Direct approach for flexoelectricity from first-principles calculations: cases for SrTiO3 and BaTiO3

Understanding the nature of flexoelectricity, which is the linear response of electric polarization to a strain gradient, has recently become crucial for nanostructured dielectrics and ferroelectrics because of their complicated strain distribution. This paper presents a direct and full approach at the atomic level to predict flexoelectricity for dielectrics based on first-principles calculations. The flexoelectric coefficients of BaTiO3 and SrTiO3 are directly calculated as the representatives of ferroelectric and paraelectric materials, respectively. For SrTiO3, the flexoelectric coefficients predicted from our approach are in good agreement with the experimental measurements. For BaTiO3, our predictions have a large discrepancy from the experimental measurements. In a practical situation, defect and surface effects are inevitable, and have a significant influence on the flexoelectricity. Direct methods have the advantage of including the extrinsic contributions from surface and defect effects.