A framework is presented for modeling and understanding magnetic excitations in localized, intermediate coupling magnets where the interplay between spin-orbit coupling, magnetic exchange, and crystal field effects are known to create a complex landscape of unconventional magnetic behaviors and ground states. A spin-orbit exciton approach for modeling these excitations is developed based upon a Hamiltonian which explicitly incorporates single-ion crystalline electric field and spin exchange terms. This framework is then leveraged to understand a canonical Van Vleck $j\rm{_{eff}}=0$ singlet ground state whose excitations are coupled spin and crystalline electric field levels. Specifically, the anomalous Higgs mode [Jain et al. Nat. Phys. 13, 633 (2017)], spin-waves [S. Kunkemöller et al. Phys. Rev. Lett. 115, 247201 (2015)], and orbital excitations [L. Das et al. Phys. Rev. X 8, 011048 (2018)] in the multiorbital Mott insulator Ca$_2$RuO$_4$ are captured and good agreement is found with previous neutron and inelastic x-ray spectroscopic measurements. Furthermore, our results illustrate how a crystalline electric field-induced singlet ground state can support coherent longitudinal, or amplitude excitations, and transverse wavelike dynamics. We use this description to discuss mechanisms for accessing a nearby critical point.

Nd-based pyrochlore oxides of the form Nd$_{2}B_{2}$O$_{7}$ have garnered a significant amount of interest owing to the moment fragmentation physics observed in Nd$_{2}$Zr$_{2}$O$_{7}$ and speculated in Nd$_{2}$Hf$_{2}$O$_{7}$. Notably this phenomenon is not ubiquitous in this family, as it is absent in Nd$_{2}$Sn$_{2}$O$_{7}$, which features a smaller ionic radius on the $B$-site. Here, we explore the necessary conditions for moment fragmentation in the Nd pyrochlore family through a detailed study of the mixed $B$-site pyrochlore Nd$_{2}$GaSbO$_{7}$. The $B$-site of this system is characterized by significant disorder and an extremely small average ionic radius. Similarly to Nd$_{2}$Sn$_{2}$O$_{7}$, we find no evidence for moment fragmentation through our bulk characterization and neutron scattering experiments, indicating that chemical pressure (and not necessarily the $B$-site disorder) plays a key role in the presence or absence of this phenomenon in this material family. Surprisingly, the presence of significant $B$-site disorder in Nd$_{2}$GaSbO$_{7}$ does not generate a spin glass ground state and instead the same all-in-all-out magnetic order identified in other Nd pyrochlores is found here.