Spontaneous Decay of High-Frequency Acoustic Phonons in CaF2

Abstract
The decay of high-frequency acoustic phonons in CaF2 at low crystal temperature is studied with use of an optical technique of tunable phonon detection. A strongly frequency-dependent lifetime is found for phonons at frequencies ν>1012 Hz. The lifetime decreases proportionally to ν5, indicating spontaneous phonon decay by anharmonic three-phonon processes. These results suggest that nonlinear elasticity theory is applicable to describe anharmonic interactions of high-frequency acoustic phonons.