  Interest in epitaxial ferroelectric nanoislands was growing rapidly in recent
years driven by their potential for devices, especially ultradense memories.
Recent advances in the "bottom- up" (self-assembly) nanometer scale techniques
have opened up the opportunities of fabricating high-quality epitaxial
ferroelectric nanoislands with extremely small thickness and lateral size on
the order of 1 nm and 20 nm, respectively. On the other hand, recent emergence
of powerful probes, such as piezoresponse force microscopy (PFM), has enabled
imaging of a local domain structure with sub-10 nm resolution. In spite of
those developments, a clear understanding of the polarization patterns in
epitaxial ferroelectric nanoislands is lacking, and some important
characteristics, like a critical lateral size for ferroelectricity, are not yet
established. Here, we perform ab-initio studies of non-electroded epitaxial
Pb(Zr0.5Ti0.5)O3 and BaTiO3 nanoislands and show the existence of novel
polarization patterns driven by the misfit strains and/or anisotropy energy.
The results allow interpretation of the data and design of the ferroelectric
nanostructures with tailored response to external field.
