Resonant inelastic X-ray scattering investigation of Hund's and spin-orbit coupling in $5d^2$ double perovskites

Abstract

B site ordered $5d^2$ double perovskites (${\mathrm{A}}_2\mathrm{B}{\mathrm{B}}^{\prime }{\mathrm{O}}_6,{\mathrm{B}}^{\prime }=5d^2)$ display a remarkable range of physical properties upon variation of the chosen B and ${\mathrm{B}}^{\prime }$ 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-insulating $\mathrm{B}{\mathrm{a}}_2\mathrm{YRe}{\mathrm{O}}_6$ and semiconducting $\mathrm{S}{\mathrm{r}}_2\mathrm{CrRe}{\mathrm{O}}_6$. 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 $\mathrm{S}{\mathrm{r}}_2\mathrm{CrRe}{\mathrm{O}}_6$ broadens and obfuscates the atomic transitions within an electron-hole continuum, while the insulating character of $\mathrm{B}{\mathrm{a}}_2\mathrm{YRe}{\mathrm{O}}_6$ 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 $\mathrm{B}{\mathrm{a}}_2\mathrm{YRe}{\mathrm{O}}_6$ 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 $\zeta =0.290(5)$ eV and $J_H=0.38(2)$ eV ($J_H/\zeta =1.30(5)$).

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• Coupled-cluster approach to vibronic effects in resonant inelastic x-ray scattering of quantum materials: Application to a $5d^1$ rhenium oxide
• Possibility of ferro-octupolar order in Ba${}_2$CaOsO${}_6$ assessed by X-ray magnetic dichroism measurements
• Hamiltonian parameter inference from resonant inelastic x-ray scattering with active learning