Clustering and magnetic anisotropy of Fe adatoms on graphene

Single Fe adatoms and clusters of Fe adatoms on graphene are studied through first-principles calculations using density functional theory (DFT) and spin density functional theory (sDFT). First, we consider computational cells containing various numbers of C atoms and one Fe adatom. We calculate the binding energy, adatom height, and magnetic moment of the adatom above a few high-symmetry positions in the cell. In all cases, the binding energy increases with decreasing cell size, suggesting that clustering of the Fe adatoms is energetically favored. We also calculate the energy of various clusters of two to four Fe atoms on graphene in computational cells of various sizes, using both DFT and sDFT. These calculations again show that, both in DFT and sDFT, the Fe adatoms strongly prefer to form clusters. The energy barrier for an isolated Fe adatom to diffuse from the center of one graphene hexagon is calculated to be 0.49 eV. This barrier is reduced for an Fe atom which is one of a pair of neighboring adatoms. Finally, by including spin-orbit interactions within sDFT, we calculate the magnetic anisotropy energy of a single Fe adatom on graphene. We find that the in-plane anisotropy energy is close to zero, while the out-of-plane anisotropy energy is $\ensuremath{\sim}$$D{S}^{2}{\mathrm{cos}}^{2}\ensuremath{\theta}$ where $S\ensuremath{\sim}2.0$, $\ensuremath{\theta}$ is the angle between the magnetic moment and the perpendicular to the graphene plane, and $D\ensuremath{\sim}0.25$ meV.