The electronic structure and magnetism of individual Dy atoms adsorbed on ferromagnetic (Gr)/Ni(111) substrate are investigated using a combination of the density functional theory with the Hubbard-I approximation to the Anderson impurity model (DFT+U(HIA)). The divalent Dy \(\phantom{0}^{2+}\) adatom in \(f^{10}\) configuration with [ \(J = 8, L=6, S=2\) ] is found. The values of spin \(M_S\) =3.4 \(\mu _B\) , orbital \(M_L\) =5.2 \(\mu _B\) , and total \(M_J\) =8.6 \(\mu _B\) magnetic moments calculated for the Dy f-shell are noticeably different from the atomic second Hund’s rule. There is almost zero moment on (Gr)-atoms. The ferromagnetic Ni substrate moments are anti-aligned to the Dy 4f-shell moment. The X-ray absorption (XAS) and magnetic circular dichroism (XMCD) spectra are calculated and can be compared to the experimental data. The magnetic anisotropy energy (MAE) is calculated from the ground state energy difference for different directions of the magnetization, E[100] - E[001] = 3.5 meV and E[010] - E[001] = 2.2 meV. This large and positive MAE can be important for ultra-high density magnetic recording. The magnetization of Dy@(Gr)/Ni(111) is tilted with respect to the (Gr)/Ni(111) substrate normal by \(38^o\) due to a competition between negative first and third order magnetic anisotropies and strong and positive second order magnetic anisotropies. Our studies assist in resolving ambiguities of conventional DFT+U applied to Dy on graphene. They can provide a viable route for further investigation and prediction of the rare-earth based magnetic nanostructures.
