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Magnetic properties of a $\sigma-$Fe$_{16}$Cr$_{14}$ alloy calculated withthe charge and spin self- consistent Korringa-Kohn-Rostoker (KKR) and combinedwith coherent potential approximation (KKR-CPA) methods are reported.Non-magnetic state as well as various magnetic orderings were considered, i.e.ferromagnetic (FM) and more complex anti-parallel (called APM) arrangements forselected sublattices, as follows from the symmetry analysis. It has been shownthat the Stoner criterion applied to non-magnetic density of states at theFermi energy, $E_F$ is satisfied for Fe atoms situated on all five latticesites, while it is not fulfilled for all Cr atoms. In FM and APM states, thevalues of magnetic moments on Fe atoms occupying various sites are dispersedbetween 0 and 2.5 $\mu_B$, and they are proportional to the number of Fe atomsin the nearest-neighbor shell. Magnetic moments of Cr atoms havin much smallervalues were found to be coupled antiparallel to those of Fe atoms. The averagevalue of the magnetic moment per atom was found to be $<\mu>=0.55 \mu_B$ thatis by a factor of 4 larger than the experimental value found for a$\sigma-$Fe$_{0.538}$Cr$_{0.462}$ sample. Conversely, admitting an anti-parallel ordering (APM model) on atoms situated on C and D sites, according tothe group theory and symmetry analysis results, yielded a substantial reductionof $<\mu>$ to 0.20 $\mu_B$. Further diminution of $<\mu>$ to 0.15 $\mu_B$,which is very close to the experimental value of 0.14 $\mu_B$, has beenachieved with the KKR-CPA calculations by considering a chemical disorder onsites B, C and D.

Magnetic properties of $\sigma$-FeCr alloy as calculated with the charge and spin self-consistent KKR(CPA) method