Observation of spin-orbit excitations and Hund's multiplets in Ca${}_2$RuO${}_4$

Abstract

We use Ru $L_3$-edge (2838.5 eV) resonant inelastic x-ray scattering (RIXS) to quantify the electronic structure of Ca${}_2$RuO${}_4$, a layered $4d$-electron compound that exhibits a correlation-driven metal-insulator transition and unconventional antiferromagnetism. We observe a series of Ru intra-ionic transitions whose energies and intensities are well described by model calculations. In particular, we find a $\mathrm{J}=0\to 2$ spin-orbit excitation at 320 meV, as well as Hund's-rule driven $\mathrm{S}=1\to 0$ spin-state transitions at 750 and 1000 meV. The energy of these three features uniquely determines the spin-orbit coupling, tetragonal crystal-field energy, and Hund's rule interaction. The parameters inferred from the RIXS spectra are in excellent agreement with the picture of excitonic magnetism that has been devised to explain the collective modes of the antiferromagnetic state. $L_3$-edge RIXS of Ru compounds and other $4d$-electron materials thus enables direct measurements of interactions parameters that are essential for realistic model calculations.

arXiv comment9 pages and 4 figures. accepted in PRB

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• Resonant inelastic x-ray scattering study of $\alpha$-RuCl${}_3$: a progress report
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• Multiple-magnon excitations shape the spin spectrum of cuprate parent compounds
• Multiple Spin-Orbit Excitons and the Electronic Structure of $\alpha$-RuCl${}_3$
• Excitonic Magnetism at the intersection of Spin-orbit coupling and crystal-field splitting
• Description of resonant inelastic x-ray scattering in correlated metals
• Distinct spin and orbital dynamics in Sr${}_2$RuO${}_4$
• Van Vleck excitons in Ca${}_2$RuO${}_4$
• BCS-BEC crossover in a $(t_{2g}{)}^4$ Excitonic Magnet
• Spin and charge excitations in the correlated multiband metal Ca3Ru2O7
• Magnetic reorientation transition in a three orbital model for $\mathrm{C}{\mathrm{a}}_2\mathrm{Ru}{\mathrm{O}}_4$ -- Interplay of spin-orbit coupling, tetragonal distortion, and Coulomb interactions
• Electronic excitations in $5d^4$ J=0 Os${}^{4+}$ halides studied by RIXS and optical spectroscopy
• Resonant Inelastic X-ray Scattering Study of Ca${}_3$Ru${}_2$O${}_7$
• Magnetization dynamics fingerprints of an excitonic condensate $t_{2g}^4$ magnet
• Hund bands in spectra of multiorbital systems
• Spin-orbit coupling and crystal-field splitting in Ti-doped Ca2RuO4 studied by ellipsometry
• Photoemission Spectrum of Ca2RuO4: Spin Polaron Physics in an S=1 Antiferromagnet with Anisotropies
• Magnetic ground state of the dimer-based hexagonal perovskite Ba${}_3$ZnRu${}_2$O${}_9$
• Spin-orbit excitons and electronic configuration of the $5d^4$ insulator Sr${}_3$Ir${}_2$O${}_7$F${}_2$
• Magnetic phases for two $t_{2g}$ holes with spin-orbit coupling and crystal field
• Spin-orbital mechanisms for negative thermal expansion in Ca2RuO${}_4$
• Orbitally-selective Breakdown of the Fermi Liquid and Simultaneous Enhancement of Metallic and Insulating States in Correlated Multi-band Systems with Spin-orbit Coupling
• Resonant Inelastic X-ray Scattering from Electronic Excitations in $\alpha$-RuCl${}_3$ Nanolayers
• Coupled spin-orbital fluctuations in a three orbital model for $4d$ and $5d$ oxides with electron fillings $n=3,4,5$ -- Application to $\mathrm{NaOs}{\mathrm{O}}_3$, $\mathrm{C}{\mathrm{a}}_2\mathrm{Ru}{\mathrm{O}}_4$, and $\mathrm{S}{\mathrm{r}}_2\mathrm{Ir}{\mathrm{O}}_4$
• Role of orbital off-diagonal spin and charge condensates in a three orbital model for $\mathrm{C}{\mathrm{a}}_2\mathrm{Ru}{\mathrm{O}}_4$ -- Coulomb renormalized spin-orbit coupling, orbital moment, and tunable magnetic order
• Spin-orbit excitons in a correlated metal: Raman scattering study of Sr2RhO4
• Photoinduced phase switching at a Mott insulator-to-metal transition
• Collective mode excitations and simulated $L$-edge resonant-inelastic x-ray scattering spectra in antiferromagnetic Ca${}_2$RuO${}_4$
• Coexistence of insulator-like paramagnon and metallic spin-orbit exciton modes in SrIrO${}_3$
• Critical magnetic fluctuations in the layered ruthenates Ca${}_2$RuO${}_4$ and Ca${}_3$Ru${}_2$O${}_7$
• Automated evaluation of imaginary time strong coupling diagrams by sum-of-exponentials hybridization fitting
• Formation of orbital molecules on a pyrochlore lattice induced by A-O bond covalency