Magnetic phase diagram of the spin-1 two-dimensional J1-J3 Heisenberg model on a triangular lattice

► The S=1 J1-J3 Heisenberg model on a triangular lattice is studied. ► The ferromagnetic nearest and AF third-nearest-neighbor couplings are considered. ► With increasing J3/|J1| the system undergoes three phase transitions. ► The model is able to describe the incommensurate short-range order in NiGa2S4.