Picosecond coherent Raman measurements of optical-phonon relaxation in LaF3Ce3+

An investigation of dephasing rates of some optical phonons in LaF3: Ce3+ (2 at.% Ce3+) crystals by picosecond time-resolved coherent anti-Stokes Raman spectroscopy is presented. At low temperature the lifetime of the 78-cm-1 phonon is 380 ps, while those of five other phonons of >200 cm-1 energy are in the range 2<T1<10 ps. The decay of the 78-cm-1 phonon is due to anharmonic spontaneous emission of two 39-cm-1 optical phonons with a cubic anharmonic matrix element B(3)78 39 390 k -k =0.15 0.05 cm-1. The decay of the other phonons studied likely occurs by an analogous process. The matrix elements for these phonons appear to be in the range 0.2-0.6 cm-1. The dephasing rate of the 78-cm-1 phonon is followed as a function of temperature to ~100 K, and the rates are well fitted by an energy relaxation model involving emission to 39-cm-1 phonons and absorption of ~40 and ~118-cm-1 thermally excited phonons. The matrix elements for absorption processes are (0.3 0.1) and (0.5 0.2) cm-1, respectively. The rate of absorption of thermally excited 78-cm-1 phonons is <10% of the rate of the other up-conversion processes, and it is suggested that this is due to a type of summetry selection rule for phonon-phonon scattering arising from small distortions away from a bimolecular unit cell to a hexamolecular cell, which creates two distinct types of phonons.