Recent progress in simulations of the paramagnetic state of magnetic materials

•Existence of disordered local moments in the paramagnetic state is essential.•The magnetic disorder makes theoretical description of the systems non-trivial.•We discuss advantages and limitations of existing theoretical tools.•Contributions from electronic, magnetic and vibrational excitations are all important.•Accurate predictions of materials properties in the paramagnetic state are possible. We review recent developments in the field of first-principles simulations of magnetic materials above the magnetic order–disorder transition temperature, focusing mainly on 3d-transition metals, their alloys and compounds. We review theoretical tools, which allow for a description of a system with local moments, which survive, but become disordered in the paramagnetic state, focusing on their advantages and limitations. We discuss applications of these theories for calculations of thermodynamic and mechanical properties of paramagnetic materials. The presented examples include, among others, simulations of phase stability of Fe, Fe–Cr and Fe–Mn alloys, formation energies of vacancies, substitutional and interstitial impurities, as well as their interactions in Fe, calculations of equations of state and elastic moduli for 3d-transition metal alloys and compounds, like CrN and steels. The examples underline the need for a proper treatment of magnetic disorder in these systems.