Disentangling the Discrepancy Between Theoretical and Experimental Curie Temperatures in Ferroelectric PbTiO$_3$

TL;DR

This study investigates the discrepancy between theoretical and experimental Curie temperatures in PbTiO$_3$, revealing that exchange-correlation functional limitations and finite-size effects significantly influence prediction accuracy, emphasizing the need for explicit long-range interactions.

Contribution

It demonstrates that exchange-correlation functional limitations and finite-size effects are key factors in predicting $T_c$, and highlights the importance of explicit long-range interactions in simulations.

Findings

Underestimation of $T_c$ mainly due to exchange-correlation functional limitations.

Short-range MLFFs coincidentally match experimental $T_c$ better due to error cancellation.

Including long-range interactions affects $T_c$ predictions depending on supercell size.

Abstract

Accurately predicting the Curie temperature ($T_c$) of ferroelectrics from first principles remains a major challenge, as theoretical estimates often fall significantly below experimental values. In this work, we investigate the origin of these discrepancies in the prototypical ferroelectric PbTiO$_3$ by performing extensive constant-pressure ab initio molecular dynamics (AIMD) simulations and benchmarking them against classical molecular dynamics (MD) using machine learning force fields (MLFFs) derived from first-principles data. Our results show that the underestimation of $T_c$ primarily stems from the limitations of the exchange-correlation functional, rather than inaccuracies in the MLFF fitting. We uncover a critical interplay between finite-size effects and the range of interatomic interactions: although short-range MLFFs appear to yield better agreement with experimental $T_c$, this improvement results from a fortuitous cancellation of errors. Incorporating explicit long-range interactions improves accuracy for larger supercells but ultimately leads to lower predicted $T_c$ values. These findings highlight that accurate finite-temperature predictions require not only high-quality training data and sufficiently large simulation cells, but also the explicit treatment of long-range interactions and improved exchange-correlation functionals.