  We present a first-principles study of RFe$_{12-x}$Cr$_{x}$ (R = Y, Nd, Sm)
crystals with ThMn$_{12}$ structure. We discuss, within the mean field
approximation, intersite magnetic couplings calculated using Liechtenstein's
formula and convert them into Curie temperatures, $T_{\rm C}$, which are found
to become larger when a small amount of Cr ($x \leq 0.5$) is introduced into
the system. This enhancement is larger than that for Co in the dilute limit, $x
\rightarrow 0$. In contrast, above $x > 0.5$, the Curie temperature decreases
as Cr concentration increases. This behavior is analyzed using an expansion of
$T_{\rm C}$ in terms of concentration.
