Transition-metal compounds with 4d and 5d electrons have become a central focus over the past two decades, as the interplay of strong spin-orbit coupling, electronic correlations, and crystal-field effects can generate local spin-orbit entangled states. These form the basis for novel phenomena such as bond-directional Kitaev interaction, which can ideally generate a possible quantum spin liquid ground state, or excitonic magnetism manifested by the exchange-driven condensation of local triplet excitations. Deviations from ideal symmetry or the competition between various parameters, however, might affect the local states and suppress such phases, making a detailed understanding of the local states essential. In this thesis, we investigate the role of spin-orbit coupling in Mott-insulating transition-metal compounds with different dN electron configurations, namely d3, d4, and d5, since the effect of spin-orbit coupling can manifest differently in each of these configurations. In the first project, we analyze the low-energy excitations of the 4d5 compound alpha-RuCl3, one of the most studied candidates for realizing the Kitaev model. Using optical spectroscopy and Raman scattering in conjunction, we identify the spin-orbit exciton, the characteristic excitation from the jeff=1/2 ground state to jeff = 3/2, and establish that the two additional higher-lying features have to be understood as the double and triple spin-orbit excitons, refuting previous interpretations that severely challenged the local jeff=1/2 picture. From the excitation energy and splitting of the spin-orbit exciton, we calculate that the ground state wavefunction in alpha-RuCl3 exhibits more than 98% of jeff=1/2 character, agreeing with theoretical predictions and the notion that this compound is a proximate Kitaev material. The second, third, and fourth projects of this thesis focus on the K2PtCl6-type antifluorite halides A2MX6 with A = K+, Rb+, X =Cl-, Br-, and M = Re4+, Os4+, Ir4+. Choosing the Re-, Os-, or Ir-based version of these compounds allows us to examine the 5d3, 5d4, or 5d5 electron configurations, respectively. The isolated MX6 octahedra in these crystals result in large Mott gaps and narrow excitation peaks, which makes these materials ideal to study with optical spectroscopy and resonant inelastic x-ray scattering at the transition-metal L3 edge. Putting these methods together yields a very comprehensive picture of the electronic structure and allows us, e.g., to uncover the origin of the splitting in the spin-orbit exciton in K2IrCl6. For the 5d4 systems A2OsX6, our data confirm a robust local J=0 scenario. The spectra display well-defined onsite multiplets, which are described best within the intermediate coupling regime, where spin-orbit coupling and Hund’s coupling must be considered on equal footing. Determining the cubic crystal-field splitting using RIXS, we compare the electronic parameters in two different approaches: the t2g-only Kanamori model and the single-site model of the entire d shell. Both models describe the energies of the intra-t2g RIXS energies equally well, which allows us to establish these compounds as solid reference systems for other Os4+ J=0 systems. For the 5d3 case in K2ReCl6, we probe the competition of spin-orbit coupling and Hund's exchange in the quest of finding a spin-orbit-induced Jahn-Teller effect. While the value of spin-orbit coupling is sizable, it is not strong enough to turn fully around the S=3/2 scenario. However, we find that spin-orbit coupling enhances the coupling to the lattice in multiplets that acquire a non-vanishing orbital moment, which alters the observed lineshapes slightly. For the 5d5 system K2IrCl6, we investigate the nature of the spin-orbit exciton. The RIXS spectra display a characteristic splitting of this excitation, which had been explained by static distortions of the octahedra in previous works. However, based on a careful analysis using a vibronic Franck-Condon picture, we can assign the observed RIXS feature to a vibronic excitation with a well-resolved phonon sideband. The strong temperature sensitivity of the lineshape agrees with a recent theoretical prediction that goes beyond the simple Franck-Condon picture and attributes the splitting to a dynamic Jahn-Teller effect involving coupling to Eg phonon modes. The ground state itself retains cubic jeff=1/2 character, while the lattice couples only to the excited jeff=3/2 state. This demonstrates that ideal jeff=1/2 moments with cubic symmetry can indeed be realized in 5d5 Mott systems. It also shows direct RIXS at the L3 edge of 5d metals is capable of resolving vibronic phonon sidebands, which can be described with a single Franck-Condon factor.
P. Warzanowski (Wed,) studied this question.