Intensity and bandwidth of multiphonon vibronic transitions of rare-earth ions in crystals

The theory of multiphonon vibronic coupling to electronic transitions is applied in analysing fluorescence spectra of Eu²⁺ in BaFCI, which consist of the 4f⁷(⁶P_7/2,) → 4f⁷(⁸S_7/2) and 4f⁶5d → 4f⁷ transitions, and the 4f⁷-4f⁶5d excitation spectrum of Ce³⁺ in YPO⁴. The 4f electrons are weakly coupled to lattice vibration modes so that only weak one- and two-phonon sidebands are observable in the 4f-4f optical transitions, whereas the electron-phonon coupling is significantly stronger for a 5d electron. Accordingly, intensive multiphonon vibronic transitions overwhelmingly dominate the 4f⁶5d → 4f⁷ spectrum. It is shown that the extended Judd-Ofelt theory for weak vibronic coupling in the framework of the M-process is equivalent to the Huang-Rhys theory for the δ-process. In the analysis of experimental data, contributions from local ligand modes and lattice acoustic modes are separated, and the coupling strength is evaluated, in terms of the Huang-Rhys parameter S, for the 4f-4f and 5d-4f vibronic transitions.