Molecular $j_{\rm eff}$ states in ternery transition metal chalcogenides $AM_4X_8$

Spin-orbit-coupling(SOC)-induced $j_{\rm eff}$ states, reported in several iridium oxide compounds, is the key ingredient in understanding the interesting cooperation between SOC and the electron correlations. From our density functional theory calculations we suggest that, a series of ternery transition metal chalcogenides $AM_4X_8$ ($A$ = Ga, $M$ = 4$d$ and 5$d$ transition metal atoms, $X$ = chalcogen atoms) host the $j_{\rm eff}$ states in a molecular form. Wide range of the bandwidth covered with the external or chemical pressure enable one to access a broad range of electron correlation strength in a single compound. Implications of our results in both the weak and strong coupling regime are discussed. Our finding provides an ideal playground in exploring the $j_{\rm eff}$ physics and the resulting emergent phenomena.