Possibility of S=1 spin liquids with fermionic spinons on triangular lattices

In this paper, we generalize the fermionic representation for S = 1/2 spins to arbitrary spins. Within a mean field theory we obtain several spin liquid states for spin S = 1 antiferromagnets on triangular lattices, including gapless f-wave spin liquid and topologically nontrivial p(x)+ip(y) spin liquid. After considering different competing orders, we construct a phase diagram for the J(1)-J(3)-K model. The application to recently discovered material NiGa(2)S(4) is discussed.