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