Density functional theory of resonant inelastic x-ray scattering in the quasi-one-dimensional dimer iridate Ba$_5$AlIr$_2$O$_{11}$

We have investigated the electronic structure of Ba$_5$AlIr$_2$O$_{11}$ within the density functional theory using the generalized gradient approximation while considering strong Coulomb correlations in the framework of the fully relativistic spin-polarized Dirac linear muffin-tin orbital band-structure method. We have investigated the x-ray absorption spectra, x-ray magnetic circular dichroism, and resonant inelastic x-ray scattering spectra (RIXS) at the Ir $K$, $L_3$ , $M_3$, $M_5$ and O K edges. The calculated results are in good agreement with experimental data. The RIXS spectrum of Ba$_5$AlIr$_2$O$_{11}$ at the Ir $L_3$ edge possesses sharp twelve features below 1.5 eV corresponding to transitions within the Ir t2g levels. The excitations located from 2 to 4 eV are due to $t_{2g} \to e_g$ and $O_{2p} \to t_{2g}$ transitions. The high energy peaks situated at 5-11 eV appear due to charge transfer transitions. The theory reproduces well the shape and polarization dependence of the oxygen O K RIXS spectrum. We have found that the dependence of the RIXS spectrum at the oxygen K edge on the incident photon energy and the momentum transfer vector Q is much stronger than the corresponding dependence at the Ir $L_3$ edge