Spectroscopic and crystal-field analysis of energy levels of Eu ³⁺ in SnO₂ in comparison with ZrO₂ and TiO ₂

We have carried out systematic crystal-field energy level calculations of Eu³⁺ ions doped in SnO₂ based on experimentally acquired luminescence spectra. In addition, with an aim of revealing systematic trends in spectra and crystal-field effects for Eu³⁺ ion in similar hosts, we have analyzed the TiO₂ (anatase):Eu³⁺ spectra as well. The obtained crystal-field parameters yield very good agreement between the calculated and observed energy levels. Emphasis has been put on analysis of the crystal-field-induced J-mixing effects and their roles in getting proper sets of crystal-field parameters and energy levels. A more general theory concerning J-mixing effects has been proposed and the relevant results will be valuable to understanding of the spectral characteristics of Eu³⁺ f-f transition spectra in other hosts. Relations between the maximum crystal-field splitting of some selected J-manifolds with J = 1 and J = 2 and crystal-field invariants have been re-visited and re-derived. The corresponding numbers of crystal-field parameters influencing the splitting of these manifolds have been taken into account in every case. The derived equations have been tested in applications to three systems (SnO₂, TiO₂ (three sites) and ZrO ₂). Consistent results have been obtained, which confirms validity of the performed crystal-field analysis and opens a way for possible applications of the suggested calculating technique to other rare-earth ions.