# Magnetic contributions to the free energy of metals: application to the different phases of iron

A key quantity in fully characterizing the thermodynamic properties of materials and steels is the Helmholtz free energy of their individual structural and magnetic phases. Simulation tools that are well established in industry, e.g., CALPHAD, use empirical interpolation formulas and experimental input to describe the temperature dependence of this energy. However, experimental input data, e.g., for novel alloy systems or metastable structures, are not always available. Therefore, there is a strong interest in incorporating ab initio results into these simulation tools. For this purpose, the ab initio determination of free energies of metals up to the melting point is decisive.

Out of the various entropy contributions to the free energy, including lattice vibrations and electronic excitations, the treatment of magnetic excitations is most challenging and developed to a much less extend. On the other hand, it is of great importance for many practical applications (e.g., steels, magnetic actuators). Within the first part of this project we developed several approaches to treat the magnetic contribution to the free energy of iron. The task of the upcoming year is an extension of these concepts to chromium and materials containing more than one magnetic species.

Until now, we have used the Heisenberg model for calculating quantitative temperature-dependent magnetic properties, which turned out to be well suited to simulate magnetic interactions in Fe-based alloys. Its exchange integrals are obtained from ab initio calculations of magnetic structures (either by setting up special collinear configurations or by considering non-collinear spin-waves). A particular focus of the investigations has been and will continue to be on the consideration of quantum effects in the thermodynamic properties of the model. We suggest the following two different directions for this purpose: On the one hand, analytical concepts of many-body theory (RPA) will be used to derive an approximation for the Hamiltonian. This approach has been successful for bcc Fe below the Curie temperature (see figure above). The challenge is an extension to the antiferromagnetic configuration of Cr. On the other hand, numerically exact Monte Carlo simulations will be used to solve the Heisenberg model. Here, it will be particularly important to compare the results of a quantum-mechanically (QMC) vs. a classical (cMC) treatment.

The results will be used to improve the databases within the SAPIENS project.