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Influence of mixing the low-valent transition metal atoms (Y,Y$^*$=Cr,Mn,Fe) on the properties of the quaternary Co$_2$[Y$_{1-x}$Y$^*_x$]Z (Z=Al,Ga,Si,Ge,Sn) Heusler compounds

We complement our study on the doping and disorder in Co$_2$MnZ compounds [I. Galanakis \textit{et al.}, Appl. Phys. Lett. \textbf{89}, 042502 (2006) and K. Özdogan \textit{et al.}, Phys. Rev. B \textbf{74}, (2006)] to cover also the quaterarny Co$_2$[Y$_{1-x}$Y$^*_x$]Z compounds with the lower-valent transition metals Y,Y$^*$ being Cr, Mn or Fe and the sp atom Z being one of Al, Ga, Si, Ge, Sn. This study gives a global overview of the magnetic and electronic properties of these compounds since we vary both Y and Z elements. Our results suggest that for realistic applications the most appropriate compounds are the ones belonging to the families Co$_2$[Mn$_{1-x}$Cr$_x$]Z with $x>0.5$ irrespectively of the nature of the $sp$ atoms since they combine high values of majority DOS at the Fermi level due to the presence of Cr, and half-metallicity with large band-gaps. On the other hand the presence of Fe lowers considerably the majority density of states at the Fermi level and when combined with an element belonging to the Si-column, it even can destroy half-metallicity.