Determination of microscopic parameters for nonresonant energy-transfer processes in rare-earth-doped crystals

A method for estimating the microscopic probability rate of phonon-assisted energy transfer between rare-earth (3+) ions in solids was developed based on Dexter's theory for phonon-assisted energy transfer. The proposed method in this paper enables one to calculate the overlap integral from fundamental cross-section spectra of nonresonant energy transfer involving a multiphonon generation in both donor and acceptor sites. A translation of the donor emission spectrum towards the acceptor absorption scaled with the N-phonon emission probability represents the m-phonon emission band which performs the energy transfer to the acceptor. A nonvanishing overlap integral 10(-2)-10(-3) limes smaller than for the resonant case is found. A multiphonon generation probability assisting the energy transfer was considered due to a combined mechanism of creation and annihilation of phonons. The participation of each phonon in the process was determined. This method was used to investigate the Tm3+(F-3(4))-->Ho3+(I-5(7)),Er3+(I-4(13/2))-->[Ho3+(I-5(7)),Tm3+(F-3(4))] direct energy transfers in LiYF4 crystals, as well the back transfers.