Effect of surface charges on the polarization distribution in ferroelectric nanotubes

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.