Low symmetry aspects in spectroscopic and magnetic susceptibility studies of Tb³⁺(4f⁸) in TbAlO₃

The three sets of crystal field parameters (CFPs) obtained from spectroscopic and magnetic susceptibility studies of Tb³⁺(4i*) ions in TbA1O₃ by Gruber et al. (J. Lumin. 128 (2008) 1271) were reanalyzed. These sets, fitted from experimental energy levels, are physically equivalent and correspond to specific choices of the axis system. Proper interpretation of experimental data for Tb³⁺ ions at monoclimc C_s symmetry sites in TbA1O₃ crystal requires clarification of several intricate low symmetry aspects, namely, (a) three equivalent forms of monoclinic CF Hamiltonian, (b) relative orientation of the crystallographic axis system w.r.t. the symmetry-adapted axis system, (c) mono-clinic standardization of CFPs, (d) distinction between the actual and apparent low symmetry effects exhibited by CFPs, and (e) nominal nature of all fitted CFP sets. For this purpose, modeling of CFPs for Tb³⁺ in TbA1O₃ was carried out using at the first stage only the Coulomb, i.e. point charge, contributions in the exchange charge model. The point charge model calculated CFPs disagree with the experimental CFPs, especially the rank k=6 CFPs. To explain this discrepancy and to verify the correctness of the theoretical CFP calculations additionally the superposition model was employed. The methods of analysis and modeling of CFP sets for monoclinic symmetry cases proposed here proved useful for the studied case as well as might be used for other ion-host systems exhibiting monoclinic or triclinic local site symmetry. Partial results for Tb³⁺ ions in TbA1O₃ were presented here, whereas detailed results were given in a follow-up paper.