Possible Way to Make MgFeGe a New Fe-based Superconductor

We propose that the contrasting low-temperature behaviors observed experimentally among isostructural and isoelectronic materials, like non-superconducting and nonmagnetic MgFeGe, magnetically ordered NaFeAs, and superconducting LiFeAs, can be well understood from itinerant weak coupling limit. We find that stronger $(\pi,\pi)$ instability appearing in the d$_{x^2-y^2}$ orbital of NaFeAs is responsible for the occurrence of weak magnetism while weaker but still prominent $(\pi,\pi)$ instability in LiFeAs leads to a superconducting state. In contrast, multiple competing instabilities coexisting in orbital-resolved momentum-dependent susceptibilities, serving as magnetic frustrations from itinerant electrons, may account for the nonmagnetic state in MgFeGe, while poorer Fermi surface nesting leads to a non-superconducting state. Based on above findings, we predict a possible way to make MgFeGe a new Fe-based superconductor.