Anharmonic lifetimes of low-frequency optical phonons in LaF3with the use of monoenergetic generation and detection

Dynamics of large-$\overrightarrow{\mathrm{k}}$ acoustic phonons and low-frequency optical phonons in La${\mathrm{F}}_3$ are investigated. Monoenergetic nonequilibrium phonons are obtained by electron-phonon relaxation of laser-excited ${\mathrm{Er}}^{3+}$ ions and are detected with phonon-induced absorption of the anti-Stokes vibronic sideband of the ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$ state of ${\mathrm{Pr}}^{3+}$. Monoenergetic phonon occupation numbers of ${10}^{-2\mathrm{}}$ are observed and the decay of these nonequilibrium phonons is interpreted with the aid of estimates of some of the parameters of the electron-phonon system. We conclude that the observed decay is dominated by anharmonic breakup of low-frequency optical phonons, which have recently been seen with inelastic neutron scattering in the (41-54)-${\mathrm{cm}}^{-1\mathrm{}}$ phonon-energy range of these experiments. Lifetimes in the 10-ns range are obtained, consistent with some theoretical estimates.