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

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.