General Learning of the Electric Response of Inorganic Materials

Abstract

We introduce \texttt{MACE-Field}, a field-aware, $O(3)$-equivariant interatomic potential that learns a single electric enthalpy functional $\mathcal{F}(\{\mathbf{R}\},\mathbf{E})$ and obtains $\mathbf{P}$, $Z^{\ast }$, and $\mathbf{\alpha }$ by exact differentiation. A uniform field couples to latent equivariant features inside the \texttt{MACE} backbone, while the scalar energy readout preserves Maxwell reciprocity, the acoustic sum rule, and crystal tensor symmetries by construction. Because this coupling is a plug-in on top of standard \texttt{MACE}, existing energy/force foundation models can be upgraded to become field-aware. Benchmarked against semilocal DFT/DFPT reference data, a directly trained cross-chemistry ferroelectric model reproduces the same-branch Berry-phase and spontaneous polarisations across diverse inorganic crystals. Starting from the multihead foundation model \texttt{mace-mp-mh-0} and its OMAT-PBE head, joint fine-tuning on dielectric, ferroelectric, and replay data yields \texttt{MACE-Field-MH-0} foundation models, which predict $Z^{\ast }$, $\mathbf{\alpha }$, derived dielectric constants, and cross-chemistry polarisation trends with fidelity that captures branch-resolved polarisation and spontaneous-polarisation, while retaining strong force-field accuracy. Further, single-material \texttt{MACE-Field} models and \texttt{MACE-Field-MH-0} reproduce \ce{BaTiO3} hysteresis loops and $\alpha$-quartz infrared, Raman, and dielectric spectra from finite-field molecular dynamics, comparable to DFPT. These results show that a simple, physics-informed field coupling can endow atomistic foundation models with transferable dielectric and ferroelectric response, while targeted single-material training remains advantageous for the most quantitative spectroscopic predictions.

22 pages, 12 figures, 43 equations

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