Efficient Ab-initio Multiplet Calculations for Magnetic Adatoms on MgO

Scanning probe microscopy and spectroscopy, and more recently in combination with electron spin resonance, have allowed the direct observation of electron dynamics on the single-atom limit. The interpretation of data is strongly depending on model Hamiltonians. However, fitting effective spin Hamiltonians to experimental data lacks the ability to explore a vast number of potential systems of interest. By using plane-wave density functional theory (DFT) as starting point, we build a multiplet Hamiltonian making use of maximally-localized Wannier functions. The Hamiltonian contains spin-orbit and electron-electron interactions needed to obtain the relevant spin dynamics. The resulting reduced Hamiltonian is solved by exact diagonalization. We compare three 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 our calculations can accurately predict the spin orientation and anisotropy of the magnetic adatom. Our method does not rely on experimental input and permits us to explore and predict the fundamental magnetic properties of adatoms on surfaces.