Thickness dependence of domain size in 2D ferroelectric CuInP2S6 nanoflakes

Two-dimensional (2D) ferroelectrics refer to those ferroelectrics with layered structure and weak interlayer interactions (e.g., van de Waals interlayer coupling). A number of basic physical issues in the framework of ferroelectricity deserve clarifications, and one of them is the size effect regarding the dependence of ferroelectricity on material thickness. In this work, we investigate the ferroelectric domain structures of 2D ferroelectric CuInP2S6 nanoflakes attached on heavily doped Si wafers and polarization switching using the piezoresponse force microscopy. While the domain structure shows highly irregular morphology and 180° domain walls, the statistics on domain size (diameter) W and nanoflake thickness d demonstrates the remarkable thickness dependence of domain size, illustrated by the shrinking domain size from 630 nm to 75 nm with decreasing thickness d from ∼130 nm to ∼11 nm. This dependence fits the Landau-Lifshitz-Kittel (LLK) scaling law with the scaling exponent of ∼0.65, slightly larger than 0.5 for 3D ferroelectrics. It is suggested that the size effect in terms of the LLK scaling law does not show an essential difference between the 2D and 3D ferroelectric systems.