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

Abstract

The Heisenberg antiferromagnet on a two-dimensional triangular lattice is a paradigmatic problem in frustrated magnetism. Even in the classical limit $S\ensuremath{\rightarrow}\ensuremath{\infty}$, its properties are far from simple. The ``120-degree'' ground state favored by the frustrated antiferromagnetic interactions contains a hidden chiral symmetry and supports two distinct types of excitation. And, famously, in an applied magnetic field, three distinct phases, including a collinear one-third magnetisation plateau, are stabilized by thermal fluctuations. 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 an applied magnetic field. At low to intermediate values of the magnetic field, we find evidence for a continuous phase transition from the paramagnet into the collinear one-third magnetization plateau, belonging to the three-state Potts universality class. We also find evidence for conventional Berezinskii-Kosterlitz-Thouless transitions from the one-third magnetization 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 the zero field case, 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.