Attenuation of elastic surface waves by anharmonic interactions at low temperatures

Abstract

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 ${\omega }^{\text{1+n}}{\mathrm{\hspace{0.17em}T}}^{\text{4−n}}\text{\hspace{0.17em}(1.9 ≲ n ≲ 2.2)}$ from that obtained in the low‐frequency region.