Pseudo Jahn-Teller effect in the origin of enhanced flexoelectricity

The controversy between the theory and experiment in explaining the origin of enhanced flexoelectricity is removed by taking into account the pseudo Jahn-Teller effect (PJTE) which, under certain conditions, creates local dipolar distortions of dynamic nature, resonating between two or more equivalent orientations. The latter become nonequivalent under a strain gradient thus producing enhanced flexoelectricity: it is much easier to orient ready-made dipoles than to polarize an ionic solid. For BaTiO₃, the obtained earlier numerical data for the adiabatic potential energy surface in the space of dipolar displacements in the Ti centers were used to estimate the flexoelectric coefficient f in the paraelectric phase in a one-dimensional model with the strain gradient along the [111] direction: f = -0.43 × 10^-6 Cm^-1. This eliminates the huge contradiction between the experimental data of f ∼ μ Cm^-1 for this case and the theoretical predictions (without the PJTE) of 3-4 orders-of-magnitude smaller values. Enhanced flexoelectricity is thus expected in solids with a sufficient density of centers that have PJTE induced dipolar instabilities. It explains also the origin of enhanced flexoelectricity observed in other solids, noticeable containing Nb perovskite centers which are known to have a PJTE instability, similar to that of Ti centers. The SrTiO₃ crystal as a virtual ferroelectric in which the strain gradient eases the condition of PJTE polar instability is also discussed.