[Paper Review] Accurate force field of two-dimensional ferroelectrics from deep learning

Jing Wu, Liyi Bai+4 more|arXiv (Cornell University)|Sep 15, 2021

Machine Learning in Materials Science86 references44 citations

TL;DR

This study develops a deep learning-based force field (DP) for monolayer α-In2Se3, a two-dimensional ferroelectric, using a concurrent learning loop that iteratively improves the first-principles training database. The model achieves DFT-level accuracy in predicting thermodynamic properties, lattice dynamics, polarization switching pathways, and a temperature-driven α → β phase transition, enabling large-scale molecular dynamics simulations of ferroelectric dynamics in 2D materials.

ABSTRACT

The discovery of two-dimensional (2D) ferroelectrics with switchable out-of-plane polarization such as monolayer $\alpha$-In$_2$Se$_3$ offers a new avenue for ultrathin high-density ferroelectric-based nanoelectronics such as ferroelectric field effect transistors and memristors. The functionality of ferroelectrics depends critically on the dynamics of polarization switching in response to an external electric/stress field. Unlike the switching dynamics in bulk ferroelectrics that have been extensively studied, the mechanisms and dynamics of polarization switching in 2D remain largely unexplored. Molecular dynamics (MD) using classical force fields is a reliable and efficient method for large-scale simulations of dynamical processes with atomic resolution. Here we developed a deep neural network-based force field of monolayer In$_2$Se$_3$ using a concurrent learning procedure that efficiently updates the first-principles-based training database. The model potential has accuracy comparable with density functional theory (DFT), capable of predicting a range of thermodynamic properties of In$_2$Se$_3$ polymorphs and lattice dynamics of ferroelectric In$_2$Se$_3$. Pertinent to the switching dynamics, the model potential also reproduces the DFT kinetic pathways of polarization reversal and 180$^\circ$ domain wall motions. Moreover, isobaric-isothermal ensemble MD simulations predict a temperature-driven $\alpha ightarrow \beta$ phase transition at the single-layer limit, as revealed by both local atomic displacement and Steinhardt's bond orientational order parameter $Q_4$. Our work paves the way for further research on the dynamics of ferroelectric $\alpha$-In$_2$Se$_3$ and related systems.

Motivation & Objective

• To develop a highly accurate, transferable classical force field for monolayer α-In2Se3, a promising 2D ferroelectric material with out-of-plane polarization.
• To overcome the limitations of conventional force fields and the high computational cost of DFT for simulating dynamic processes in 2D ferroelectrics.
• To enable large-scale molecular dynamics simulations of polarization switching and phase transitions in 2D ferroelectrics with DFT-level accuracy.
• To investigate the mechanisms of polarization reversal and 180° domain wall motion in monolayer α-In2Se3 using the trained deep potential.
• To explore the thermodynamic stability and phase transition behavior of monolayer α-In2Se3 under thermal stress using isobaric-isothermal MD.

Proposed method

• A deep neural network potential (DP) is trained using a concurrent learning workflow that dynamically selects and labels high-error configurations from MD simulations for DFT re-evaluation.
• The training database is iteratively updated using model deviation (E) as an error indicator for importance sampling, ensuring efficient coverage of rare or high-energy configurations.
• Four models are trained simultaneously on DFT-calculated energies, atomic forces, and stress tensors to ensure full consistency with first-principles data.
• The model is validated against DFT for energy, forces, phonon dispersion, and potential energy surfaces across multiple polymorphs of In2Se3.
• Isobaric-isothermal (NPT) molecular dynamics simulations are performed using the DP to probe temperature-driven phase transitions and structural evolution.
• Steinhardt’s bond orientational order parameters (Q4 and Q6) are computed to quantitatively characterize the local symmetry changes during phase transitions.

Experimental results

Research questions

• RQ1 Can a deep learning-based force field accurately reproduce the complex polarization switching dynamics in monolayer α-In2Se3, including 180° domain wall motion?
• RQ2 What is the kinetic pathway and energy barrier for out-of-plane polarization reversal in monolayer α-In2Se3 as predicted by DFT and captured by the DP?
• RQ3 Does the monolayer α-In2Se3 undergo a thermally driven phase transition from ferroelectric α to paraelectric β phase, and at what temperature?
• RQ4 How do local atomic displacements and bond order parameters evolve during the α → β phase transition in monolayer In2Se3?
• RQ5 To what extent does the deep potential maintain accuracy across diverse structural motifs, including metastable β′ phases with in-plane polarization?

Key findings

• The deep potential achieves DFT-level accuracy, with a mean absolute error of 11.5 meV/atom for energy and 0.02 eV/Å for forces, as validated on the final training database.
• The model accurately reproduces the DFT-calculated energy barriers for polarization reversal: 0.68 eV (DFT) and 0.76 eV (DP) for direct switching, and 0.80 eV (DFT) and 0.49 eV (DP) for multistep switching via concerted layer motion.
• The DP successfully captures the 180° domain wall motion in α-In2Se3, with energy barriers of 1.04 eV (DFT) and 1.024 eV (DP) for the initial pathway, and 1.06 eV (DFT) and 0.89 eV (DP) for the second pathway.
• NPT molecular dynamics simulations reveal a temperature-driven α → β phase transition in monolayer α-In2Se3 at approximately 650 K, confirmed by increasing atomic displacement (Dz) of the central Se sublayer.
• The phase transition is quantitatively characterized by a drop in Q4 and Q6 order parameters and a change in the 2D map of Q4, indicating a loss of local six-fold symmetry.
• The model predicts a stable ferroelectric phase up to ~650 K, consistent with experimental reports of a high Curie temperature (~700 K), validating its predictive power for real materials.