Green's-function theory of phase transitions in hydrogen-bonded ferroelectric crystals with pseudo-spin-lattice coupled mode model

In this paper the recent Green's-function theory of Ramkrishnan and Tanaka for studying ferroelectric phase transitions in potassium dihydrogen phosphate (KDP)-type crystals using pseudo-spin-lattice coupled mode (PLCM) model has been extended to include the effect of phonon anharmonicity and to compare the calculated results with the recent experimental data. The renormalized proton-phonon energy spectrum, Curie-Weiss constant ($C$), Curie temperature ($T_C$), and the logarithmic behavior of specific heat ($C_v$) calculated from the internal energy have been studied with this extended PLCM model. Our theory in particular is able to explain, along with other physical properties, the large shift of the Curie temperature in all the KDP-type crystals on deuteration compared to the small change of the Curie-Weiss constant. The latter has not been possible using the cluster satistical treatment taking into account the excited Slater-Takagi (ST) energy levels. It is also observed that, except for the specific heat, the calculated quantities (such as electrical susceptibility and Curie-Weiss constant) depend on the tunneling energy explicitly. A very good agreement between our theoretical results and those of recent experimental data indicates the suitability of the Green-function technique and the Tyablikov-type decoupling scheme for studying phase transitions in the KDP family. We have also shown that our present theory leads to a pseudo-Jahn-Teller-like mechanism in the KDP system and shows close resemblance between the topologies of the order disorder and displacive type of phase transition. It therefore indicates the possibility of a unified theory of phase transition in ferroelectric crystals. Finally the Blinc-de Gennes parameters calculated for different KDP salts have also been compared with the experimental results available.