Phase diagram of the classical Heisenberg antiferromagnet on a triangular lattice in applied magnetic field

TL;DR

This study maps the finite-temperature phase diagram of the classical Heisenberg antiferromagnet on a triangular lattice under magnetic field, revealing various phase transitions including Potts and Berezinskii-Kosterlitz-Thouless types.

Contribution

It provides the first detailed Monte Carlo simulation-based phase diagram of this model, identifying new transition behaviors and universality classes.

Findings

Evidence for a three-state Potts transition into the magnetisation plateau.

Identification of Berezinskii-Kosterlitz-Thouless transitions from plateau to canted phases.

Discovery of a non-conventional continuous transition into the 2:1 canted phase.

Abstract

The Heisenberg antiferromagnet on a two-dimensional triangular lattice is a paradigmatic problem in frustrated magnetism. Even in the classical limit, its properties are far from simple. The "120 degree" ground state favoured by the frustrated antiferromagnetic interactions contains a hidden chiral symmetry, and supports two distinct types of excitation. And famously, three distinct phases, including a collinear one-third magnetisation plateau, are stabilised by thermal fluctuations in applied magnetic field. The questions of symmetry-breaking raised by this model are deep and subtle, and after more than thirty years of study, many of the details of its phase diagram remain surprisingly obscure. In this paper we use modern Monte Carlo simulation techniques to determine the finite-temperature phase diagram of the classical Heisenberg antiferromagnet on a triangular lattice in applied magnetic field. At low to intermediate values of magnetic field, we find evidence for a continuous phase transition from the paramagnet into the collinear one-third magnetisation plateau, belonging to the three-state Potts universality class. We also find evidence for conventional Berezinskii-Kosterlitz-Thouless transitions from the one-third magnetisation plateau into the canted "Y-state", and into the 2:1 canted phase found at high fields. However, the phase transition from the paramagnet into the 2:1 canted phase, while continuous, does not appear to fall into any conventional universality class. We argue that this, like the chiral phase transition discussed in zero field, deserves further study as an interesting example of a finite-temperature phase transition with compound order-parameter symmetry. We comment on the relevance of these results for experiments on magnetic materials with a triangular lattice.