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Almost pure $J_{\mathrm{eff}} = 1/2$ Mott state of In$_2$Ir$_2$O$_7$ in the limit of reduced inter-site hopping

The pyrochlore iridate In$_2$Ir$_2$O$_7$ is a strong $J_{\mathrm{eff}} = 1/2$ Mott insulator with frustrated magnetism. Despite the large trigonal crystal field, a small admixture of $J_{\mathrm{eff}} = 3/2$ component in the $J_{\mathrm{eff}} = 1/2$ bands and a small splitting of $J_{\mathrm{eff}} = 3/2$ bands are observed as compared with other pyrochlore iridates A$_2$Ir$_2$O$_7$ (A: trivalent cation). We argue that the reduced inter-site hopping between the $J_{\mathrm{eff}} = 1/2$ and the $J_{\mathrm{eff}} = 3/2$ manifold plays a predominant role in the distinct behavior of In$_2$Ir$_2$O$_7$ compared with other A$_2$Ir$_2$O$_7$. The effect of the intersite hopping should not be dismissed in the local physics of spin-orbital-entangled $J_{\mathrm{eff}} = 1/2$ Mott insulators.