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The stable polarization distributions of freestanding ferroelectric nanotubes with different surface charges are investigated numerically using a phase field model based on the time-dependent Ginzburg – Landau equation. For a nanotube without surface charges, a pure vortex structure is formed as a result of the energy minimization. When the uniform surface charges are applied on the upper and lower surfaces, the out-of-plane components become nonzero. The out-of-plane components of polarizations are found to be proportional to the density of surface charge. When the density of surface charge exceeds a critical value, the in-plane components of polarizations disappear. This makes ferroelectric nanotubes experience an unusual transition from a vortex state to a single-domain state. Due to the different geometries, the critical charge density for the transition in nanotubes is larger than that of nanodots.

Effect of surface charges on the polarization distribution in ferroelectric nanotubes