  This work reports on first principles calculations of the electronic and
magnetic structure of tetragonal Heusler compounds with the composition
Rh$_2$Fe$_{x}$Co$_{1-x}$Sb ($0\leq x\leq1$). It is found that the magnetic
moments increase from 2 to 3.4~$\mu_B$ and the Curie temperature decreases from
500 to 464~K with increasing Fe content $x$. The $3d$ transition metals make
the main contribution to the magnetic moments, whereas Rh contributes only
approximately 0.2~$\mu_B$ per atom, independent of the composition. The paper
focuses on the magnetocrystalline anisotropy of the borderline compounds
Rh$_2$FeSb, Rh$_2$Fe$_{0.5}$Co$_{0.5}$Sb, and Rh$_2$CoSb. A transition from
easy-axis to easy-plane anisotropy is observed when the composition changes
from Rh$_2$CoSb to Rh$_2$FeSb. The transition occurs at an iron concentration
of approximately 40\%.
