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The structural, electronic, and magnetic properties of the full-Heusler compounds CoMnZ ( Z = Al, Ge, Si, Ga) have been investigated using the first-principles calculations with the full-potential linear-augmented plane wave method within the density functional theory. The electronic structures and magnetic properties of the CoMnZ ( Z = Al, Ge, Si, Ga) compounds with both HgCuTi- and CuMnAl-type structures are studied. It is found that the calculated lattice constants are in good agreement with the theoretical values. Using the general gradient approximation, we observe that the CuMnAl-type structure is more stable than the HgCuTi type. The CoMnZ ( Z = Al, Ge, Si, Ga) compounds were half-metallic ferromagnets in the CuMnAl-type structure. The total magnetic moments of the CoMnZ ( Z = Al, Ge, Si, Ga) compounds in the CuMnAl-type structure were 4, 5, 5, and 4 μ respectively, which is in agreement with the Slater-Pauling rule, m = N−24 Furthermore, the origin for the appearance of the half-metallic band gap in the CoMnZ compound was also discussed which shows them to be promising materials for possible spintronics applications. [ABSTRACT FROM AUTHOR]