Magnetism and superconductivity in the layered hexagonal transition metal pnictides

We investigate the electronic and magnetic structures of the 122 (AM$_2$B$_2$) hexagonal transition-metal pnictides with A=(Sr, Ca), M=(Cr, Mn, Fe, Co, Ni) and B=(As, P, Sb). It is found that the family of materials share critical similarities with those of tetragonal structures that include the famous iron-based high temperature superconductors. In both families, the next nearest neighbor(NNN) effective antiferromagnetic(AFM) exchange couplings reach the maximum value in the iron-based materials. While the NNN couplings in the latter are known to be responsible for the C-type AFM state and to result in the extended s-wave superconducting state upon doping, they cause the former to be extremely frustrated magnetic systems and can lead to an time reversal symmetry broken $d+id$ superconducting state upon doping. The iron-based compounds with the hexagonal structure, thus if synthesized, can help us to determine the origin of high temperature superconductivity.