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

Tuning the magnetic properties of half-metallic semi-Heusler alloys by sp-electron substitution: The case of AuMnSn$_{1-x}$Sb$_x$ quaternary alloys