Theoretical exploration of mixed-anion antiperovskite semiconductors M3XN(M=Mg,Ca,Sr,Ba;

Antiperovskites have recently been attracting considerable attention because of their intriguing physical properties. We theoretically investigate polymorphism of mixed-anion antiperovskites ${M}_{3}^{2+}{X}^{3\ensuremath{-}}{\mathrm{N}}^{3\ensuremath{-}}\phantom{\rule{4pt}{0ex}}(M$ = Mg, Ca, Sr, Ba; $X$ = P, As, Sb, Bi) using the seven representative crystal-structure prototypes of $AB{Z}_{3}$ compounds. Stable crystal-structure exploration for four unreported compounds $({\mathrm{Mg}}_{3}\mathrm{PN},{\mathrm{Sr}}_{3}\mathrm{PN},{\mathrm{Ba}}_{3}\mathrm{PN}$, and ${\mathrm{Mg}}_{3}\mathrm{BiN})$ is also performed using ab initio evolutionary crystal-structure-search and lattice-dynamics calculations, which have consistently identified antiperovskite phases as their ground states. As a result of crystal-structure exploration, the orthorhombic perovskite $Pbnm$ phases of ${\mathrm{Mg}}_{3}\mathrm{PN},{\mathrm{Sr}}_{3}\mathrm{PN}$, and ${\mathrm{Ba}}_{3}\mathrm{PN}$ are obtained, while the cubic perovskite $Pm\overline{3}m$ phase is stable in ${\mathrm{Mg}}_{3}\mathrm{BiN}$. We show that the octahedral rotational distortions in ${M}_{3}\mathrm{PN}$ and ${M}_{3}\mathrm{AsN}$ reduce their Madelung energies, which is not common in conventional perovskites. Further, we estimate the ionic radii of anionic nitrogen ${\mathrm{N}}^{3\ensuremath{-}}$ and pnictogen ${X}^{3\ensuremath{-}}$ to explain the chemical trends for the phase stability, lattice distortion amplitude, total energies, valence bandwidths, and band gaps of ${M}_{3}X\mathrm{N}$ using the Goldschmidt tolerance factor. We also report the electronic structures of ${M}_{3}X\mathrm{N}$ with and without the rotational distortions and spin-orbit coupling. The valence bands of ${\mathrm{Mg}}_{3}X\mathrm{N}$ are created mainly from $p\text{\ensuremath{-}}p$ hybridization, whereas those of ${M}_{3}^{\ensuremath{'}}X\mathrm{N}\phantom{\rule{4pt}{0ex}}({M}^{\ensuremath{'}}$ = Ca, Sr, Ba) are constructed mainly from $d\text{\ensuremath{-}}p$ hybridization. We then explain the mechanism of the band-gap changes owing to the rotational distortions and spin-orbit coupling. The effective masses for the relevant ground-state phases of ${M}_{3}X\mathrm{N}$ are found to be comparable to preexisting compound semiconductors. Finally, we propose potential applications of earth-abundant semiconductors ${\mathrm{Mg}}_{3}\mathrm{PN}$ and ${\mathrm{Sr}}_{3}\mathrm{PN}$ as light absorbers and emitters utilizing their direct-type band structures and high optical absorption coefficients. The present study provides a clear picture and recipe for the understanding and design of mixed-anion antiperovskites.