Polar structure evolution of ultrathin BaTiO$_3$ films: in-situ LEED I-V

Understanding the fundamental physics of ferroelectricity in ultrathin films is a key issue of a critical size, of which a strong debate has erupted over the existence for decades. Ferroelectricity has previously been observed experimentally down to a few unit cells, depending on a complex interplay of electrostatic depolarization energy, domain formation, and so on. Using in situ Low Energy Electron Diffraction (LEED) I-V, we have systematically examined the structure evolution of ultrathin fully strained BaTiO$_{3}$ films (1-12 ML) on Nb-doped SrTiO$_{3}$. Comparison of observed diffraction intensities for 10 ML films at 300 K with calculated intensities reveals a vertical displacement of the central Ti, corresponding to a single-domain upward polar state. To investigate the polar structure evolution of ultrathin films, we have calculated all R-factors between two sets of experimental curves from 1 ML to 12 ML with 10 ML polar structure curve as a reference. As a result, we demonstrate that 8-12 ML thick BaTiO$_{3}$ films have very similar polar structures, whereas thinner films (1-7 ML) have continuously evolved from uncorrelated to correlated polar structures.