Comparative crystal field analysis of energy level schemes and nephelauxetic effect for Cr⁴⁺, Cr³⁺, and Mn⁴⁺ ions in Y₂Sn₂O₇ pyrochlore

The electronic energy levels of the six-coordinated Cr⁴⁺, Cr³⁺, and Mn⁴⁺ ions in the pyrochlore, Y ₂Sn₂O₇, were calculated using the exchange charge model of crystal field theory. For these transition metal ions, the calculated energy levels and their trigonal splitting are in good agreement with experimental data. The calculations of the crystal field parameters show that the increased crystal field strength is related to the increased values of the moments of the 3d electron density in the sequence Mn⁴⁺ → Cr⁴⁺ → Cr³⁺. The nephelauxetic effect (degree of covalency) in Y₂Sn₂O₇ was deduced by comparing the energies of the first spin-forbidden transitions of the free Cr ⁴⁺, Cr³⁺, and Mn⁴⁺ ions with the experimentally determined values and with the estimation of the Racah parameter ratio in the crystal and in the free state. It was observed that the covalency increases in the sequence Mn⁴⁺ → Cr⁴⁺ → Cr³⁺, which is not easy to understand.