Multiple-phonon nonradiative relaxation: Experimental rates in fluoride crystals doped with Er3+ and Nd3+ ions and a theoretical model.

Abstract

The multiphonon relaxation (MR) rates for a large number of 3- to 5-phonon transitions of ${\mathrm{Er}}^{3+}$ ions in ${\mathrm{LiYF}}_{4}$ and ${\mathrm{LaF}}_{3}$ crystals were measured at 77 K. The MR rates of ${\mathrm{Nd}}^{3+}$ and ${\mathrm{Er}}^{3+}$ ions in these crystals have been analyzed with a point-charge (or ionic) nonlinear relaxation mechanism and a covalent nonlinear relaxation mechanism, rather than the traditional linear relaxation mechanism. The functional dependencies of the experimental MR rates on the number of phonons n participating in the radiationless transitions were explained in terms of the two nonlinear coupling mechanisms. The mean values of the parameter of the theory \ensuremath{\eta}=${\mathit{u}}^{2}$/${\mathit{R}}_{0}^{2}$, where ${\mathit{R}}_{0}$ is the equilibrium minimal distance between the rare-earth ion and the ligands and u is the amplitude of the vibrations of the ligands, have been evaluated in these crystals for n=3--4 where the contribution of the exchange interaction is small. On the basis of these calculations it was established that the strength of dynamic electron-phonon coupling is larger in ${\mathrm{LaF}}_{3}$ than in ${\mathrm{LiYF}}_{4}$. Also, the influence on the MR rates of the exchange interaction between the 4f electron and the ligands has been analyzed. Its inclusion gives higher theoretical MR probabilities and better agreement with the experimental relaxation rates.