Mode-mode coupling in incipient ferroelectrics

Abstract

The softening of the lowest infrared active vibration which leads to the ferroelectric instability in perovskite crystals is currently explained in terms of mode-mode interactions.1 There exists, at the present time, no microscopic basis for the calculation of the coupling coefficients, which had to be taken as parameters of the theory. We show here that these interactions have the same origin as the strong Raman scattering observed in oxide perovskites, namely a non-linear anisotropic electron-ion interaction localized at the oxygen ion. This explains also why only oxide perovskites exhibit such a behaviour. We use a shell model with an anisotropic core-shell coupling at the oxygen ion, which includes a quartic term.2 The adiabatic interaction between electrons (shells) and phonons (cores) leads to an effective fourth order phonon-phonon interaction. The temperature dependence of all the phonons and in particular the ferroelectric soft mode is obtained within the self-consistent Hartree approximation. This result, as well as the second order Raman spectra are in very good agreement with experimental data of SrTiO3 and KTaO3. The anisotropic enhancement of the oxygen polarkability is attributed to phonon modulated hybridization of the oxygen p states with d states of the transition metal ions. Preliminary results on a microscopic calculation of this effect are given. The extension of the theory to the oxide perovskites which become ferroelectric at finite temperature as e.g. BaTiO3 and KNbO3 is discussed as well.