  We study the electronic and magnetic properties of the quaternary
AuMnSn$_{1-x}$Sb$_{x}$ Heusler alloys using first principles calculations. We
determine their magnetic phase diagram and we show that they present a phase
transition from a ferromagnetic to an antiferromagnetic state with increasing
Sb concentration. For large Sb concentrations the antiferromagnetic
superexchange coupling dominates over the ferromagnetic RKKY-like exchange
mechanism. This behavior is similar to the one demonstrated by the isovalent
Ni$_{1-x}$Cu$_x$MnSb alloy studied recently by the authors [I. Galanakis et al,
Phys. Rev. B. \textbf{77}, 214417 (2008)]. Thus the variation of the
concentration of the \textit{sp}-electrons (Sn and Sb atoms) and the variation
of the concentration of the non-magnetic \textit{3d} atoms (Cu) lead to a
similar tuning of the the magnetic properties of the Heusler alloys. We show
that the inclusion of correlation effects does not alter the phase diagram.
Calculated results are in good agreement with the available experimental data.
