Brillouin spectroscopy of polarization fluctuations in a a ${\mathrm{Rb}}_{1\mathrm{-}\mathit{x}}$(${\mathrm{NH}}_4$${)}_{\mathit{x}}$${\mathrm{H}}_2$${\mathrm{PO}}_4$ glass

Brillouin scattering spectra of modes coupling linearly to the polarization have been obtained on a single crystal of the mixed ferroelectric-antiferroelectric system ${\mathrm{Rb}}_{1\mathrm{-}\mathrm{x}}$(${\mathrm{NH}}_4$ ${)}_{\mathrm{x}}$ ${\mathrm{H}}_2$ ${\mathrm{PO}}_4$ with x=0.35, a concentration where a structural glass forms at low temperatures. A phenomenological description of the dielectric susceptibility is used which accounts perfectly for all aspects of the unusual line shapes observed. Crucial parameters of that theory are found in agreement with values derived from other independent measurements, such as dielectric-constant ones, giving strong support to the phenomenological description. Evidence for the existence of a broad distribution of relaxation times and of a dynamic central peak below the onset of freezing is presented. Besides the piezoelectric coupling effects, couplings of higher order in the polarization are found to play an important role as well, in particular for longitudinal modes.