Long-range interaction effects on the phase transition, mechanical effect, and electric field response of BaTiO3 by machine learning potentials

Abstract: Bulk materials are governed by both short-range and long-range interactions, both of which are naturally captured in conventional density functional theory (DFT) calculations through Ewald summation of electrostatic contributions. In contrast, machine learning potentials (MLPs) typically rely on local atomic environment descriptors, and long-range interactions are often neglected. Such approximations may introduce systematic energetic errors and lead to inaccuracies in predicted material properties. To systematically investigate the impact of long-range interactions in ferroelectric BaTiO3 within the framework of MLPs, we developed a long-range MACELES model and compared its performance with the previously reported BaTiO3 MACE model across four key properties (phonon dispersion, phase transition behavior, mechanical response, and ferroelectric properties including dielectric constants). We find that qualitative behaviors, including phase transitions, stress-induced polarization switching, and polarization-electric field hysteresis, are consistently reproduced by both models. In contrast, quantitative properties such as transition temperatures, elastic constants, and dielectric constants exhibit systematic improvements in MACELES model, highlighting the importance of incorporating long-range electrostatics for accurately describing the structural and dielectric responses of BaTiO3. These results suggest that while long-range interactions play a role in improving quantitative accuracy, their omission does not significantly alter the qualitative ferroelectric behavior of BaTiO3.

• The paper demonstrates that incorporating latent Ewald summation into ML potentials significantly improves quantitative predictions of BaTiO3 properties.
• It highlights enhanced recovery of LO-TO splitting, elevated phase transition temperatures, and refined dielectric constants compared to short-range models.
• The study establishes that while short-range models capture qualitative phase behavior, explicit long-range electrostatics are essential for vibrational and elastic accuracy.

Long-Range Interaction Effects on Ferroelectric BaTiO₃: Rigorous Assessment via Machine Learning Potentials

Introduction

The study "Long-range interaction effects on the phase transition, mechanical effect, and electric field response of BaTiO₃ by machine learning potentials" (2603.29198) systematically investigates the impact of explicit long-range electrostatic interactions in the context of machine learning potential (MLP)-driven ferroelectric molecular dynamics simulations. BaTiO₃, a prototypical perovskite ferroelectric, serves as the testbed for contrasting conventional short-range MACE potentials against the MACELES model, which incorporates latent Ewald summation for long-range electrostatics. The work addresses quantitative and qualitative property prediction across phonon spectra, phase stability, mechanical response, and dielectric behavior, delivering a framework for the practical deployment of MLPs in materials modeling.

Methodology Overview

A consistent AIMD-derived training database comprising 4,045 configurations was employed for both MACE and MACELES models, spanning BaTiO₃'s rhombohedral, orthorhombic, tetragonal, and cubic phases from 1 to 4000 K. The LES augmentation in MACELES infers latent atomic charges from local geometries and applies Ewald summation, bridging both data-driven and conventional electrostatics. Benchmarking involved phonon dispersion via finite displacement, phase transition sequences under NPT heating, mechanical elasticity and stress-induced polarization switching, and ferroelectric P-E loops simulated through in-situ Born effective charge estimation.

Phonon Dispersion and LO-TO Splitting

Phonon dispersion is decisively sensitive to long-range Coulombic interactions manifested as LO-TO splitting near zone boundaries. The study evidences that MACELES successfully recovers LO-TO splitting, converging with supercell size toward DFPT results with non-analytic correction (NAC), while MACE remains insensitive to this feature regardless of cell size. The presence of Gibbs oscillations in MACELES (absent in MACE) reflects limitations in finite-displacement representations of non-analytic behavior, yet confirms that latent charge-based Ewald summation suffices for qualitative electrostatic character. Notably, the quantitative shape of the LO branch near the I point in MACELES deviates from DFPT with NAC, underlining incomplete reproduction of Born effective charge-driven electrostatics absent explicit charge supervision.

