Complex Orbital State Stabilized by Strong Spin-Orbit Coupling in a Metallic Iridium Oxide IrO${}_2$

Resonant x-ray diffraction experiments were performed for the metallic iridium oxide IrO${}_2$. We observed anisotropic tensor of susceptibility (ATS) scattering, the spectrum of which shows a sharp contrast between the $L_3$ and $L_2$ edges. At the $L_3$ edge, resonance excitations were clearly observed from the core 2$p$ orbitals to both the 5$d$ $t_{2g}$ and $e_g$ orbitals. In contrast, the resonance mode associated with 5$d$ $t_{2g}$ orbitals was indiscernible at the $L_2$ edge. This contrasting behavior indicates that Ir 5$d$ $t_{2g}$ orbitals are fairly close to the $J_{\mathrm{e}\mathrm{f}\mathrm{f}}$ = 1/2 state due to the strong spin–orbit coupling in 5$d$ transition metal ions, as in the Mott insulator Sr${}_2$IrO${}_4$. Our results clearly demonstrate that ATS scattering is a useful probe for investigating complex orbital states in a metallic state. Such states induce novel phenomena such as the spin Hall effect.