Nonequilibrium phonon dynamics in LaF3:Pr3+

The presence of low-lying optical modes in LaF3 can introduce additional decay processes which cause the frequency dependence of the phonon relaxation rate to deviate from the ω+5$/ dependence predicted by the isotropic dispersionless model. In this paper we investigate the frequency dependence of the phonon relaxation rate in LaF3:Pr3+ over a wide range of frequencies using a combination of defect-induced one-phonon absorption and absorption vibronic sideband spectroscopy. For comparison with our experimental results, we calculate the phonon relaxation rates for a system with low-lying optical modes. In our model, we consider that both the dispersion curves and the three-phonon coupling constants are isotropic.