Magnetic anisotropy of a Dy atom on a graphene/Cu(111) surface

The electronic structure and magnetism of individual Dy atoms adsorbed on the graphene/Cu(111) surface is investigated using the combination of the density functional theory with the Hubbard-I approximation to the Anderson impurity model ($\mathrm{DFT}+\mathrm{U}+\mathrm{HIA}$). We find that the results of the $\mathrm{DFT}+\mathrm{U}+\mathrm{HIA}$ depend on the choice of the double-counting term. For fully localized limit, the divalent ${\mathrm{Dy}}²⁺$ adatom is found, with the total magnetic moment of $9.71\phantom{\rule{4pt}{0ex}}{\ensuremath{\mu}}_B$. The spin and orbital magnetic moments are evaluated, and compared with the x-ray magnetic circular dichroism data. The calculated positive magnetic anisotropy energy determines the out-of-plane orientation of the Dy adatom magnetic moment, in agreement with available experimental data.