Unusual superexchange pathways in a Ni triangular lattice of NiGa$_2$S$_4$ with negative charge-transfer energy

We have studied the electronic structure of the Ni triangular lattice in NiGa$_2$S$_4$ using photoemission spectroscopy and subsequent model calculations. The cluster-model analysis of the Ni 2$p$ core-level spectrum shows that the S 3$p$ to Ni 3$d$ charge-transfer energy is $sim$ -1 eV and the ground state is dominated by the $d^9L$ configuration ($L$ is a S 3$p$ hole). Cell perturbation analysis for the NiS$_2$ triangular lattice indicates that the strong S 3$p$ hole character of the ground state provides the enhanced superexchange interaction between the third nearest neighbor sites.