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 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.

二维三角晶格上的海森堡反铁磁体是受挫磁性中的一个典型问题。即使在经典极限下，其性质也远非简单。受挫的反铁磁相互作用所青睐的“120度”基态包含一种隐藏的手性对称性，并支持两种不同类型的激发。而且著名的是，在施加磁场的情况下，热涨落稳定了三个不同的相，包括一个共线的三分之一磁化平台。这个模型所提出的对称性破缺问题深刻而微妙，经过三十多年的研究，其相图的许多细节仍然令人惊讶地模糊不清。在本文中，我们使用现代蒙特卡罗模拟技术来确定在施加磁场的情况下三角晶格上经典海森堡反铁磁体的有限温度相图。在低到中等磁场值时，我们发现了从顺磁体到共线三分之一磁化平台的连续相变的证据，该相变属于三态波茨普适类。我们还发现了从三分之一磁化平台到倾斜的“Y态”以及到高场下发现的2:1倾斜相的常规别列津斯基 - 科斯特利茨 - 索利斯相变的证据。然而，从顺磁体到2:1倾斜相的相变虽然是连续的，但似乎不属于任何常规的普适类。我们认为，这与在零场中讨论的手性相变一样，作为具有复合序参量对称性的有限温度相变的一个有趣例子，值得进一步研究。我们对这些结果与三角晶格磁性材料实验的相关性进行了评论。