  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.
