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

The calculation of free energies from first principles enables the prediction of phase stability of materials 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 simulations [Stockem et al., PRL 121, 125902 (2018)], where energies and interatomic forces are calculated with density functional theory. We employ the method to calculate the phase stability of Fe at ambient pressure from 800 up to 1800 K. The Gibbs free energy difference between fcc and bcc Fe at zero pressure is calculated with thermodynamic integration over temperature and over stress-strain variables and, for the best set of exchange interactions employed, the Gibbs free energy difference between the two structures is within 5 meV/atom from the CALPHAD estimate, corresponding to an error in transition temperature below 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.