Spin-orbit coupled systems in the atomic limit: rhenates, osmates, iridates

Motivated by RIXS experiments on a wide range of complex heavy oxides, including rhenates, osmates, and iridates, we discuss the theory of RIXS for site-localized t2g orbital systems with strong spin-orbit coupling. For such systems, we present exact diagonalization results for the spectrum at different electron fillings, showing that it accesses ``single-particle'' and ``multiparticle'' excitations. This leads to a simple picture for the energies and intensities of the RIXS spectra in Mott insulators such as double perovskites which feature highly localized electrons, and yields estimates of the spin-orbit coupling and Hund's coupling in correlated $5d$ oxides. We present new higher resolution RIXS data at the Re L₃ edge in Ba₂YReO₆ which finds a previously unresolved peak splitting, providing further confirmation of our theoretical predictions. Using ab initio electronic structure calculations on Ba₂MReO₆ (with M=Re, Os, Ir) we show that while the atomic limit yields a reasonable effective Hamiltonian description of the experimental observations, effects such as t2g-eg interactions and hybridization with oxygen are important. Our ab initio estimate for the strength of the intersite exchange coupling shows that, compared to the d³ systems, the exchange is one or two orders of magnitude weaker in the d² and d⁴ materials, which may partly explain the suppression of long-range magnetic order in the latter compounds. As a way to interpolate between the site-localized picture and our electronic structure band calculations, we discuss the spin-orbital levels of the MO₆ cluster. This suggests a possible role for intracluster excitons in Ba₂YIrO₆ which may lead to a weak breakdown of the atomic Jeff=0 picture and to small magnetic moments.