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Stability and magnetization of free-standing and graphene-embedded iron membranes

Inspired by recent experimental realizations of monolayer Fe membranes in graphene perforations, we perform ab initio calculations of Fe monolayers and membranes embedded in graphene in order to assess their structural stability and magnetization. We demonstrate that monolayer Fe has a larger spin magnetization per atom than bulk Fe and that Fe membranes embedded in graphene exhibit spin magnetization comparable to monolayer Fe. We find that free-standing monolayer Fe is structurally more stable in a triangular lattice compared to both square and honeycomb lattices. This is contradictory to the experimental observation that the embedded Fe membranes form a square lattice. However, we find that embedded Fe membranes in graphene perforations can be more stable in the square lattice configuration compared to the triangular. In addition, we find that the square lattice has a lower edge formation energy, which means that the square Fe lattice may be favored during formation of the membrane.