases occurring for generic parameters. The five phases are: (i) a coplanar, 2-fold degenerate, state with vanishing magnetization (${\sf A_1}$), (ii) a noncoplanar, 2-fold degenerate, state with magnetization perpendicular to the kagome plane (${\sf A_2}$), (iii) a coplanar, 6-fold degenerate, state with magnetization lying within the kagome plane (${\sf E}$-coplanar), (iv) a noncoplanar, 6-fold degenerate, state with magnetization lying within a mirror plane of the lattice (${\sf E}$-noncoplanar$_{6}$), (v) a noncoplanar, 12-fold degenerate, state with magnetization in an arbitrary direction (${\sf E}$-noncoplanar$_{12}$). All five are translation invariant (${\bf q}=0$) states. Having found the set of possible ground states, the ground state phase diagram is obtained by comparing numerically optimized energies for each possibility as a function of the coupling parameters. The state ${\sf E}$ noncoplanar$_{12}$ is extremely rare, occupying $<1\%$ of the full phase diagram, so for practical purposes there are four main ordered states likely to occur in anisotropic kagome magnets with dominant nearest neighbor interactions. These results can aid in interpreting recent experiments on ``tripod kagome'' systems R$_3$A$_2$Sb$_3$O$_{14}$, as well as materials closer to the isotropic limit such as Cr- and Fe- jarosites.