Quadrupolar Correlations, Bond Order and Spin Freezing in S=1 Triangular Lattice Antiferromagnets

Motivated by experiments on the $S=1$ triangular lattice antiferromagnet NiGa$_2$S$_4$ and theoretical predictions that it has a quadrupolar/spin-nematic ground state, we discuss how quadrupolar correlations may actually be more relevant at \emph{finite} temperature, giving rise to an unusual two peak structure in the specific heat. Moreover, dominant third-neighbor Heisenberg exchange in the clean system can lead to a breaking of lattice rotational symmetry at finite temperature, although the sensitivity of the phase to arbitrarily weak non-magnetic disorder could explain the lack of long range order and the slow dynamics observed in experiment. To justify these predictions, we implemented a novel semiclassical approximation that allows $T>0$ quantum effects to be simulated efficiently using classical Monte Carlo. Current efforts include treating quantum effects exactly, reproducing an experimentally observed even-odd spin impurity effect and providing other experimental signatures of the quadrupolar correlations.