Melting curve of correlated iron at Earth's core conditions from machine-learned DFT+DMFT

TL;DR

A machine-learning accelerator for charge self-consistent DFT+DMFT is developed by training E(3)-equivariant graph neural networks to predict the local self-energy and Fermi level from atomic environments, providing an efficient warm start to the DMFT self-consistency loop.

Abstract

Reliable constraints on iron's melting curve at Earth's inner-core boundary require accurate finite-temperature electronic correlations, yet DFT+DMFT calculations remain too costly for large-scale thermodynamic sampling. Here, we develop a machine-learning accelerator for charge self-consistent DFT+DMFT by training E(3)-equivariant graph neural networks to predict the local self-energy and Fermi level from atomic environments, providing an efficient warm start to the DMFT self-consistency loop. Using high-throughput data for Fe, FeO, and NiO, we obtain a 2-4 times reuduction in DMFT iterations. Leveraging this improvement, we generate correlated energies and forces for Fe at core pressures, train a neural-network interatomic potential, and determine the melting curve via two-phase coexistence simulations. We obtain a predicted melting temperature of 6225 K at 330 GPa.

Figures (3)

• Figure 1: Top row: Predicted real (red) and imaginary (blue) parts of the self energy vs DMFT (black) self-energies for 4 randomly selected structures in test sets of Fe, FeO and NiO. Bottom row: Convergence for Fe, FeO and NiO versus number of DFT+DMFT iterations.
• Figure 2: Density profile along the long axis of simulation cell taken at 20 ps into equilibration for simulation at 307.8 GPa. Shown in the insets are a snapshot of the atomic configuration at 20 ps as well as the temperature variation over the length of the simulation, which stabilizes around 15 ps. The 2 coexistence interfaces can been seen on both sides of the liquid.
• Figure 3: Full melting curve of Iron as predicted by our 2-phase simulations and compared to data from various experimental emcAnzellini2013emcSinmyo2019emcLi2020emcKraus2022emcBalugani2024 computational studies aimcAlfe2009aimcGonzalez2023aimcSun2022aimcSun2023aimcBelonoshko2021aimcStixrude2014aimcAlfe2002aimcBelonosko2000aimcWu2024aimcSola2009.