Relationship between Lattice Deformation and Polarization in BaTiO₃

Abstract

The relationship between lattice deformation and electrical polarization in tetragonal BaTiO 3 is investigated. The density functional theory within the local density approximation using the full-potential-linear-augmented-plane-wave (FLAPW) method is adopted to obtain internal atom positions and one-electron wave functions. Electric polarization is calculated using the Berry-phase theory. We have found that a lattice strain of the order of 1% along the c -axis enhances polarization considerably. However, for that of the order of 0.1%, polarization hardly changes. We assume that these responses of the polarization to lattice strain are related to the stress sensitivity of the polarization in ferroelectric-thin films through nanoscale domains, especially ferroelectric-90-degree domains. We have also found that the polarization of BaTiO 3 can be scaled linearly by the distance between Ti and its nearest-neighbor oxygen (apical site in oxygen octahedron). This indicates that the covalency between Ti and the apical oxygen is the only driving force for the ferroelectricity in BaTiO 3 . We suggest that this covalency softens Young's modulus of BaTiO 3 in the ferroelectric states compared to the paraelectric states through the increase of the degree of freedom for atomic displacements in a unit cell.