Prediction of the Curie temperature considering the dependence of the phonon free energy on magnetic states

TL;DR

This paper introduces a first-principles thermodynamic method that considers the mutual influence of phonons and magnetic states to more accurately predict the Curie temperature, demonstrated on bcc Fe.

Contribution

It presents a novel approach that incorporates phonon-magnetism feedback effects into Curie temperature prediction, improving accuracy over traditional zero-temperature-based methods.

Findings

Significant reduction of Curie temperature in bcc Fe due to feedback effects

Use of exchange coupling constants for disordered local moment states

Framework enhances understanding of finite-temperature magnetism

Abstract

Prediction of the Curie temperature is of significant importance for the design of ferromagnetic materials. Even though the Curie temperature has been estimated using the Heisenberg model, magnetic exchange coupling parameters widely used is thus far based on first-principles calculations at zero temperature. In the explicit consideration of temperature effects, it is important to minimise the total free energy, because the magnetic and phonon free energies correlate with each other. Here, we propose a first-principles thermodynamic approach to minimise the total free energy considering both the influences of magnetism on phonons and the feedback effect from phonons to magnetism. By applying our scheme to bcc Fe, we find a significant reduction of the Curie temperature due to the feedback effect. This result inevitably enforces us to change our convention as follows: we should use exchange coupling constants for the disordered local moment state, not for the ferromagnetic state, in the prediction of the Curie temperature. Our results not only change the fundamental understanding of finite-temperature magnetism but also provide a general framework to predict the Curie temperature more accurately.