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Appearance of Half-Metallicity in the Quaternary Heusler Alloys

I report systematic first-principle calculations of the quaternary Heusler alloys like Co$_2$[Cr$_{1-x}$Mn$_x$]Al, Co$_2$Mn[Al$_{1-x}$Sn$_x$] and [Fe$_{1-x}$Co$_x$]$_2$MnAl. I show that when the two limiting cases (x=0 or 1) correspond to a half-metallic compound, so do the intermediate cases. Moreover the total spin moment $M_t$ in $μ_B$ scales linearly with the total number of valence electrons $Z_t$ (and thus with the concentration $x$) following the relation $M_t=Z_t-24$, independently of the origin of the extra valence electrons, confirming the Slater-Pauling behavior of the normal Heusler alloys. Finally I discuss in all cases the trends in the atomic projected DOSs and in the atomic spin moments.