  In this letter, we apply the mixed-bond spin-1 Ising model to the study of
the magnetic properties of Fe-Mn alloys in the $\alpha$ phase by employing the
effective field theory (EFT). Here, we suggest a new approach to the
ferromagnetic coupling between nearest neighbours Fe-Fe that depends on the
ratio between the Mn-Mn coupling and Fe-Mn coupling and of second power of the
Mn concentration $q$ in contrast with linear dependence proposed in the other
papers. Also, we propose a new probability distribution for binary alloys with
mixed-bonds based on the distribution for ternary alloys and we obtain a very
good agreement for all considered values of $q$ in $T-q$ plane, in particular
for $q>0.11$.
