Charge ordering in Ir dimers in the ground state of Ba5AlIr2O11

It has been well established experimentally that the interplay of electronic correlations and spin-orbit interactions in ${\mathrm{Ir}}⁴⁺$ and ${\mathrm{Ir}}⁵⁺$ oxides results in insulating ${J}_{\mathrm{eff}}=1/2$ and ${J}_{\mathrm{eff}}=0$ ground states, respectively. However, in compounds where the structural dimerization of iridium ions is favorable, the direct Ir $d\text{\ensuremath{-}}d$ hybridization can be significant and takes a key role. Here, we investigate the effects of direct Ir $d\text{\ensuremath{-}}d$ hybridization in comparison with electronic correlations and spin-orbit coupling in ${\mathrm{Ba}}₅{\mathrm{AlIr}}₂{\mathrm{O}}₁₁$, a compound with Ir dimers. Using a combination of ab initio many-body wave-function quantum chemistry calculations and resonant inelastic x-ray scattering experiments, we elucidate the electronic structure of ${\mathrm{Ba}}₅{\mathrm{AlIr}}₂{\mathrm{O}}₁₁$. We find excellent agreement between the calculated and the measured spin-orbit excitations. Contrary to expectations, the analysis of the many-body wave function shows that the two Ir (${\mathrm{Ir}}⁴⁺$ and ${\mathrm{Ir}}⁵⁺$) ions in the ${\mathrm{Ir}}₂{\mathrm{O}}₉$ dimer unit in this compound preserve their local ${J}_{\mathrm{eff}}$ character close to 1/2 and 0, respectively. The local point group symmetry at each of the Ir ions plays an important role, significantly limiting the direct $d\text{\ensuremath{-}}d$ hybridization. Our results emphasize that minute details in the local crystal field environment can lead to dramatic differences in the electronic states in iridates and $5d$ oxides in general.