Damping of optical phonons in Ga_{1-x}Al_{x}As alloys

We measure for the first time the average mechanical response of a III-V mixed crystal with a two-mode behavior, ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Al}}_{\mathit{x}}$As, to a vibrational excitation at frequencies in the gap between the two optical-phonon branches. These frequencies are selected by the boundary conditions applied to the optical phonons confined in the GaAs layers of GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Al}}_{\mathit{x}}$As superlattices. We measure their variations with the composition of the alloy layer. The alloy lattice dynamics predicted in the coherent potential approximation is perfectly verified: The gap is shown to be divided into GaAs- and AlAs-type ranges. At the cutoff frequency the average damping becomes infinite.