Evidence for a Quasi-Two-Dimensional Proton Glass State in Cs5H3\(SO4\)4 ˙ xH2O Crystals

We describe damping of hypersonic and ultrasonic longitudinal acoustic (LA) phonons in crystals of Cs ₅H ₃\(SO ₄\)₄˙xH ₂O (PCHS) between 100 and 360 K. The damping of LA phonons exhibits strong dispersion caused by relaxation processes in the region of transformation into the glasslike phase \(T_g~260 K\). Near T_g the damping of ultrasonic phonons propagating in the basal plane reflects the cooperative freezing of acid protons. The damping of LA phonons propagating perpendicular to the basal plane can be fit by the Debye model and is due to the interaction between protons and LA phonons. This suggests that the proton glass state that is realized at T<T_g has a quasi-two-dimensional nature.