Hybrid ab initio method for examining thermal properties in magnetic materials

A hybrid ab initio theoretical approach for examining thermal properties in magnetic systems of unknown entropy is presented. Commonly used theoretical approaches interrogate thermal properties from Gibbs/Helmholtz free energies, which require an accurate model of magnetic interactions. The present approach avoids this requirement by instead calculating system pressure from thermally disordered microstates that properly incorporate vibrational and spin subsystems at each temperature as well as the coupling between these subsystems. In place of a specific model for magnetic interactions, the approach integrates measurements of temperature dependent magnetization of the studied material. We apply the approach to calculate phonon modes and to investigate the anomalously low thermal expansion of the classical Invar alloy, Fe_0.65Ni_0.35. The calculated phonon dispersions for Invar are in excellent agreement with measured data. The Invar thermal expansion is shown to remain small between 50 K and room temperature, consistent with the experimentally observed low thermal expansion value in this same temperature range. This anomalously small thermal expansion is directly connected to a small positive contribution from lattice thermal disorder that is nearly canceled by a large negative magnetic disorder contribution. By contrast, calculations for bcc Fe show a much larger thermal expansion, consistent with experiment, which is dominated by a large contribution from lattice thermal disorder that is reduced only slightly by a small negative contribution from that of magnetism. These findings give insights into the unusual nature of magnetism and spin-lattice coupling in Invar and Fe, and they support the presented new methodology as a complementary way to investigate thermal properties of magnetic materials.