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We theoretically studied the electronic structure, magnetic properties, andlattice dynamics of a series of $3d$ transition-metal antiperovskite compoundsAXM$_{3}$ by density function theory. Based on the Stoner criterion, we drewthe magnetic phase diagram of carbon-based antiperovskites ACM$_{3}$. In thephase diagram, compounds with non-magnetic ground state but locating near theferromagnetic boundary are suggested to yield sizeable electron-phonon couplingand behave superconductivity. To approve this deduction, we systematicallycalculated the phonon spectra and electron-phonon coupling of a series ofCr-based antiperovskites ACCr$_{3}$ and ANCr$_{3}$. The results show thatAlCCr$_{3}$, GaCCr$_{3}$, and ZnNCr$_{3}$ could be moderate coupling BCSsuperconductors. The influence of spin fluctuation on superconductivity arediscussed. Furthermore, other potential superconducting AXM$_{3}$ includingsome new Co-base and Fe-based antiperovskite superconductors are predicted fromthe magnetic phase diagram.

Prediction of superconductivity of $3d$ transition-metal based antiperovskites via magnetic phase diagram