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Fe clusters (Fe$_n$, n=1-6) chemisorbed on vacancy defects in graphene: Stability, spin-dipole moment and magnetic anisotropy

In this work, we have studied the chemical and magnetic interactions of Fe$_n$ ; n=1-6 clusters with vacancy defects (monovacancy to correlated vacancies with six missing C atoms) in a graphene sheet by ab-initio density functional calculations combined with Hubbard U corrections for correlated Fe- d electrons. It is found that the vacancy formation energies are lowered in the presence of Fe, indicating an easier destruction of the graphene sheet. Due to strong chemical interactions between Fe clusters and vacancies, a complex distribution of magnetic moments appear on the distorted Fe clusters which results in reduced averaged magnetic moments compared to the free clusters. In addition to that, we have calculated spin-dipole moments and magnetic anisotropy energies. The calculated spin-dipole moments arising from anisotropic spin density distributions, vary between positive and negative values, yielding increased or decreased effective moments. Depending on the cluster geometry, the easy axis of magnetization of the Fe clusters shows in-plane or out-of-plane behavior.