Electronic structure of metallic antiperovskite compound GaCMn${}_3$

We have investigated electronic structures of antiperovskite GaCMn${}_3$ and related Mn compounds SnCMn${}_3$, ZnCMn${}_3$, and ZnNMn${}_3$. In the paramagnetic state of GaCMn${}_3$, the Fermi surface nesting feature along the $\mathrm{\Gamma }\mathrm{R}$ direction is observed, which induces the antiferromagnetic (AFM) spin ordering with the nesting vector {\bf Q} $\sim \mathrm{\Gamma }\mathrm{R}$. Calculated susceptibilities confirm the nesting scenario for GaCMn${}_3$ and also explain various magnetic structures of other antiperovskite compounds. Through the band folding effect, the AFM phase of GaCMn${}_3$ is stabilized. Nearly equal densities of states at the Fermi level in the ferromagnetic and AFM phases of GaCMn${}_3$ indicate that two phases are competing in the ground state.