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 ${t}_{2g}$ 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 ${L}_{3}$ edge in ${\mathrm{Ba}}_{2}{\mathrm{YReO}}_{6}$ which finds a previously unresolved peak splitting, providing further confirmation of our theoretical predictions. Using ab initio electronic structure calculations on ${\mathrm{Ba}}_{2}\mathcal{M}{\mathrm{ReO}}_{6}$ (with $\mathcal{M}=\mathrm{Re}$, Os, Ir) we show that while the atomic limit yields a reasonable effective Hamiltonian description of the experimental observations, effects such as ${t}_{2g}\ensuremath{-}{e}_{g}$ interactions and hybridization with oxygen are important. Our ab initio estimate for the strength of the intersite exchange coupling shows that, compared to the ${d}^{3}$ systems, the exchange is one or two orders of magnitude weaker in the ${d}^{2}$ and ${d}^{4}$ 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 $\mathcal{M}{\mathrm{O}}_{6}$ cluster. This suggests a possible role for intracluster excitons in ${\mathrm{Ba}}_{2}{\mathrm{YIrO}}_{6}$ which may lead to a weak breakdown of the atomic ${J}_{\mathrm{eff}}=0$ picture and to small magnetic moments.

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