Intrinsic switching of polarization vortex in ferroelectric nanotubes

The response of polarization vortex in ferroelectric nanotubes under different levels of curled electric fields is studied by using the phase field method. A critical curled electric field is found, at which the switching of polarization vortex takes place. The vortex switching initiates through the formation of local vortices near the outer surface with the highest energy density. The new vortex grows and the old one shrinks with the motion of local vortices between them. The coexistence of new vortex with original vortex in ferroelectric nanotubes is completely different from that in ferroelectric nanodisks where the coexistence never occurs. It is also found that the interplay between polarizations and strains first retards the nucleation of new vortex. However, once the new vortex appears, the interplay becomes the main driving force for the growth of new vortex.