Asymmetric flux-closure domains in compositionally graded nanoscale ferroelectrics and unusual switching of toroidal ordering by an irrotational electric field

A reversal of polarization vortexlike domains in ferroelectric nanostructures plays important roles for next generations of electronic nanodevices. However, a direct switching of the polarization vortexlike domains in ferroelectrics is a nontrivial task since the toroidal moment is conjugated to a curled electric field rather than a homogeneous one. This work is dedicated to developing an approach to directly switch the toroidal ordering under...