Phase stability of Fe from first-principles: atomistic spin dynamics coupled with ab initio molecular dynamics simulations and thermodynamic integration

TL;DR

This study demonstrates a first-principles method combining atomistic spin dynamics and ab initio molecular dynamics to accurately predict phase stability and transition temperatures in magnetic iron across a wide temperature range.

Contribution

It introduces a novel approach for calculating free energies in magnetic materials using coupled ASD-AIMD simulations and thermodynamic integration, achieving high accuracy in phase stability predictions.

Findings

Accurately predicts phase transition temperatures of Fe.

Gibbs free energy differences match CALPHAD estimates within 5 meV/atom.

Method enables first-principles free energy calculations with ~1 meV/atom accuracy.

Abstract

The calculation of free energies from first principles in materials is a formidable task which enables the prediction of phase stability with high accuracy; these calculations are complicated in magnetic materials by the interplay of electronic, magnetic, and vibrational degrees of freedom. In this work, we show the feasibility and accuracy of the calculation of phase stability in magnetic systems with ab initio methods and thermodynamic integration by sampling the magnetic and vibrational phase space with coupled atomistic spin dynamics-ab initio molecular dynamics (ASD-AIMD) simulations [Stockem et al., PRL 121, 125902 (2018)], where energies and interatomic forces are calculated with density functional theory (DFT). We employ the method to calculate the phase stability of Fe at ambient pressure from 800 K up to 1800 K. The Gibbs free energy difference between fcc and bcc Fe at zero pressure as a function of temperature is calculated carrying out thermodynamic integration over temperature on the energies at the DFT level from ASD-AIMD, using a reference free energy difference calculated in the paramagnetic state at temperatures much higher than the magnetic transition temperatures with thermodynamic integration over stress-strain variables with disordered local moment (DLM)-AIMD simulations. We show the importance of the magnetic ordering temperature of bcc Fe on the $\alpha$ to $\gamma$ structural transition temperature, whereas the $\gamma$ to $\delta$ transition is well reproduced independently of the exchange interactions. The Gibbs free energy difference between the two structures is within 5 meV/atom from the CALPHAD estimate, and both transition temperatures are reproduced within 150 K. The present work paves the way to free energy calculations in magnetic materials from first principles with accuracy in the order of 1 meV/atom.