$B$ site ordered $5d^2$ double perovskites ($A_{2}B{B}^{\prime }{\text{O}}_6,B^{\prime }=5d^2)$ display a remarkable range of physical properties upon variation of the chosen $B$ and $B^{\prime }$ site ions. This sensitivity to chemical substitution reflects the delicate balance and profound impact of strong electronic correlation and spin-orbit coupling in such systems. We present rhenium $L_2$ and $L_3$ resonant inelastic x-ray scattering (RIXS) measurements of two such physically dissimilar materials, Mott-insultating ${\mathrm{Ba}}_2\mathrm{Y}\mathrm{Re}{\mathrm{O}}_6$ and semiconducting ${\mathrm{Sr}}_2\mathrm{Cr}\mathrm{Re}{\mathrm{O}}_6$. Despite these differences, our RIXS results reveal similar energy scales of Hund's ($J_H$) and spin-orbit coupling ($\zeta$) in the two materials, with both systems firmly in the intermediate Hund's coupling regime where $J_H/\zeta \sim 1$. However, there are clear differences in their RIXS spectra. The conductive character of ${\mathrm{Sr}}_2\mathrm{Cr}\mathrm{Re}{\mathrm{O}}_6$ broadens and obfuscates the atomic transitions within an electron-hole continuum, while the insulating character of ${\mathrm{Ba}}_2\mathrm{Y}\mathrm{Re}{\mathrm{O}}_6$ results in sharp atomic excitations. This contrast in their RIXS spectra despite their similar energy scales reflects a difference in the itinerancy-promoting hopping integral and illustrates the impact of the local crystal environment in double perovskites. Finally, $L_2$ and $L_3$ edge analyses of the atomic excitations in ${\mathrm{Ba}}_2\mathrm{Y}\mathrm{Re}{\mathrm{O}}_6$ reveal that the ordering of the low lying excited states is inverted compared to previous reports, such that the appropriate energy scales of Hund's and spin-orbit coupling are significantly modified. We present exact diagonalization calculations of the RIXS spectra at both edges which show good agreement with our results for new energy scales of $\zeta =0.290\left(5\right)\mathrm{eV}$ and $J_H=0.38\left(2\right)\mathrm{eV}$ $[J_H/\zeta =1.30\left(5\right)]$.

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• Spin-orbit coupling
• Mott insulators
• Perovskites
• Strongly correlated systems
• Electron-correlation calculations
• Resonant inelastic x-ray scattering