$\textit{J}$ = 0 nonmagnetic insulating state in K 2 OsX 6 ($\textit{X}$ = F, Cl, and Br)
In 4$\textit{d}$ /5$\textit{d}$ transition-metal systems, many interesting physical properties arise from the interplay of bandwidth, electronic correlations, and spin-orbit interactions. Here, using ab initio density functional theory, we systematically study the double-perovskite-like system K 2 OsX6 ($\textit{X}$ = F, Cl, and Br) with a $5d^4$ electronic configuration. In this work, our main result is that the $\textit{J}$ = 0 nonmagnetic insulating state develops in this system, induced by strong spin-orbit coupling (SOC). Specifically, the well-separated OsX 6 octahedra lead to the cubic crystal-field limit and result in dramatically decreasing hoppings among nearest neighbor Os-Os sites. In this case, the three degenerate $t_{2g}$ orbitals are reconstructed into two “effective” $j_{\text{eff}}$ ($j_{\text{eff}}$ = 1/2 and $j_{\text{eff}}$ = 3/2 states) states separated by the strong SOC, opening a gap with four electrons occupying the$j_{\text{eff}}$ = 3/2 orbitals. Furthermore, the hybridization between the Os 5$\textit{d}$ orbitals and the $\textit{X}$ ($\textit{X}$ = F, Cl, and Br) $\textit{p}$ orbitals increases from F to Br, leading the electrons in K 2 OsF 6 to be more localized than in K 2 OsCl 6 and K 2 OsBr 6 , resulting in a smaller bandwidth for K 2 OsF 6 than in the Cl- or Br-cases. Our results provide guidance to experimentalists and theorists working on this interesting family of osmium halides.