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

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