The electronic structure and magnetism of an individual Dy atom adsorbed on the MgO(001) substrate is investigated using a combination of the density functional theory with the Hubbard-I approximation to the Anderson impurity model. The divalent ${\mathrm{Dy}}^{2+}$ adatom in $f^{10}$ configuration is found. The calculated x-ray absorption and magnetic circular dichroism spectra are compared to the experimental data. Quantum tunneling between degenerate $|J=8.0,J_z=\pm 4.0\rangle$ states leads to the formation of a $|J=8.0,J_z=0.0\rangle$ ground state with an in-plane orientation of the magnetic moment. It explains the absence of remanent magnetization in a Dy adatom on the top of the MgO(001) substrate. Our studies can provide a viable route for further investigation and prediction of the rare-earth single-atom magnets.

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• Electronic structure
• First-principles calculations
• Molecular magnets