Enhanced polarization in strained BaTiO$_3$ from first principles

The structure, polarization, and zone-center phonons of bulk tetragonal BaTiO$_3$ under compressive epitaxial stress are calculated using density functional theory within the local density approximation. The polarization, computed using the Berry-phase formalism, increases with increasing tetragonality and is found to be enhanced by nearly 70% for the largest compressive misfit strain considered (-2.28%). The results are expected to be useful for the analysis of coherent epitaxial BaTiO$_3$ thin films and heterostructures grown on perovskite substrates having a smaller lattice constant, such as SrTiO$_3$.