Structural Phase Transitions

Both models correctly reproduce the sequence R-O-T-C, matching experimental and theoretical precedent. MACELES yields slightly higher transition points (R→O: 180 K, O→T: 245 K, T→C: 297 K) compared to MACE (150, 225, 290 K), aligning with a marginally enlarged unit-cell volume in MACELES, attributable to softened phonon modes and reduced tetragonality. Polarization orientation analyses reveal larger supercells exhibiting increased deviation from the ideal <001> axis (38.9° in MACELES vs 34.5° in MACE for 8×8×8), correlating with structural distortions and subtle phase boundary shifts. Importantly, the qualitative topology of the phase diagram remains unaltered by long-range effects.

Mechanical Response and Elasticity

The inclusion of LES in MACELES yields elastic constants systematically reduced relative to MACE, and closely matching GGA-PBEsol values. Both models demonstrate stress-induced polarization switching at ~120 MPa, congruent with experimental coercive stress values. The mechanical response thus evidences that quantitative softness (i.e., lattice mechanical compliance) is modulated by long-range interactions, yet the switching threshold and qualitative stress-polarization relationship endure across model types.

Ferroelectric Properties and Dielectric Constants

P-E hysteresis loops generated with both models feature nearly identical remnant polarization and coercive field values, as well as two-step polarization switching signatures. Quantitative differences arise in the dielectric constants: MACELES achieves ε_c = 171 and ε_a = 1440, with the latter demonstrating a significant (~35%) increase over the MACE model (ε_c = 153, ε_a = 1070). The study associates the increase in ε_a with decreased c/a tetragonality (1.018 for MACELES, 1.023 for MACE), linking lattice distortion to enhanced in-plane polarization fluctuations and dielectric response. Despite improvements, both models underestimate experimental dielectric constants, implicating residual approximations in the potential construction and the data-driven latent charge approach.

PES Topology vs. Quantitative Curvature: Interpretation

The findings illuminate a principled dichotomy in MLP behavior: short-range models robustly capture the qualitative topology of BaTiO₃’s energy landscape (i.e., stable phases and transition pathways), whereas quantitative properties requiring accurate curvature (second derivatives of the PES) such as phonon frequencies, elastic constants, and dielectric constants, are augmented by explicit long-range modeling. The latent Ewald summation framework modifies PES curvature and produces moderate shifts in equilibrium properties without altering the identity or connectivity of phase minima, corroborating prior theoretical models and simulation studies. These results anchor the criterion for MLP selection: short-range models suffice for qualitative exploration, but quantitative agreement necessitates long-range electrostatics, especially for vibrational and dielectric applications.

Practical and Theoretical Implications

This comprehensive comparison underscores that practical deployment of MLPs for ferroelectric perovskites can be tailored by property-specific requirements. For exploratory phase behavior, short-range potentials afford expedient and accurate sampling. When precision in vibrational and dielectric phenomena is mandatory, LES-enhanced models provide improvements without excessively burdening computational resources. The study also exposes the limits of present latent charge machine learning—more accurate and physically constrained charge supervision may be required for rigorous quantitative parity with first-principles approaches.

Theoretically, the separation between PES topology and curvature as affected by long-range interaction encapsulates a broader paradigm for materials simulation, suggesting generalizable frameworks for other polar and complex oxides and prompting further development of hybrid or hierarchical MLPs.

Conclusion

The explicit inclusion of long-range electrostatics in machine learning potentials via latent Ewald summation achieves systematic quantitative improvements in BaTiO₃ simulations—manifest in LO-TO splitting, transition temperatures, elastic constants, and dielectric response—while preserving qualitative phase sequence, mechanical switching behavior, and ferroelectric hysteresis. The study establishes a clear selection criterion for MLP complexity based on target property class, and suggests directions for enhanced charge modeling. These insights inform both practical simulation protocols and fundamental understanding of ferroelectric energetics, with implications spanning broader materials informatics and atomistic modeling domains.