Stability of Two-Dimensional Iron Carbides Suspended across Graphene Pores: First-Principles Particle Swarm Optimization

Inspired by recent experimental realizations of two-dimensional (2D) metals and alloys, we theoretically investigate the stability and electronic properties of monolayer (ML) Fe–C compounds and pure Fe. According to our theoretical results and those of others, ML pure Fe square lattices embedded in graphene (Gr) pores that proposed by the experiment ( Science 2014, 343, 1228) are energetically unstable compared to Fe triangular lattices in Gr. To solve the above contradiction, we search for the stable structures of ML Fe–C with various Fe to C ratios (as a generalization of ML Fe in Gr) using ab initio particle swarm optimization technique. A Fe 1 C 1 square lattice embedded in Gr is found. We propose and demonstrate that the square lattices observed in the experiment were iron carbides (Fe–C) but not pure Fe from the square-lattice shape, Fe–Fe lattice constant, and energetic considerations. Note that the coexistence of C with Fe cannot be excluded from the experiment. More importantly, we find a lowest-energy and dynamically stable structure, ML Fe 2 C 2, with Fe atoms forming distorted square lattices. High-spin polarization around the Fermi level is predicted for different 2D Fe–C structures due to significant orbital hybridization between C and Fe.