Nematic and chiral orders for planar spins on triangular lattice

We propose a variant of the antiferromagnetic XY model on the triangular lattice to study the interplay between the chiral and nematic orders in addition to the magnetic order. The model has a significant bi-quadratic interaction of the planar spins. When the bi-quadratic exchange energy dominates, a large temperature window is shown to exist over which the nematic and the chiral orders co-exist without the magnetic order, thus defining a chiral-nematic state. The phase diagram of the model and some of its critical properties are derived by means of the Monte Carlo simulation.