Effective point-charge analysis of crystal fields: Application to rare-earth pyrochlores and tripod kagome magnets R3Mg2Sb3 O14

An indispensable step to understand collective magnetic phenomena in rare-earth compounds is the determination of spatially anisotropic single-ion properties resulting from spin-orbit coupling and crystal field (CF). The CF Hamiltonian has a discrete energy spectrum - accessible to spectroscopic probes such as neutron scattering - controlled by a number of independent parameters reflecting the point symmetry of the magnetic sites. Determining these parameters in low-symmetry systems is often challenging. Here, we describe a general method to analyze CF excitation spectra using adjustable effective point-charges. We benchmark our method to existing neutron-scattering measurements on pyrochlore rare-earth oxides and obtain a universal point-charge model that describes a large family of related materials. We adapt this model to the newly discovered tripod kagome magnets (R3Mg2Sb3O14, R = Tb, Ho, Er, Yb) for which we report broadband inelastic neutron-scattering spectra. Analysis of these data using adjustable point-charges yields the CF wave functions for each compound. From this, we calculate thermomagnetic properties that accurately reflect our measurements on powder samples and predict the effective gyromagnetic tensor for pseudospin degrees of freedom - a crucial step to understand the exotic collective properties of these kagome magnets at low temperature. We present further applications of our method to other tripod kagome materials and triangular rare-earth compounds RMgGaO4 (R =Yb, Tm). Overall, this study establishes a widely applicable methodology to predict CF and single-ion properties of rare-earth compounds based on interpretable and adjustable models of effective point charges.