  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.

Mesoscale and Nanoscale Physics;Materials Science