ISING-MODEL IN A TRANSVERSE TUNNELING FIELD AND PROTON-LATTICE INTERACTION IN H-BONDED FERROELECTRICS

The addition of a BijSixSjx-type coupling between the tunneling motion of one proton and the tunneling motion of another to the Ising model in a transverse-field Hamiltonian, or the addition of the probably larger SixFixQi-type pseudospin phonon coupling (describing the modulation of the distance between the two equilibrium sites in an O-H • • • O bond by nonpolar phonons), results in a temperature-dependent renormalization of the proton tunneling integral. This is important close to TC, where the soft-mode frequency vanishes, ωcrit→0. This may lead to large isotope shifts in TC on deuteration even for small values of the tunneling intergal and may explain some phenomena recently observed in PbHPO4 and squaric acid as well as the dependence of the effective proton-lattice interaction constant on hydrostatic pressure in KH2PO4-type systems. This last effect may be also due to the presence of a SixDixQi2 term in addition to the Kobayashi SizFizQi term when coupling with polar optic phonons is taken into account. When the lattice motion is so anharmonic that the lattice ions move in a double-well potential, and the proton-lattice coupling so strong that the protons can tunnel in only one out of the two possible lattice configurations, two Curie temperatures may appear. © 1979 The American Physical Society.