Bonding, moment formation, and magnetic interactions in ${\mathrm{Ca}}_{14}{\mathrm{MnBi}}_{11}$ and ${\mathrm{Ba}}_{14}{\mathrm{MnBi}}_{11}$

“14-1-11” phase compounds, based on magnetic Mn ions and typified by ${\mathrm{Ca}}_{14}{\mathrm{MnBi}}_{11}$ and ${\mathrm{Ba}}_{14}{\mathrm{MnBi}}_{11},$ show an unusual magnetic behavior, but the large number (104) of atoms in the primitive cell has precluded any previous full electronic structure study. Using an efficient, local-orbital-based method within the local-spin-density approximation to study the electronic structure, we find a gap between a bonding valence-band complex and an antibonding conduction-band continuum. The bonding bands lack one electron per formula unit of being filled, making them low carrier density p-type metals. The hole resides in the ${\mathrm{MnBi}}_4$ tetrahedral unit, and partially compensates for the high-spin $d^5\hspace{0.5em}\mathrm{Mn}$ moment, leaving a net spin near $4{\mu }_B$ that is consistent with experiment. These manganites are composed of two disjoint but interpenetrating “jungle gym” networks of spin-$\frac{4}{2}$ ${\mathrm{MnBi}}_4^{9-}$ units with ferromagnetic interactions within the same network, and weaker couplings between the networks whose sign and magnitude is sensitive to materials parameters. ${\mathrm{Ca}}_{14}{\mathrm{MnBi}}_{11}$ is calculated to be ferromagnetic as observed, while for ${\mathrm{Ba}}_{14}{\mathrm{MnBi}}_{11}$ (which is antiferromagnetic) the ferromagnetic and antiferromagnetic states are calculated to be essentially degenerate. The band structure of the ferromagnetic states is very close to half metallic.