Multiphonon relaxation rates measurements and theoretical calculations in the frame of non-linear and non-Coulomb model of a rare-earth ion-ligand interaction

The fluorescence kinetics decay from F-3(3), H-3(5), H-3(4), F-3(4) multiplets of Tm3+ and F-5(5), I-5(5), S-5(2) + I-5(6), I-5(7), multiplets of Ho3+ ions in Y3Al5O12, Lu3Al5O12 and LiYF4 crystals was directly measured. On the basis of these measurements the multiphonon relaxation (MPR) rates of the transitions were determined. The theoretical dependence of multiphonon relaxation rates on the rare-earth ionic radii was derived using the non-linear (NL) theory of multiphonon relaxation. A good qualitative agreement of this dependence with new and earlier measured MPR rates in rare-earth ions in the row from Tm3+ to Pr3+ in YAG, YLF, and LaF3 crystals was obtained. The dependence of multiphonon relaxation rates on the crystal type is also considered.