A ferroelectric nanostructure formed as a low dimensional nano-scale ferroelectric material having at least one vortex ring of polarization generating an ordered toroid moment switchable between multi-stable states. A stress-free ferroelectric nanodot under open-circuit-like electrical boundary conditions maintains such a vortex structure for their local dipoles when subject to a transverse inhomogeneous static electric field controlling the direction of the macroscopic toroidal moment. Stress is also capable of controlling the vortex's chirality, because of the electromechanical coupling that exists in ferroelectric nanodots.
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
This work was supported by the Office of Naval Research (Grant Nos. N00014-01-1-0365, N00014-03-1-0598, N00014-01-1-0600, and N00014-04-1-0413), National Science Foundation (Grant Nos. DMR-0116315, DMR-9983678, and DMR-0404335, and MRI Grant No. 0421099), and the Department of Energy (Grant No. DE-FG02-05ER46188). The government has certain rights in the invention.