Evaluating SCAN and r$^2$SCAN meta-GGA functionals for predicting transition temperatures in antiferromagnetic materials

TL;DR

This study evaluates the accuracy of the meta-GGA r$^2$SCAN and SCAN functionals in predicting antiferromagnetic transition temperatures, showing they outperform traditional methods and closely match experimental data across 48 materials.

Contribution

It introduces a comprehensive validation of r$^2$SCAN and SCAN functionals for magnetic transition predictions, demonstrating their superior performance over standard GGA and GGA+$U$ methods.

Findings

r$^2$SCAN and SCAN achieve high correlation with experimental transition temperatures (0.98 and 0.97).

Meta-GGA functionals outperform hybrid HSE06 in predicting transition temperatures.

Both functionals accurately reproduce magnetic energy differences.

Abstract

Recent advancements in exchange-correlation functionals within density functional theory highlight the need for rigorous validation across diverse types of materials properties. In this study, we assess the performance of the newly developed meta-GGA r$^2$SCAN and its predecessor, SCAN, in predicting the N\'eel transition temperature of antiferromagnetic materials. Our analysis includes 48 magnetic materials, spanning both simple and complex systems. Using DFT, we compute the energies of various magnetic configurations and extract exchange interaction parameters through a least-squares fitting approach. These parameters are then used in classical Monte Carlo simulations to estimate the transition temperatures. Our results demonstrate that both SCAN and r$^2$SCAN greatly outperform standard GGA and GGA+$U$ methods, yielding predictions that closely align with experimental values. The Pearson correlation coefficients for SCAN and r$^2$SCAN are 0.97 and 0.98, respectively, when compared to experimental transition temperatures. Additionally, we calculate the energy differences between antiferromagnetic and ferromagnetic configurations to assess the performance of the hybrid HSE06 functional. We found that the HSE06 functional underestimates transition temperatures compared to the meta-GGA functionals and experimental values.