Saturation of multiphonon relaxation rates of rare-earth ions in glasses and phonon localization in disordered structures

Abstract

The effect of temperature on the saturation of the multiphonon relaxation rate is investigated. The relaxation rate is deduced from the decay time of the 3H 4 multiplet of Tm 3+ ions, measured from 10 K up to 550 K for different excitation powers in a tellurite glass. Increasing the temperature, at fixed excitation power, the multiphonon-relaxation rate ( W nr) increases as usual. However, an hysteresis is observed, a discontinuity appears at 350 K due to an irreversible compositional change of the glass as confirmed by thermal analysis. Two domains shall be considered: before (phase I) and after (phase II) the glass modification. In each of these domains, at fixed excitation density, the non-radiative decay rate follows the classical law, the mediating phonon frequency remains unchanged whatever the excited state density. Applying our modified model for the W nr dependence with the excited state density, at fixed temperature, allows to deduce the phonon diffusion length. We find that this critical distance is in good agreement with the glass cohesive length deduced from the boson peak recorded by Raman scattering. The results are discussed in the frame of phonon localization in disordered structures.