  Recently, the observation of atomic thin film SnTe with a Curie temperature
(Tc) 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 phenomenon has yet been thoroughly investigated,
which hinder the understanding and design of novel materials with ferroic
orders at 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 the 2D SnTe automatically
transform into periodical bilayer structure, resulting from the surface effect.
Moreover, based on the double-well potential and atomic distortion analysis, we
found the Tc of the 2D SnTe is higher than the bulk counterpart, and more
surprisingly, the Tc exhibits an unusual non-monotonous dependence of
thickness, featuring a pronounced atomic distortion and Curie temperature
maximum at 8 atomic-layers. In addition, this non-monotonous dependence is
sensitive to the external strain and it can be tuned easily by the external
compressive strain.
