Role of long-range dipolar interactions in the simulation of the properties of polar crystals using effective atomic potentials

TL;DR

The work addresses whether long-range dipole–dipole interactions must be explicitly included in second-principles atomic potentials for polar materials, using BaTiO3 and a controlled set of $q$-point grids to separate interaction ranges. It systematically compares models with and without the analytic long-range DD term across multiple meshes, revealing that short-range terms can capture the ferroelectric instability and much of the phonon spectrum, but neglecting DD introduces artifacts in LO branches and can yield fake metastable polar states. Including the long-range contribution cures these LO-related artifacts and stabilizes the correct energy landscape, though not all properties require DD corrections. The findings offer a practical diagnostic and actionable strategies to incorporate long-range corrections in AI-driven potentials, with implications for thin films, superlattices, and topological textures where depolarizing fields are significant.

Abstract

Driven by novel approaches and computational techniques, second-principles atomic potentials are nowadays at the forefront of computational materials science, enabling large-scale simulations of material properties with near-first-principles accuracy. However, their application to polar materials can be challenging, particularly when longitudinal-optical phonon modes are active on the material, as accurately modeling such systems requires incorporating the long-range part of the dipole-dipole interactions. In this study, we challenge the influence of these interactions on the properties of polar materials taking BaTiO$_3$ as paradigmatic example. By comparing models with and without the long-range part of the electrostatic contributions in a systematic way, we demonstrate that even if these interactions are neglected, the models can still provide an overall good description of the material, though they may lead to punctual significant artifacts. Our results propose a pathway to identify when an atomistic potential may be inadequate and needs to be corrected through the inclusion of the long-range part of dipolar interactions.

Figures (6)

• Figure 1: (a) Schematic representation of the dipole-dipole (DD, red) and short-range (SR, blue) contributions to the total interatomic force constants (IFC). (b) When activating the explicit treatment of DD interactions, the latter are computed analytically and infinite range while the SR IFC are obtained by subtracting the DD part from the total IFC and their range limited to that of a supercell defined by the $q$-point grid used for the calculations. (c) When deactivating the explicit treatment of DD interactions, the SR IFC correspond to the total IFC but truncated at the range of the supercell defined by the $q$-point grid.
• Figure 2: Illustration of the relationship between $1\times1\times1$ (blue), $2\times2\times2$ (red) and $4\times4\times4$ (green) real-space supercells (projected on the $x$-$y$ plane) and reciprocal-space $q$-point grids (along $k_x$). The real-space atomic distortion patterns allowed in a given supercell are restricted to the $q$-points of the associated reciprocal-space grid. due to the periodic boundary conditions, simulations within a given supercell only provide access to interatomic force constants up to the range defined by the supercell. On the other hand, atomic displacements compatible with a given supercell are restricted to linear combination of the eigenvectors of the phonon modes associated to the associated $q$-point grid.
• Figure 3: Phonon dispersion curves of BaTiO$_3$ obtained from three distinct models each capturing a specific range of interactions (8, 2 and 2 from top to bottom rows) with varying levels of resolution in the phonon band structure (2, 4 and 8 from left to right columns). The first two models (blue, green) include analytically the dipole-dipole interactions that extend to infinite range M8+Dip and M2+Dip, while the third (red) omits them M2. The solid blue line present in all panels represents the reference model (8$\times$8$\times$8 $q$-point mesh with analytic treatment of the dipolar interactions).
• Figure 4: (a) Phase diagram of BaTiO$_3$, and (b) hysteresis loop of the $R3m$ phase at 50 K, reproduced using the M2 and M8+Dip models, as indicated in the legend. The supercell size used for the calculations was 12$\times$12$\times$12.
• Figure 5: Phonon dispersion curves of BaTiO$_3$ along the $\Gamma-X$ branch for the same three models as described in Fig. \ref{['fig:phonons']}. Blue lines corresponds to the phonon dispersion curves computed with the reference model.