Lattice Relaxation in Epitaxial BaTiO₃ Thin Films

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We have investigated the out-of-plane lattice relaxation related to the ferroelectric transitions in epitaxial BaTiO₃ (BTO) films using synchrotron X-ray diffraction. Under either compressive strain or tensile strain, there is evidence for two structural phase transitions as a function of temperature. The transition temperature TC is a strong function of strain, which can be as much as 100 K above the corresponding TC in bulk. Under compressive strain, the tetragonality of BTO unit cell implies that the polarization of the first ferroelectric phase is out-of-plane, while under tensile strain, the polarization is in-plane. The transitions at lower temperature may correspond to the aa→ r or c→ r transitions, following the notations by Pertsev et al. The orientations of the domains are consistent with theoretical predictions.