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Scanning probe microscopy and spectroscopy, and more recently in combinationwith electron spin resonance, have allowed the direct observation of electrondynamics on the single-atom limit. The interpretation of data is stronglydepending on model Hamiltonians. However, fitting effective spin Hamiltoniansto experimental data lacks the ability to explore a vast number of potentialsystems of interest. By using plane-wave density functional theory (DFT) asstarting point, we build a multiplet Hamiltonian making use ofmaximally-localized Wannier functions. The Hamiltonian contains spin-orbit andelectron-electron interactions needed to obtain the relevant spin dynamics. Theresulting reduced Hamiltonian is solved by exact diagonalization. We comparethree prototypical cases of 3d transition metals Mn (total spin $S=5/2$), Fe($S=2$) and Co ($S=3/2$) on MgO with experimental data and find that ourcalculations can accurately predict the spin orientation and anisotropy of themagnetic adatom. Our method does not rely on experimental input and permits usto explore and predict the fundamental magnetic properties of adatoms onsurfaces.

Efficient Ab-initio Multiplet Calculations for Magnetic Adatoms on MgO