Thermodynamic stability of BaTiO3 nano-domains

Nano-ferroelectric domains were observed in ultra-thin BaTiO3 films (2-10 nm thick). The thickness of each domain is in the range of 0.4-0.8 nm, which is equivalent to 1-2 unit cells of the BaTiO3 phase. The films exhibit a ferroelectric behavior characterized by a polarization hysteresis loop. The thermodynamic stability of the nano-domains is examined experimentally and theoretically. The nano-domains oriented in parallel to the film plane are thermally stable up to about 110 °C due to a high tensile stress in the film. A thermodynamic balance between strain, polarization, surface and depolarization free energies shows that stable nano-domains, having a thickness of even one unit cell of the BaTiO3 phase, can be formed via the twining mechanism in a film with high tensile stress.