Measurement of the "soft" mode and coupled modes in the paraelectric and ferroelectric phases of K${\mathrm{H}}_2$P${\mathrm{O}}_4$ at high pressure

Measurements of the pressure and temperature dependences of the soft-mode Raman spectra of potassium dihydrogen phosphate (KDP) in both the paraelectric (PE) and ferroelectric (FE) phases are reported. The soft-mode response is overdamped throughout the PE phase at atmospheric pressure, but can be made underdamped with pressure in this phase. Measurements at high pressure in the PE phase where the response is underdamped therefore allow a more accurate determination of the parameters for the coupled-mode system than one can obtain from measurements at atmospheric pressure. Measurement of the pressure dependence in the FE phase allows one to identify the soft mode of the system in this phase, and the results demonstrate that the proton motion remains coupled to an optic mode of the lattice for $T<\mathrm{}{T}_C$. The temperature and pressure dependences of the microscopic parameters are examined within the framework of both the pure tunneling and the coupled proton-optic-mode models for the phase transition. It is found that the pure tunneling model is inadequate for a detailed description of the spectra, whereas the modified tunneling model, or coupled-mode model, gives a more quantitative description of the results. While this model can be used for quantitative comparison between the Raman scattering and dielectric measurements in these materials, there are inadequacies of the model in describing the microscopic interactions. These features are discussed in detail.