Theoretical studies of electron-vibrational 4f N–4f N−1 5d spectra in LiYF 4:RE 3+ crystals

Abstract

The UV and VUV inter-configuration 4f N –4f N−1 5d spectra of rare-earth ions in insulators consist of broad electron-vibrational bands which sometimes have a resolved fine structure. In the present work, the low-temperature absorption band shapes of the impurity Ce 3+, Pr 3+ and Nd 3+ ions in LiYF 4 crystals have been simulated in the framework of the microscopic theory operating with the real phonon spectrum of the host crystal lattice. The energy levels and wave functions of the ground (4f N ) and excited (4f N−1 5d) electronic configurations of rare-earth ions were obtained from the numerical diagonalization of the Hamiltonian containing energies of electrostatic Coulomb and exchange interactions between electrons, spin–orbit interactions and the crystal field interaction. Crystal field parameters and electron–phonon coupling constants were treated in the framework of the exchange charge model. Form-functions of the spectral bands proportional to the calculated integral intensities of electric dipole transitions are obtained as a sum of convolutions of spectral densities of multiphonon correlation functions and form-functions of zero-phonon lines with the widths determined by distributions of random lattice strains and non-radiative transition probabilities. The calculated values of the Huang–Rhys parameters of crystal field states in mixed 4f N−1 5d configurations vary in the range from 0.1 to 15 and correspond to intermediate or strong electron–phonon interactions. Results of simulations of the spectral envelopes agree satisfactorily with the experimental data available from the literature.