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

TL;DR

This study combines first-principles calculations with the deep potential method to show that vibrational entropy stabilizes a ferrielectric state as the ground state in multilayer CuInP$_2$S$_6$, reconciling experimental and theoretical discrepancies.

Contribution

It introduces the deep potential method to accurately predict the finite-temperature stability of polarization states in CIPS thin films, revealing the importance of vibrational entropy.

Findings

Intralayer FE ordering is energetically favored in monolayers.

An AFE state is lowest in energy for thicker films without vibrational effects.

Including phonon free energy, the FiE state becomes the ground state in multilayers.

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.