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We consider electronic correlation effects and their impact on magneticproperties of tetragonally distorted chemically ordered FeCo alloys (L1$_0$structure) being a promising candidate for rare-earth-free permanent magnets.We employ a state-of-the-art method combining density functional and dynamicalmean-field theory. According to our results, the predicted Curie temperaturereduces with increase of lattice parameters ratio $c/a$ and reaches nearly 850K at ${c/a=1.22}$. For all considered $c/a$ from 1 to $\sqrt{2}$, we findwell-localized magnetic moments on Fe sites, which are formed due to strongcorrelations originating from Hund's coupling. At the same time, magnetism ofCo sites is more itinerant with a much less lifetime of local magnetic moments.However, these short-lived local moments are also formed due to Hund'sexchange. Electronic states at Fe sites are characterized by anon-quasiparticle form of self-energies, while the ones for Co sites are foundto have a Fermi-liquid-like shape with quasiparticle mass enhancement factor${m^*/m\sim 1.4}$, corresponding to moderately correlated metal. The strongelectron correlations on Fe sites leading to Hund's metal behaviour can beexplained by peculiarities of the density of states, which has pronounced peaksnear the Fermi level, while weaker many-body effects on Co sites can be causedby stronger deviation from half-filling of their $3d$ states. The obtainedmomentum dependence of magnetic susceptibility suggests that the ferromagneticordering is the most favourable one except for the near vicinity of the fccstructure and the magnetic exchange is expected to be of RKKY type.

Coulomb correlations and magnetic properties of L1$_0$ FeCo: a DFT+DMFT study