Taking into account the bilinear coupling between the tunneling protons and the displacements of the electron shells of the surrounding ${\mathrm{PO}}_4$ groups, we present a new model of hydrogen-bonded ferroelectrics. The model is an extension of both the tunneling model and the nonlinear polarizability model and includes the geometrical aspects of the hydrogen bond. It leads to a structural phase transition and describes the isotope effect due to the substitution $\mathrm{H}/\mathrm{D}$ in ${\mathrm{KH}}_2{\mathrm{PO}}_4$ and the pressure dependence.

• Received 6 October 1997

DOI:https://doi.org/10.1103/PhysRevLett.80.2173