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 $A=(\text{Sr},\text{Ca}),M=(\text{Cr},\text{Mn},\text{Fe},\text{Co},\text{Ni})$, and $B=(\text{As},\text{P},\text{Sb})$. It is found that the family of materials shares 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 a time-reversal symmetry-broken $d+id$ superconducting state upon doping. Thus, if synthesized, iron-based compounds with hexagonal structure can help us to determine the origin of high-temperature superconductivity.