Octupolar ordering of classical kagome antiferromagnets in two and three dimensions

TL;DR

This study uses Monte Carlo simulations to explore octupolar ordering in classical kagome antiferromagnets in two and three dimensions, revealing distinct phase transitions and symmetry-breaking states characterized by third-rank spin tensor order parameters.

Contribution

It provides the first detailed analysis of octupolar order in kagome antiferromagnets, identifying phase transitions and the nature of low-temperature ordered states.

Findings

Sharp crossover to coplanar state at T_k ~ 0.004J in 2D kagome

First-order transition at T_c ~ 0.002J in 3D hyperkagome

Long-range octupole order in the 3D phase

Abstract

Classical Heisenberg antiferromagnets on two-dimensional kagome and three-dimensional hyperkagome lattices are investigated by Monte Carlo simulations. For both models the symmetry-breaking states at low temperatures are described by non-zero octupole moments or third-rank spin tensor order parameters. In the case of the two-dimensional kagome antiferromagnet, a sharp crossover into a coplanar state takes place at T_k ~ 0.004J, which we attribute to proliferation of fractional vortices. The three-dimensional model exhibits a first-order transition at T_c ~ 0.002J into a phase with critical spin correlations, which possesses a long-range order of octupole moments.