Size dependence of initial polarization direction in nanosized epitaxial $PbTiO3$ islands fabricated by hydrothermal epitaxy below Curie temperature

Nanosized epitaxial $PbTiO3$ (PTO) islands with a mono $c$ domain were fabricated via self-assembly on a Nb-$SrTiO3$ (NSTO) substrate at 160 °C by hydrothermal epitaxy without undergoing the paraelectric to ferroelectric phase transition. The direction of the polarization at the as-fabricated state was observed with an island size up to a lateral area of $104nm2$ and thickness of 12 nm (determined by atomic force microscope) using a piezoresponse force microscope. We found a critical size below which the negative polarization is stable at the as-fabricated state and above which the positive polarization is stable. This phenomenon was discussed under two assumptions: that the PTO islands are grown initially with positive polarization during fabrication, and the energy barrier for the transition from the positive polarization state to the negative polarization state is dependent on the ferroelectric island size.