Attenuation of elastic surface waves by anharmonic interactions at low temperatures

Based on the theory of surfons, we present a formalism to calculate the attenuation rate of elastic surface waves at low temperatures in the high-frequency region. A general formula for the attenuation rate due to the cubic anharmonic terms in the elastic energy of an isotropic elastic continuum is given by means of a temperature-dependent Green's function. In a frequency region between 20 and 40 GHz at T=1°K, our result shows quite different frequency and temperature dependence ω1+n T4−n (1.9 ≲ n ≲ 2.2) from that obtained in the low-frequency region.