Ferroelectricity and Tetragonality in UltrathinPbTiO3Films

The evolution of tetragonality with thickness has been probed in epitaxial $c$-axis oriented ${\mathrm{P}\mathrm{b}\mathrm{T}\mathrm{i}\mathrm{O}}_3$ films with thicknesses ranging from 500 down to $24\AA$. High resolution x ray pointed out a systematic decrease of the $c$-axis lattice parameter with decreasing film thickness below $200\AA$. Using a first-principles model Hamiltonian approach, the decrease in tetragonality is related to a reduction of the polarization attributed to the presence of a residual unscreened depolarizing field. It is shown that films below $50\AA$ display a significantly reduced polarization but still remain ferroelectric.