  Body-centered cubic (bcc) Fe-Mn systems are known to exhibit a complex and
atypical magnetic behaviour from both experiments and 0 K electronic-structure
calculations, which is due to the half-filled 3d-band of Mn. We propose
effective interaction models for these alloys, which contain both atomic spin
and chemical variables. They were parameterized on a set of key density
functional theory (DFT) data, with the inclusion of non-collinear magnetic
configurations being indispensable. Two distinct approaches, namely a
knowledge-driven and a machine-learning approach have been employed for the
fitting. Employing these models in atomic Monte Carlo simulations enables the
prediction of magnetic and thermodynamic properties of the Fe-Mn alloys, and
their coupling, as functions of temperature. This includes the decrease of
Curie temperature with increasing Mn concentration, the temperature evolution
of the mixing enthalpy and its correlation with the alloy magnetization. Also,
going beyond the defect-free systems, we determined the binding free energy
between a vacancy and a Mn atom, which is a key parameter controlling the
atomic transport in Fe-Mn alloys.
