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 → ∞, 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.

Singular Field Response and Singular Screening of Vacancies in Antiferromagnets

“…For details see text. For the triangular-lattice AF, an anomalously large ground-state degeneracy exists at the classical level for h = 0, which is lifted both by fluctuations and by additional interactions [15][16][17][18]. Two cases are important: (a) "coplanar" and (b) "umbrella" states, see Fig.…”

Deformed triangular lattice antiferromagnets in a magnetic field: Role of spatial anisotropy and Dzyaloshinskii-Moriya interactions

“…Readers interested in properties of such phase transitions in a similar context are instead referred to the recent detailed study in Ref. 40.…”

“…40 We would like to emphasize again that our main focus is on identifying possible phases rather than studying the nature of the transitions between them. Readers interested in properties of such phase transitions in a similar context are instead referred to the recent detailed study in Ref.…”

Phase diagram of thespin−12triangularJ1−J2Heisenberg model on a three-leg cylinder

“…Exact diagonalization methods [18,[26][27][28]34] suffer from the exponentially growing size of the Hilbert space, which is especially a problem in two or more dimensions, while QMC techniques [35] suffer from the sign problem for frustrated lattices, and projected entangled pair states (PEPSs) [36,37] for this model are complex and computationally costly, even though, in principle, PEPSs have good computational scaling properties in two dimensions. More recently some numerical methods have been developed that are especially useful for frustrated systems and applied to the THM, for example, the large-scale parallel tempering Monte Carlo [38] and some tensor networks methods including entangled-plaquette states [39] and the multiscale entanglement renormalization ansatz (MERA) [40].…”