Quadrupolar correlations and spin freezing in S=1 triangular lattice antiferromagnets

Motivated by experiments on NiGa₂S₄, we discuss characteristic (finite-temperature) properties of spin S=1 quantum antiferromagnets on the triangular lattice. Several recent theoretical studies have suggested the possibility of quadrupolar (spin-nematic) ground states in the presence of sufficient biquadratic exchange. We argue that quadrupolar correlations are substantially more robust than the spin-nematic ground state and give rise to a two-peak structure of the specific heat. We characterize this behavior by a T>0 semiclassical approximation, which is amenable to efficient Monte Carlo simulations. Turning to low temperatures, we consider the effects of weak disorder on incommensurate magnetic order, which is present when interactions beyond nearest-neighbor exchange are substantial. We show that nonmagnetic impurities act as random fields on a component of the order parameter, leading to the disruption of long-range magnetic order even when the defects are arbitrarily weak. Instead, gradual freezing phenomena are expected on lowering the temperature, with no sharp transition but a rapid slowing of dynamics and the development of substantial spin-glass-like correlations. We discuss these observations in relation to measurements of NiGa₂S₄.