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

## TL;DR

This paper extends fermionic spinon representations to S=1 spins, proposing various spin liquid states on triangular lattices and analyzing their phase diagram, with implications for materials like NiGa2S4.

## Contribution

It introduces a generalized fermionic representation for S=1 spins and identifies new spin liquid states on triangular lattices using mean field theory.

## Key findings

- Identified gapless f-wave and topological p+ip spin liquids for S=1 on triangular lattices.
- Constructed a phase diagram for the J1-J3-K model.
- Discussed relevance to NiGa2S4 material.

## Abstract

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 $\mathrm{NiGa_2S_4}$ is discussed.