Atomic scale study of the anti-vortex domain structure in polycrystalline ferroelectric

A modified first-principles-based atomistic method incorporating the anisotropic shell model is developed for the simulation of the vortex-type polarisation in polycrystalline ferroelectric. Based on the modified model, a series of distinct vortex and anti-vortex polarisation configurations are obtained at atomic scale simulation in which the anti-vortex polarisation configuration in polycrystalline ferroelectric has never been reported in the open literature. In this study, a standard definition is given to the polarised anti-vortex in mathematics and polarisation topology. The accurate distribution has been obtained from the simulation and validated by analogy of the vortex field using the Landau-Ginzburg-Devonshire theory. The properties of the anti-vortex are studied to establish the relationship among the polarisation value of the vector, the radius and the streamlines curvature of the anti-vortex. Based on the polarisation mechanism, a method is proposed for experimenters to observe clearly and position accurately the polarisation anti-vortex and vortex, which could combine as novel domain structure.