Unusual Superexchange Pathways in anNiS2Triangular Lattice with Negative Charge-Transfer Energy

We have studied the electronic structure of the Ni triangular lattice in ${\mathrm{NiGa}}_{2}{\mathrm{S}}_{4}$ using photoemission spectroscopy and subsequent model calculations. The cluster-model analysis of the Ni $2p$ core-level spectrum shows that the S $3p$ to Ni $3d$ charge-transfer energy is $\ensuremath{\sim}\ensuremath{-}1\text{ }\text{ }\mathrm{eV}$ and the ground state is dominated by the ${d}^{9}L$ configuration ($L$ is a S $3p$ hole). Cell perturbation analysis for the ${\mathrm{NiS}}_{2}$ triangular lattice indicates that the strong S $3p$ hole character of the ground state provides the enhanced superexchange interaction between the third-nearest-neighbor sites.