Ferroelectric properties of nanometer-scale barium titanate films from first principles

Ferroelectric properties of nanometer-scale barium titanate films with one, two, and three TiO6 octahedral layers stacking along the [001] direction have been studied by the first-principles calculation method. The freestanding barium titanate films are found to be ferroelectric with spontaneously formed electric dipoles parallel to the films by the existence of double-well potentials. The depth of the potential well of the free standing film is found to decrease with the increase of the thickness. However, when the substrate effect is considered, the depth of the potential well becomes deeper for thicker films, which suggests an enhancement of the ferroelectric property for thicker films.