Self-energy of zone-boundary phonons in germanium:  Ab initiocalculations versus neutron spin-echo measurements

We present ab initio calculations and spin-echo measurements of the anharmonic self-energy of phonons at the X point of the Brillouin zone for germanium. The mechanisms that contribute to these self-energies are different from those usually displayed by phonons at the center of the Brillouin zone. Each mode shows trends representative of the variety of anharmonic mechanisms that are responsible for the scattering and the decay of phonons. The transverse acoustic phonons at the X point are very long lived at low temperatures; i.e., their probability of decay approaches zero, as a consequence of an unusual decay mechanism allowed by energy conservation. We have identified the microscopic processes that determine these self-energies. The calculated self-energies and their temperature dependence agree well with experiment.