Quadrupolar phases of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice

Using mean-field theory, exact diagonalizations and SU(3) flavour theory, we have precisely mapped out the phase diagram of the $S=1$ bilinear-biquadratic Heisenberg model on the triangular lattice in a magnetic field, with emphasis on the quadrupolar phases and their excitations. In particular, we show that ferroquadrupolar order can coexist with short-range helical magnetic order, and that the antiferroquadrupolar phase is characterized by a remarkable 2/3 magnetization plateau, in which one site per triangle retains quadrupolar order while the other two are polarized along the field. Implications for actual $S=1$ magnets, such as NiGa$_2$S$_4$, are discussed.