Nanoscale 180 Degree Stripe Domains in PbTiO$_{3}$ Films*

Nanoscale 180 degree stripe domains have been found to be the equilibrium structure of ultrathin ferroelectric films on insulating substrates [Fong, D. D. \textit{et al.}, \textit{Science }\textbf{304}, 1650 (2004)]. Here we report a study of the morphology of these stripe domains in PbTiO$_{3}$ films using room-temperature AFM imaging and high-temperature synchrotron x-ray scattering. The stripes can be aligned with surface steps, or with the underlying crystal lattice, depending upon film thickness and temperature. These equilibrium domains provide a new class of electrically active, controllable ``soft'' patterns in a hard material that are promising for self-assembly of oppositely charged adsorbates on sub-lithographic length scales.