  A reduction of polarization in ultra-thin ferroelectric films appears to be
fundamental to ferroelectricity at the nanoscale. For the model system PbTiO3
on SrTiO3, we report observation of the polarization vs. thickness relation.
Distinct periodicity changes of ferroelectric domains obtained from x-ray
diffraction and total energy calculations reveal a linear lowering of the
polarization below a critical thickness of ~12 nm. Independent polarization and
tetragonality measurements provide insight into the fundamental relation
between polarization and tetragonality in nanoscale ferroelectrics.
