We study the electronic structures and magnetic properties of ${\mathrm{Mn}}_{2}\mathrm{Co}Z$ $(Z=\mathrm{Al},\mathrm{Ga},\mathrm{In},\mathrm{Si},\mathrm{Ge},\mathrm{Sn},\mathrm{Sb})$ compounds with ${\mathrm{Hg}}_{2}\mathrm{Cu}\mathrm{Ti}$-type structure using first-principles full-potential linearized-augmented plane-wave calculations. It is found that the compounds with $Z=\mathrm{Al}$, Si, Ge, Sn, and Sb are half-metallic ferrimagnet. Experimentally, we successfully synthesized the ${\mathrm{Mn}}_{2}\mathrm{Co}Z$ $(Z=\mathrm{Al},\mathrm{Ga},\mathrm{In},\mathrm{Ge},\mathrm{Sn},\mathrm{Sb})$ compounds. Using the x-ray diffraction method and Rietveld refinement, we confirm that these compounds form ${\mathrm{Hg}}_{2}\mathrm{Cu}\mathrm{Ti}$-type structure instead of the conventional $L{2}_{1}$ structure. Based on the analysis on the electronic structures, we find that there are two mechanisms to induce the minority-spin band gap near the Fermi level, but only the $d\text{\ensuremath{-}}d$ band gap determines the final width of the band gap. The magnetic interaction is quite complex in these alloys. It is the hybridization between the $\mathrm{Mn}(C)$ and Co atom that dominates the magnitude of magnetic moment of the Co atom and the sign of the $\mathrm{Mn}(B)\text{\ensuremath{-}}\mathrm{Co}$ exchange interaction. The ${\mathrm{Mn}}_{2}\mathrm{Co}Z$ alloys follow the Slater-Pauling rule ${M}_{H}={N}_{V}\ensuremath{-}24$ with varying $Z$ atom. It was further elucidated that the molecular magnetic moment ${M}_{H}$ increases with increasing valence concentration only by decreasing the antiparallel magnetic moment of $\mathrm{Mn}(C)$, while the magnetic moments of $\mathrm{Mn}(B)$ and Co are unaffected.

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Mn2CoZ(Z=Al,Ga,<...