Characteristics and signatures of dipole vortices in ferroelectric nanodots: First-principles-based simulations and analytical expressions

Characteristics and signatures of dipole vortex in ferroelectric nanodots are determined via the use of first-principles-based simulations and by analytical developments. For instance, the dependency of such vortex on size, shape, material, and temperature is provided. Moreover, peculiar features associated with such vortex, such as unique behaviors of the inhomogeneous and homogeneous strains and of the induced electric fields, are revealed. Finally, energetics of interacting vortices is also discussed.