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We study the electronic state of an inverse spinel compound MnMg$_{2}$O$_{4}$based on first-principles calculations. The high-spin state is realized in Mnions on the diamond lattice, resulting in that this material is found to be ahalf-metallic semimetal with the minority spin-gap about 3eV, and also withline nodes in the Brillouin zone. The intrinsic anomalous Hall conductivity(AHC) is also computed as a function of the chemical potential of the systemassuming the rigid band structure, and is found to exhibit a peak structurewith a maximum value of 200 S/cm at only 15 meV above the Fermi level. Therelation between the large AHC and Berry curvature in the Brillouin zone isalso discussed.

Ab initio study on the possible magnetic topological semimetallic state in MnMg$_{2}$O$_{4}$}