Microwave Sound Absorption by Anharmonic Three-Phonon Interactions in TiO2

Hypersonic attenuation has been measured, for both polarizations, along the c axis of rutile single crystals in the frequency range from 0.5 to 3 GHz and at temperatures from 4 to 60°K. For shear waves, the attenuation varies roughly as $\Omega T^4$. For longitudinal waves, the attenuation gradually departs from this behavior towards a lower frequency dependence and a higher temperature dependence as the crystal temperature is reduced. For both types of waves, the frequency and temperature dependence of the absorption coefficient is in good agreement with those theories that include finite thermal-phonon lifetime and acoustic dispersion effects in the absorption of hypersonic waves by anharmonic interactions with thermal phonons.