  Large magnetic anisotropy energy (MAE) is desirable and critical for
nanoscale magnetic devices. Here, using ligand-field level diagrams and density
functional calculations, we well explain the very recent discovery [I. G. Rau
et al., Science 344, 988 (2014)] that an individual Co adatom on a MgO (001)
surface has a large MAE of more than 60 meV. More importantly, we predict that
a giant MAE up to 110 meV could be realized for Ru adatoms on MgO (001), and
even more for the Os adatoms (208 meV). This is a joint effect of the special
ligand field, orbital multiplet, and significant spin-orbit interaction, in the
intermediate-spin state of the Ru or Os adatoms on top of the surface oxygens.
The giant MAE could provide a route to atomic scale memory.
