Ferroelectric mode and molecular structure in the hydrogen-bonded ferroelectric arsenates and their deuterated isomorphs

Light-scattering measurements of the temperature dependence of the Raman-active modes of vibration in both the paraelectric and ferroelectric states of the hydrogen-bonded ferroelectrics K${\mathrm{H}}_2$As${\mathrm{O}}_4$, Rb${\mathrm{H}}_2$As${\mathrm{O}}_4$, and Cs${\mathrm{H}}_2$As${\mathrm{O}}_4$ and their deuterated isomorphs K${\mathrm{D}}_2$As${\mathrm{O}}_4$, Rb${\mathrm{D}}_2$As${\mathrm{O}}_4$, and Cs${\mathrm{D}}_2$As${\mathrm{O}}_4$ are reported. Through examination of these spectra we have identified the protonic or deuteronic, transverse-optic, As$\mathrm{O}_4^{}{}_{}{}^{3-}$ internal, and O-H-O or O-D-O valence vibrations in the Raman scattering and determined their symmetries and temperature dependence. Evidence for the collective protonic or deuteronic motions is observed in both the low-frequency $B_2$ and $E$ spectra in the paraelectric phase of each arsenate. The low-frequency $B_2$ spectra for the hydrogenated compounds are well fitted by a coupled-oscillator system representing the ferroelectric mode and a low-frequency phonon. The low-frequency $B_2$ spectra for the deuterated materials reveals the ferroelectric mode to be coupled to at least two low-frequency phonons, but, in a limited way, the spectra can be fitted to a coupled-oscillator system representing the ferroelectric mode and the lowest $B_2$ phonon. The results reveal the $\frac{T}{\tau }$ for the ferroelectric mode of all the compounds to decrease linearly with decreasing temperature; for real coupling the $\frac{T}{\tau }$ extrapolate to zero well below the transition temperature but for imaginary coupling the $\frac{T}{\tau }$ vanish much closer to the transition. In the limit of small damping, the results for real coupling are found to be in only partial agreement with the Kobayashi model, while the results for imaginary coupling are in accord with the Cowley-Coombs anharmonic theory of the transition and reveal the anomalous self-energy to be small compared to the conventional anharmonic self-energy of the soft mode.