Off-centre displacements and ferroelectric phase transition in dilute KTa_1-xNb_xO₃

We present a theory of the Nb-on off-centre displacements and ferroelectric phase transition in dilute KTa_1-xNb_xO₃. We believe that this theory is generally applicable to ferroelectric transitions in incipient ferroelectrics induced by impurities. We show that the non-uniform strong intraband electron-phonon interaction leads to the localization of virtual conduction band electrons around the Nb ions and to the off-centre displacements of these ions. We consider the off-centre displacements as pseudospins and show that their interaction with the soft phonon mode of the host lattice (KTaO₃) plays a fundamental role in the phase transition dynamics. The model quantitatively reproduces the basic experimental data in the quantum regime: the temperature dependence of the inverse dielectric function Ε^-1(T), the impurity and temperature dependence of the renormalized softmode vibrational frequency ω̃(x, T) and the impurity concentration dependence of the transition temperature T_C(x). In particular we show that the critical concentration x* is determined by the ion tunnelling frequency, the parameters for the bare soft mode and the pseudospin-phonon coupling constant.