Non-monotonic thickness dependence of Curie temperature and ferroelectricity in two-dimensional SnTe film

Recently, the observation of atomic thin film SnTe with a Curie temperature (T_c) higher than that of the bulk [Chang et al., Science 353, 274 (2016)] has boosted the research on two-dimensional (2D) ferroic materials tremendously. However, the origin of such a phenomenon is yet to be thoroughly investigated, which hinders the understanding and design of materials with ferroic orders at the 2D limit. By using the density functional theory, we investigated the structural and ferroelectrical properties of 2D SnTe to reveal the thickness dependence. The calculated results demonstrate that 2D SnTe automatically transforms into a periodical bilayer structure, resulting from the surface effect. Moreover, based on the double-well potential and atomic distortion analysis, we found that the T_c of 2D SnTe is higher than that of the bulk counterpart, and more surprisingly, T_c exhibits a non-monotonous dependence of thickness, featuring a pronounced atomic distortion and Curie temperature maximum at 8 atomic-layers (4 unit cells). In addition, this non-monotonous dependence is sensitive to the external strain and it can be easily tuned by the external compressive strain.