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.
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