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Abstract

In order to understand f-electron systems, one needs access to the interactions, hybridisation, and bonding of f-orbitals with their chemical environment. Local physics in the f-shell is governed by atomic multiplet theory and spin-orbit coupling, but is also sensitive to its crystal environment. This not only gives rise to crystal-field splitting of atomic multiplet states, but can also result in heavy-fermion band formation, Kondo physics, magnetic and orbital ordering, or unusual bonding properties. Resonant Inelastic X-ray Scattering (RIXS) has become an established technique in the field of correlated materials over the last two decades, largely due to improvements in the energy resolution. RIXS spectra probe element-specific excitations in quantum materials. RIXS spectra can be measured in many different experimental geometries and light polarisations. To decouple the polarisation dependence of RIXS spectra from material-intrinsic properties, we developed a tensor framework for RIXS. This framework allows the spectra to be decomposed into a set of fundamental components associated with excitations of specific symmetry in the material. Experimental RIXS spectra of several 4f and 5f compounds are compared with theory to study bonding, covalence, and hybridisation of f orbitals. A symmetry-based sector approach for the single-impurity Anderson model is implemented and used to compute temperature-dependent RIXS spectra for representative Ce-based Kondo compounds. The lineshape of the 4f¹ crystal-field excitations can be linked to the hybridisation function between the impurity and the electronic bath, and thus to the Kondo scale. In addition, 4f⁰ final-state intensities for CeSi are shown to scale with the thermal weight of the Kondo singlet in the ground state. Atomic multiplet and ligand-field calculations are performed for several 3d4f RIXS spectra of a series of actinide compounds, and show how multiplet intensities can be used to relate spectral features to symmetry-defined valence in these materials.