Electron - Phonon theory of ferroelectricity and the isotope effect in perovskite oxides

In perovskite oxides (BaTiO3, etc.) the dynamical interband hybridization o f the oxygen 2p states (the valence band) and the titanium 3d states (the c onduction band) by active TO vibrations induces the ferroelectricity. The f ree energy of such type vibronic ferroelectrics is obtained taking into acc ount the electron-phonon interaction between Ti(Nb) 3d and O 2p states, the coupling of electrons with strains, the phonon and electron-phonon anharmo nicities, including nonlinear interband electron-phonon interactions and th e coupling of TO phonons with acoustical vibrations. Electron-phonon intera ctions lead to essential higher-order vertex terms in the expression for th e soft frequency of the TO phonon. It is concluded that a light-isotope-enr iched ferroelectric shows higher T-c than a ferroelectric with a heavier is otope as observed. The calculated T-s(Delta M) line for BaTiO3 agrees with the experiment.