The ground state of CuInP$_2$S$_6$ thin films: A study of the deep potential method

Abstract

The two-dimensional ferroelectric (FE) material CuInP$_2$S$_6$ (CIPS) has garnered considerable interest due to its out-of-plane ferroelectricity at room temperature. However, a notable discrepancy exists between experiments and density functional theory (DFT) calculations regarding the ground state of CIPS thin films: experiments suggest a state with net polarization, while DFT predicts an antiferroelectric (AFE) state as the lowest-energy state. Here, we investigate the stability of polarization states in CIPS thin films by combining first-principles calculations with the deep potential (DP) method. Our results reveal that for films thicker than the bilayer, an AFE state that has intralayer AFE ordering in the inner layers and intralayer FE ordering in the two surface layers has the lowest electronic energy. This state is significantly lower than the uniform FE state. In addition, we find that a ferrielectric (FiE) state with pure intralayer FE ordering is very close to the AFE state in energy. By using the DP model, we calculated the phonon free energy of CIPS thin films. For the monolayer, the intralayer FE ordering possesses a lower phonon free energy than the intralayer AFE ordering. This energetic preference for the intralayer FE ordering maintains as the thickness grows. Consequently, when the phonon-free energy is incorporated, the FiE state becomes energetically favorable over the AFE state for multilayers CIPS. Our findings demonstrate that the inclusion of vibrational entropy stabilizes the FiE state as the ground state in multilayers CIPS at finite temperatures, reconciling the previous discrepancy between experimental observations and DFT predictions. This insight is vital for understanding the FE properties of CIPS and its potential applications in devices.

Figures (9)

• Figure 1: Geometric structures of CIPS monolayer and bilayer with different polarization configurations. The white and black arrows denote the upward and downward polarizations, respectively.
• Figure 2: Benchmark calculations of the DP model. Comparison of energies (a) and forces (b) predicted by the DP model and DFT results for all the configurations in the training datasets. (c) The phonon spectrum of the FE state for bulk CIPS from DP (blue dashed line) and DFT (red solid line) calculations. (d) The net polarization of the bulk CIPS as a function of temperature calculated from MD simulations.
• Figure 3: Energetics of various polarization configurations obtained from DFT calculations for 3L$-$(a), 4L$-$(b), and 6L$-$CIPS (c), respectively. The total energy of the AFE state is used as a reference. The polarization configuration is given below each color bar. For 6L$-$CIPS, those with high energies are not shown.
• Figure 4: Comparison of the electronic energies of the FE and AFE states for the CIPS thin films as a function of the thickness. The energy of the AFE state is taken as the reference. The configurations of the AFE states for the films in different thicknesses are exactly the same as those shown in Figs. \ref{['fig1']} and \ref{['fig3']}.
• Figure 5: Phonon free energy of CIPS thin films. The phonon free energy of the monolayer (a), bilayer (b), and 6L$-$CIPS (c). For monolayer and bilayer CIPS, the energy of the AFE state is used as the reference. For 6L-CIPS, we use the energy of the FE state as the reference.