Attenuation process of the longitudinal phonon mode in a TeO2 crystal in the 20-GHz range

We experimentally investigated the hypersonic attenuation process of a longitudinal mode (L-mode) sound wave in TeO2 from room temperature to a lower temperature using Brillouin scattering and impulsive stimulated thermal scattering (ISTS) measurements. For precise measurement of the Brillouin linewidth at low temperatures, whereby the mean free path of the phonon becomes longer than the sample length, it is indispensable that the phonon should propagate along the phonon-resonance direction. To figure out the suitable direction, we defined two indices characterizing a degree of phonon divergence and a purity of propagation direction. The best direction that we found from these indices is [110] direction in TeO2, and it was used to discuss the temperature and frequency dependences of Brillouin spectra. We extracted the temperature dependence of the attenuation rate of T4 from the modulated Brillouin spectra due to the phonon resonance below Debye temperature. The frequency dependence ω1 of the hypersonic attenuation was also estimated from the polarization dependence of the Brillouin linewidth. Theoretically, it predicted that the L-mode phonon attenuation at low temperatures in TeO2 is a result of Herring's process, which shows the attenuation behavior of ω2T3. The ω1T4 dependence is not allowed in Herring's process but is allowed by the L+L→L process, which has been considered to be forbidden so far. We evaluated the thermal phonon lifetime using ISTS and established that it was finite even at 20 K, thereby allowing the L+L→L process. Therefore, we conclude that the L+L→L process dominates the attenuation of an L-mode phonon in TeO2 in the low-temperature region.