Relationship between lattice deformation and polarization in BaTiO3

The relationship between lattice deformation and electrical polarization in tetragonal BaTiO3 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 BaTiO3 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 BaTiO3, We suggest that this covalency softens Young's modulus of BaTiO3 in the ferroelectric states compared to the paraelectric states through the increase of the degree of freedom for atomic displacements in a unit cell.