Quasimolecular electronic structure of the trimer iridate Ba$_4$NbIr$_3$O$_{12}$

The insulating mixed-valent Ir$^{+3.66}$ compound Ba$_4$NbIr$_3$O$_{12}$ hosts two holes per Ir$_3$O$_{12}$ trimer unit. We address the electronic structure via resonant inelastic x-ray scattering (RIXS) at the Ir $L_3$ edge and exact diagonalization. The holes occupy quasimolecular orbitals that are delocalized over a trimer. This gives rise to a rich intra-$t_{2g}$ excitation spectrum that extends from 0.5 eV to energies larger than 2 eV. Furthermore, it yields a strong modulation of the RIXS intensity as a function of the transferred momentum q. A clear fingerprint of the quasimolecular trimer character is the observation of two modulation periods, $2\pi/d$ and $2\pi/2d$, where d and 2d denote the intratrimer Ir-Ir distances. We discuss how the specific modulation reflects the character of the wavefunction of an excited state. Our quantitative analysis shows that spin-orbit coupling $\lambda$ of about 0.4 eV is decisive for the character of the electronic states, despite a large hopping $t_{a_{1g}}$ of about 0.8 eV. The ground state of a single trimer is described very well by both holes occupying the bonding j=1/2 orbital, forming a vanishing quasimolecular moment with J=0.