Unit-cell scale mapping of ferroelectricity and tetragonality in epitaxial ultrathin ferroelectric films

Typically, polarization and strain in ferroelectric materials are coupled, leading to the generally accepted direct relation between polarization and unit-cell tetragonality. Here, by means of high-resolution transmission electron microscopy we map, on the unit-cell scale, the degree of tetragonality and the displacements of cations away from the centrosymmetry positions in an ultrathin epitaxial PbZr"0"."2Ti"0"."8O"3 film on a SrRuO"3 electrode layer deposited on a SrTiO"3 substrate. The lattice is highly tetragonal at the centre of the film, whereas it shows reduced tetragonality close to the interfaces. Most strikingly, we find that the maximum off-centre displacements for the central area of the film do not scale with the tetragonality. This challenges the fundamental belief in a strong polarization-tetragonality coupling in PbTiO"3-based ferroelectrics, at such thicknesses. Furthermore, a systematic reduction of the atomic displacements is measured at the interfaces, suggesting that interface-induced suppression of the ferroelectric polarization plays a critical role in the size effect of nanoscale ferroelectrics.