Adiabatic approximations of coupled dipole-proton model for hydrogen-bonded ferroelectrics

In several hydrogen-bonded ferroelectrics, such as KH2PO4-type ferroelectrics, the protons are strongly coupled to the dipoles produced in the heavy-ion sublattice. It is not clear whether such a coupled dipole-proton system can be described by two traditional simple models, the model of interacting tunneling protons and the model of interacting dipoles, and which one is more appropriate. We show that both models follow from the coupled dipole-proton model under the opposite adiabatic approximations, and that the model of interacting dipoles seems to correspond better with the experiments.