The physical properties of two new quaternary Heusler alloys CoMnVSn and CoMnVSb were systematically studied by using first-principles calculation. The results show that the type-1 structures of ferromagnetic phase for these two alloys are the most stable. They all exhibit half-metallic behavior at equilibrium, and their half-metallic characteristics are maintained in the lattice region of 5.73-6.19 Angstrem for CoMnVSn and 5.82-6.18 Angstrem for CoMnVSb. The calculated magnetic moment Mt of each molecular unit in the half-metal lattice region strictly follows the Slater-Pauling empirical rule M_t=Z_t-24, where Z_t is the number of valence electrons. The elastic constants show that the mechanical properties of the two compounds are stable at equilibrium, and the anisotropy factor and three-dimensional Young's modulus confirm that they have anisotropy. It is expected that the CoMnVSn and CoMnVSb alloys are promising candidates in spintronics. Keywords: quaternary Heusler alloy, electronic structure, half-metal, first principles.

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