Monte Carlo study on low-temperature phase diagrams of the J1−J2 classical XY kagome antiferromagnet

Frustrated magnets with degenerate ground states exhibit exotic ground states and rich phase structures when perturbations and/or thermal fluctuations lift the degeneracy. In two-dimensional models with short-range interactions, continuous symmetries cannot spontaneously break at finite temperatures, leading to the suppression of conventional magnetic long-range ordering. In this paper, we numerically study the classical ${J}₁\text{\ensuremath{-}}{J}₂$ $XY$ antiferromagnet on the kagome lattice as a prototype model of such frustrated magnets, where ${J}₂$ denotes the next-nearest-neighbor exchange interaction. We map out the ${J}₂\text{\ensuremath{-}}T$ phase diagram of this model employing extensive classical Monte Carlo simulations. The obtained phase diagram features Berezinskii-Kosterlitz-Thouless transitions of $q=0$, $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ magnetic orders, and octupole orders, in addition to finite-temperature phase transitions of both ferrochiral and antiferrochiral long-range orders. Additionally, we find a nontrivial first-order transition for antiferromagnetic ${J}₂/{J}₁<0$. The origin of this transition is discussed in the context of nonlocal loop structures present in local ${120}^{\ensuremath{\circ}}$ spin structures.