Intrinsic Origin of Enhancement of Ferroelectricity in SnTe Ultrathin Films

Previous studies showed that, as ferroelectric films become thinner, their Curie temperature ($T_c$) and polarization below $T_c$ both typically decrease. In contrast, a recent experiment [Chang et al., Science 353, 274 (2016)] observed that atomic-thick SnTe films have a higher $T_c$ than their bulk counterpart, which was attributed to extrinsic effects. We find, using first-principles calculations, that the 0-K energy barrier for the polarization switching (which is a quantity directly related to $T_c$) is higher in most investigated defect-free SnTe ultrathin films than that in bulk SnTe, and that the 5-unit-cell (UC) SnTe thin film has the largest energy barrier as a result of an interplay between hybridization interactions and Pauli repulsions. Further simulations, employing a presently developed effective Hamiltonian, confirm that freestanding, defect-free SnTe thin films have a higher $T_c$ than bulk SnTe, except for the 1-UC case. Our work, therefore, demonstrates the possibility to intrinsically enhance ferroelectricity of ultrathin films by reducing their thickness.

Figure 1

Crystal structures of SnTe thin films. Ferroelectric (FE) phases of (a) 1-UC and (c) 2-UC SnTe thin films. The corresponding paraelectric phases are shown in (b) and (d). The red arrows indicate that polarizations are along the [110] direction. (e) The FE displacements of ${\mathrm{Sn}}^{2+}$ ions at different layers as a function of the layer number.

Figure 2

Energy differences between the PE and FE phases of SnTe films. (a) The lateral lattice constants $a$ and $b$ are fully optimized. (b) Lattice constants $a$ and $b$ are fixed to the bulk lattice constant of 4.525 Å. (c) Lattice constants $a=b=4.900$ (a 7.2% tensile strain). The horizontal dashed line shows the result for bulk SnTe.

Figure 3

Layer force constants of ${\mathrm{Sn}}^{2+}$ ions as a function of the layer number, as fitted with the DFT total energies. (Inset) The force constant of the surface ${\mathrm{Sn}}^{2+}$ ion as a function of film thickness.

Figure 4

(a) Layer force constants of ${\mathrm{Sn}}^{2+}$ ions as a function of layer number, as fitted with the TB band energies. (b) Decomposition of layer force constants $k_{\mathrm{DFT}}^i$ into $k_{\text{intra}}^i$ and $k_{\text{inter}}^i$ for the 5-UC SnTe thin film (see the main text).