Ferroelectricity and Phase Transitions in Monolayer Group-IV Monochalcogenides

Ferroelectricity usually fades away as materials are thinned down below a critical value. We reveal that the unique ionic-potential anharmonicity can induce spontaneous in-plane electrical polarization and ferroelectricity in monolayer group-IV monochalcogenides $MX$ ($M=\mathrm{Ge}$, Sn; $X=\mathrm{S}$, Se). An effective Hamiltonian has been successfully extracted from the parametrized energy space, making it possible to study the ferroelectric phase transitions in a single-atom layer. The ferroelectricity in these materials is found to be robust and the corresponding Curie temperatures are higher than room temperature, making them promising for realizing ultrathin ferroelectric devices of broad interest. We further provide the phase diagram and predict other potentially two-dimensional ferroelectric materials.

Figure 1

(a) Top view of the structure of monolayer group-IV monochalcogenides. The black line rectangle is the first Brillouin zone, $a$ is the lattice constant along the armchair direction ($x$), and $b$ is that along the zigzag direction ($y$). (b) The schematic side views of the two distorted degenerate polar structures ($B$ and $B^{\prime }$) and the high symmetry nonpolar phase ($A$). (c) The free-energy contour plot of monolayer SnSe according to the tilting angles (${\theta }_1$ and ${\theta }_2$). The phases $A$, $B$, and $B^{\prime }$ are marked.

Figure 2

(a) and (b) Phonon spectra of the structures $A$ and $B$ of monolayer SnSe, respectively. (c) Double-well potential of monolayer SnSe. Red points are the DFT-calculated total energy and the blue line is from the model. (d) Double-well potential vs polarization. $E_G$ is the ground-state energy (potential barrier) and $P_s$ is the spontaneous polarization.

Figure 3

(a) The dipole-dipole interaction of monolayer SnSe by using mean-field theory. The red points are the DFT-calculated total energy of different $P_i-⟨P_j⟩$. The blue line is fitted by the harmonic approximation. (b) Temperature dependence of polarization obtained from MC simulations of monolayer SnSe.

Figure 4

(a) Curie temperature vs the spontaneous polarization. The blue points and error bars are MC simulations and the red line is the fitted result using the model function in Eq. (4). (b) Phase diagram of monolayer SnSe under strain. (c) $M\text{−}X$ bond covalency $C_{M,X}$ vs cophonicity $C_{\mathrm{ph}}(M–X)$ with different covariant angles. (d) Curie $T_C$ and spontaneous polarization $P_s$ vs $M\text{−}X$ bond covalency $C_{M,X}$. (e) Polarization at zero temperature vs the layer number of $MX\mathrm{s}$.