A ferroelectric nanostructure formed as a low dimensional nanoscale ferroelectric material having at least one vortex ring of polarization generating an ordered toroid moment switchable between multi-stable states. Such a nanostructure is capable of achieving ultrahigh recording density in non-volatile ferroelectric random access memory (NFERAM) and may have applications in piezoelectric sensors, efficient actuators, nano-scale dielectric capacitors for energy storage, and nano-scale ultrasounds for medical use.