Influence of magnetic excitations on the phase stability of metals and steels

•We review the modeling of magnetic contributions to the free energy of materials.•A fully quantum-mechanical description of magnetic excitations is needed.•Effective Heisenberg models describe Fe-based systems very well.•Microscopic interatomic forces often depend on the magnetic state.•A spin-space averaging method captures the impact of the paramagnetic state.

Within this article we highlight recent advances in the modeling of magnetic contributions to the finite temperature phase stability of structural materials. A key quantity in this context is the specific heat capacity CpCp, since it provides a sensitive link to thermophysical and calorimetric experiments and to established thermodynamic databases. For iron-based materials, the Heisenberg model and its extensions are used as an elegant way for coupling ground-state ab initio   calculations with concepts of many-body theory to simulate the temperature dependence. Besides analytical concepts to derive the free energy of the Heisenberg model, our work is mainly devoted to numerical approaches such as Monte-Carlo methods. In particular, we highlight the need to go beyond a classical to a fully quantum-mechanical description of magnetic excitations. In order to achieve a quantitative description of CpCp, also lattice and electronic degrees of freedom as well as their dependence on magnetism are addressed. Due to the large variety of experimental data, pure iron is best suited to discuss the method developments and to perform evaluations. Nevertheless, the application to other magnetic elements (e.g. Co, Ni) and Fe-based materials (e.g. Fe3C) will also be addressed.