| Summary: | High-throughput density functional calculations are used to investigate the effect of interstitial B, C, and N atoms on 21 alloys reported to crystallize in the cubic Cu_{3}Au structure. It is shown that the interstitials can have a significant impact on the magnetocrystalline anisotropy energy (MAE), the thermodynamic stability, and the magnetic ground-state structure, making these alloys interesting for hard magnetic, magnetocaloric, and other applications. For 29 alloy-interstitial combinations the formation of stable alloys with interstitial concentrations above 5% is expected. In Ni_{3}Mn interstitial N induces a tetragonal distortion with substantial uniaxial MAE for realistic N concentrations. Mn_{3}XN_{x} (X = Rh, Ir, Pt, and Sb) compounds are identified as alloys with strong magnetocrystalline anisotropy. For Mn_{3}Ir we find a strong enhancement of the MAE upon N alloying in the most stable collinear ferrimagnetic state as well as in the noncollinear magnetic ground state. Mn_{3}Ir and Mn_{3}IrN also show interesting topological transport properties. The effects of N concentration and strain on the magnetic properties are discussed. Further, the huge impact of N on the MAE of Mn_{3}Ir and a possible impact of interstitial N on amorphous Mn_{3}Ir, a material that is indispensable in today's data storage devices, are discussed in relation to the electronic structure. For Mn_{3}Sb, noncollinear, ferrimagnetic, and ferromagnetic states are very close in energy, making this material potentially interesting for magnetocaloric applications. For the investigated Mn alloys and competing phases, the determination of the magnetic ground state is essential for a reliable prediction of the phase stability.
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