Ferroelectricity in ultra-thin and thick ferroelectric films of~Pb$_{0.35}$Sr$_{0.65}$TiO$_{3}$ studied by second~harmonic generation*

Second harmonic generation (SHG) measurements were performed in the reflection geometry using the femtosecond Ti:Sapphire pulse laser at the wavelength of 810 nm for a 16-nm-thick ultra-thin Pb$_{0.35}$Sr$_{0.65}$TiO$_{3}$ film and a 243-nm-thick Pb$_{0.35}$Sr$_{0.65}$TiO$_{3}$ film, which were epitaxially deposited on (001) MgO substrates by pulsed laser ablation (PLD). It is concluded that in the ultra-thin film the ferroelectric phase is still present and a remarkably sharp ferroelectric phase transition was observed. In contrast, the thick film exhibits a pronounced diffuse phase transition. Theoretical analysis based on the polarization diagrams show the compensated c-domain fraction is dominant in both films whereas the nonlinear susceptibility of the ultra-thin film has a different tensor property from the thick film.