A pseudo-Jahn-Teller vibronic model of d³ ions in cubic crystals; the luminescence band shape and lifetimes of CdIn₂S₄:Cr³⁺

A new model for the vibronic problem of the luminescence of 3d³ impurity ions in the cubic environment is proposed. The approach developed is based on the numerical quantum-mechanical solution of the dynamic pseudo-Jahn-Teller vibronic problem for the excited states. The spin-orbit splitting of the ⁴T₂ term, and its mixing with ²E, as well as the vibronic interaction with the full-symmetric (A_1g) local mode, are taken into account, resulting in the (Γ₈+Γ₈′+Γ₈″) ⊗a₁ vibronic problem, and the Γ₆⊗ a₁ and Γ₇⊗a₁ adiabatic problems. The effective dipole moment operator is built with due regard for a weak odd-parity trigonal crystal-field component. The vibronic wave-functions are used for the calculation of the band shape of the luminescence in the R line and U band, as well as for the evaluation of the temperature dependence of the lifetime decay emission of Cr³⁺ ions in CdIn₂S₄:Cr single crystals. The proposed model provides a very good explanation of the experimental data.