Chiral phase of a simple two-dimensional spin-1 quantum magnet

We investigate the evolution of the ground state of a simple spin-1 antiferromagnet with easy-axis single-ion anisotropy $D (S^z)^2$, with $D < 0$, on a two-dimensional triangular lattice. The ground state changes from a quantum paramagnet one, at sufficiently large $|D|$, to a magnetically ordered $120^\circ$ one at small $D\sim 0$. Besides breaking the continuous $U(1)$ symmetry of global spin rotations along the $z$-axis, this non-collinear ordering also breaks the discrete $Z_2$ {\em chiral} symmetry, which raises the possibility of an intermediate chiral spin liquid state, spontaneously breaking spatial inversion and mirror symmetries. We show that this interesting novel state indeed appears as a result of the condensation of bound $\langle S^+_n S^-_m- S^-_n S^+_m\rangle$ pairs. The resulting Ising-like nematic state supports a regular pattern of spin currents on the bonds of the triangular lattice. It represents quantum analogue of the classical chiral spin liquid proposed by Villain in 1977.