Atomistic determination of flexoelectric properties of crystalline dielectrics

Abstract

Upon application of a uniform strain, internal sublattice shifts within the unit cell of a noncentrosymmetric dielectric crystal result in the appearance of a net dipole moment: a phenomenon well known as piezoelectricity. A macroscopic strain gradient on the other hand can induce polarization in dielectrics of any crystal structure, even those which possess a centrosymmetric lattice. This phenomenon, called flexoelectricity, has both bulk and surface contributions: the strength of the bulk contribution can be characterized by means of a material property tensor called the bulk flexoelectric tensor. Several recent studies suggest that strain-gradient induced polarization may be responsible for a variety of interesting and anomalous electromechanical phenomena in materials including electromechanical coupling effects in nonuniformly strained nanostructures, ``dead layer'' effects in nanocapacitor systems, and ``giant'' piezoelectricity in perovskite nanostructures among others. In this work, adopting a lattice dynamics based microscopic approach we provide estimates of the flexoelectric tensor for certain cubic crystalline ionic salts, perovskite dielectrics, $III\text{\ensuremath{-}}V$ and $II\text{\ensuremath{-}}VI$ semiconductors. We compare our estimates with experimental/theoretical values wherever available and also revisit the validity of an existing empirical scaling relationship for the magnitude of flexoelectric coefficients in terms of material parameters. It is interesting to note that two independent groups report values of flexoelectric properties for perovskite dielectrics that are orders of magnitude apart: Cross and co-workers from Penn State have carried out experimental studies on a variety of materials including barium titanate while Catalan and co-workers from Cambridge used theoretical ab initio techniques as well as experimental techniques to study paraelectric strontium titanate as well as ferroelectric barium titanate and lead titanate. We find that, in the case of perovskite dielectrics, our estimates agree to an order of magnitude with the experimental and theoretical estimates for strontium titanate. For barium titanate however, while our estimates agree to an order of magnitude with existing ab initio calculations, there exists a large discrepancy with experimental estimates. The possible reasons for the observed deviations are discussed.