Vibronic (pseudo Jahn-Teller) theory of ferroelectricity: Novel aspects and applications

Abstract

In a semi-review paper, the fundamentals of the vibronic (pseudo Jahn-Teller) theory of ferroelectricity in perovskite crystals of ABO₃ type, its main achievements and significant applications, are given. The theory is derived from first principles. First, the pseudo Jahn-Teller effect (PJTE) is introduced and shown to be the only source of polar instability that triggers the spontaneous polarization of the crystal. The driving force of the PJTE is added covalency by distortion, which is essentially of local (chemical) origin. Then, the earlier more qualitative, but physical transparent results in application of the PJTE theory to ABO₃ perovskites are presented, followed by the rigorous formulation in terms of Greens’ functions theory. The form of the adiabatic potential energy surface (APES) for the metal B sites with eight equivalent minima, obtained analytically, is confirmed by DFT calculations, and its parameter numerical values were estimated for BaTiO₃. It explains the occurrence of the three ferroelectric and one paraelectric phases, and order-disorder transitions between them as due to temperature dependent gradual overcome of the consecutive barriers between its eight equivalent minima. The theoretical treatment of the phase transitions is carried out in the mean-field approximation yielding near-to-experimental Curie temperatures.

An important further development of this theory was reached more recently, for the first time revealing the role of spin in ferroelectric polarization of perovskites with the electronic dⁿ configuration of the B ion. It was shown that, subject to the PJTE, not only d⁰ configurations may be unstable to produce ferroelectricity (“the d⁰ mystery”), but some other specific dⁿ configurations with unpaired electrons may be dipolar active too, the crystal being thus both magnetic and ferroelectric (multiferroic). The necessary conditions for such multiferroicity are formulated for the whole n = 0,1,…10 variety of perovskites, and it is shown to be different in the two (or more) possible spin arrangements of the same ion, high-spin or low-spin for n = 3, 4, …7. In conditions of spin crossover this leads to a magnetic-ferroelectric crossover that can be manipulated by external perturbations, including electric magnetization, already realized experimentally.

A novel chapter is opened in application of the vibronic PJTE theory to important problems of materials science by analyzing the interaction of the ferroelectric perovskites with external perturbations. For the paraelectric phase of BaTiO₃ with local dynamic-polar instability, any external electric field, strain, or stress violates the equivalency of the eight minima of the APES, quenching the polar dynamics, thus contributing an orientational polarization (like in polar liquids). It increases the permittivity, flexoelectricity, electrostriction, and external pressure effects by several orders of magnitude, confirmed experimentally. The theory explains also the formation of polar nanoregions and laxor properties in the paraelectric phase as due to the “local drops formation” when two phases may coexist locally (which is not possible in displacive theories where the formation of a polarized phase requires long-range interaction).

A significant part of the paper is devoted to discussion and comparison of the vibronic PJTE theory of ferroelectricity with other theories and empirical data. It is shown that a series of experimentally observed specific properties of perovskite ferroelectrics encounter fundamental difficulties in attempt to explain their origin by means of displacive theories. This is related to the B ion being (instantly) polar displaced along the trigonal axis in all the phases, the order-disorder character of the phase transitions, the role of the spin of the B ion in the ferroelectric polarization, the strong dependence of ferroelectricity and multiferroicity on the chemical composition, the giant effects in interaction with external perturbations, the formation of polar nanoregions in nonpolar phases leading to relaxor behavior, etc. All these unique properties of perovskite ferroelectrics follow directly from the vibronic (PJTE) theory.

Acknowledgment

I am thankful to Dr. V. Polinger for continuous cooperation, help, and discussions of the problems of this paper.