  The structural, electronic and magnetic properties of small ${\rm Fe}_m {\rm
Rh}_n$ clusters having $N = m+n \leq 8$ atoms are studied in the framework of a
generalized-gradient approximation to density-functional theory. The
correlation between structure, chemical order, and magnetic behavior is
analyzed as a function of size and composition. For $N = m+n \leq 6$ a thorough
sampling of all cluster topologies has been performed, while for N = 7 and 8
only a few representative topologies are considered. In all cases the entire
concentration range is systematically investigated. All the clusters show
ferromagnetic-like order in the optimized structures. As a result, the average
magnetic moment per atom $\bar\mu_N$ increases monotonously, which is almost
linear over a wide range of concentration with Fe content. A remarkable
enhancement of the local Fe moments beyond 3 $\mu_B$ is observed as result of
Rh doping. This is a consequence of the increase in the number of Fe $d$ holes,
due to charge transfer from Fe to Rh, combined with the extremely reduced local
coordination. The Rh local moments, which are important already in the pure
clusters ($N\le 8$) are not significantly enhanced by Fe doping. However, the
overall stability of magnetism, as measured by the energy gained upon spin
polarization, increases when Rh is replaced by Fe. The composition dependence
of the electronic structure and the influence of spin-orbit interactions on the
cluster stability are discussed.
