Magnetic dipole and vibronically induced electric dipole intensities of the ⁵D₄→⁷F_J transitions of Tb³⁺ in Cs₂NaTbCl₆

Abstract

An analysis of the emission intensities associated with the ⁵D₄→⁷F _J (J=2, 3, 4, 5, and 6) transitions of Tb³⁺ in crystalline Cs₂NaTbCl₆ is performed. The energy levels and crystal-field states associated with the octahedral (O_h ) TbCl₆ ^3- clusters are calculated using a weak-field crystal-field model. Magnetic-dipole strengths are calculated for all transitions occurring between the crystal-field components of ⁵D₄ and the crystal-field components of ⁷F₂, ⁷F₃, ⁷F₄, ⁷F₅, and ⁷F₆. Vibronically induced electric-dipole strengths are also calculated for the transitions between the ⁵D₄→⁷F _J (J=2, 3, 4, 5, and 6) crystal-field components. In the vibronic intensity model, both ‘static’ and ‘dynamic’ coupling between the electronic charge distributions on the metal ion (Tb³⁺) and ligands (Cl^-) are included. Only the ungerade vibrational modes localized within the TbCl₆ ^3- cluster are considered as intensity-promoting modes. Assuming a thermally equilibrated ⁵D₄ emitting level and lorentzian band shapes, emission spectra are calculated for the ⁵D₄→⁷F₂, ⁷F₃, ⁷F₄, ⁷F₅, and ⁷F₆ transitions of the Tb³⁺ ion. These calculated spectra are compared with the experimentally determined emission spectra for Cs₂NaTbCl₆ (at T=77 K). The observed dominance of magnetic-dipole intensity in the transitions of ΔJ = ±1 free-ion parentage is well accounted for by our intensity calculations. The observed near-equivalence of the magnetic-dipole and vibronically induced electric-dipole contributions to the intensities of the transitions of ΔJ=0, ±2 free-ion parentage is also reproduced by our intensity calculations. In general, the intensity model leads to excellent agreement between the calculated and experimental emission spectra in all regions except that associated with the ³D₄→⁷F₄ transition.