Photoemission study of triangular lattices in NiGa$_2$S$_4$, FeGa$_2$S$_4$, and Fe$_2$Ga$_2$S$_5$*

The newly-discovered NiGa$_2$S$_4$ (Ni$^{2+}$, $S$=1) and FeGa$_2$S$_4$ (Fe$^{2+}$, $S$=2) form frozen spin-disordered states within the triangular lattice [1,2]. The spins of both compounds have no long range order even at lowest temperature. We have performed photoemission spectroscopy of NiGa$_2$S$_4$, FeGa$_2$S$_4$, and Fe$_2$Ga$_2$S$_5$. The photoemission results and subsequent model calculations indicate that the ground state of NiGa$_2$S$_4$ has the $d^9L$ character ($L$ is a S 3$p$ hole) and that the strong S 3$p$ hole character of the ground state provides the enhanced superexchange interaction between the third nearest neighbor sites. In contrast, the ground state of FeGa$_2$S$_4$ is dominated by the $d^6$ configuration and the superexchange interactions between the second and third neighbor sites are less important. [1] S. Nakatsuji, {\it et al}., Science 309, 1697 (2005). [2] S. Nakatsuji, {\it et al}., Phys. Rev. Lett. 99, 157203 (2007).