Probing Multiphonon Luminescence Bandsin Eu²⁺-Doped Thiogallate Phosphors via Spectral Moments Approach

Although the method of spectral moments offers unique insight into electron-phonon interactions in activated crystals, it has not been sufficiently exploited to date. Here, we use the spectral distribution moment method as a tool for the analysis of multiphonon luminescence bands in thiogallate phosphors MGa2S4 (M= Ca, Sr and Ba) doped with Eu2+ ions. The exact quantum-mechanical expressions for the first three spectral moments are presented using the traditional (basic) model of the impurity ion, which deals with the two well separated electronic levels, takes into account only linear electron-phonon interaction and implies harmonic approximation for the lattice vibrations. By analyzing the experimental data on the profiles of the emission bands corresponding to the to 4f7(8S7/2) transitions combined with the Raman spectra, we identify vibrational mode producing dominant contribution to the observed optical bands and evaluate the first three spectral moments and the Pekar-Huang-Rhys parameters quantifying the vibronic interaction strength. When discussing the relationship between the Stokes shift and the heat release parameters in the vibronically assisted emission of MGa2S4: Eu2+ crystals, special attention is paid to the ambiguity of the diverse existing expressions for the Stokes shift. Finally, based on the analysis of the spectral moments in a more general context, we discuss the challenges emerging in the problem of comparison of the optical emission bands of thiogallate phosphors in the framework of the basic model, such as role of the quadratic vibronic interaction and phonon dispersion.