Abstract
Ferroelectric nanostructures are attracting considerable attention due to their unusual physical properties and potential applications in memory devices and nanoelectromechanical systems. It has been found that low-dimensional ferroelectrics, such as ferroelectric nanodots, ferroelectric nanotubes and ferroelectric thin films, exhibit polarization vortices or vortex-like domain structures due to the strong depolarization field and the size effect. The polarization vortex is regarded as a new toroidal order in ferroelectrics which is different from the rectilinear order of polarization. The vortex states of polarization are bistable and can be switched from one state to the other, which holds the potential application in next generation ferroelectric memories. This paper briefly reviews the recent work on the phase field studies of polarization vortex in ferroelectric nanostructures. The homogeneous bulk thermodynamics of ferroelectrics is first introduced based on the Landau–Devonshire theory. To describe the inhomogeneous polarization distribution in ferroelectrics, the phase field model including interface thermodynamics is then presented in the form of time-dependent Ginzburg–Landau equations.
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