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

Abstract 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 an irrotational (homogeneous) electric field with the use of compositionally graded ferroelectric (cgFE) nanodots. The variation in material compositions induces an additionally broken spatial inversion symmetry at a scale beyond unit-cell level, giving rise to a formation of asymmetric flux-closure domain (FCD) in a cgFE nanodot. More interestingly, such an asymmetric character facilitates to a switch of FCD by an irrotational electric field. In particular, the rotation of polarization can be directly switched from counter-clockwise to clockwise rotations and vice versa without a formation of intermediate domain structures during the switching process. This switching behavior is distinguished from that in homogeneous counterparts. We further demonstrate that the variation in material compositions tailors the distributions of electrostatic and total free energies in the cgFE nanodot that can control the annihilation/initiation process of FCD under irrotational electric field, providing fundamental reason for the direct switching of the toroidal moment. Another interesting issue is found that both the amplitude and frequency of applied electric field strongly affect the switching behavior of FCD in cgFE nanodot.