Domain patterns in free-standing nanoferroelectrics

A real space three-dimensional (3-D) Ginzburg–Landau framework is used to investigate the domain patterns in free-standing ferroelectric nanostructures undergoing cubic to tetragonal transitions. The study is motivated by the recent progress in fabricating free-standing single crystalline ferroelectric nanostructures which exhibit complex ferroelastic domain patterns. We demonstrate that for nanostructures with uncompensated surface charges internal stresses generated due to the coupling between electrostatic and elastic interactions can induce bulk-like ferroelastic domain patterns in free-standing ferroelectrics, without invoking any extrinsic mechanisms such as non-transforming surface layers. Further, we show that for very small structures the interplay between electrostatics and elasticity leads to a large diversity of domain patterns that can be observed in 3-D free-standing nanostructures.