  The electronic structure and magnetic properties of a single Fe adatom on a
CuN surface have been studied using density functional theory in the local spin
density approximation (LSDA), the LSDA+U approach and the local density
approximation plus dynamical mean-field theory (LDA+DMFT). The impurity problem
in LDA+DMFT is solved through exact diagonalization and in the Hubbard-I
approximation. The comparison of the one-particle spectral functions obtained
from LSDA, LSDA+U and LDA+DMFT show the importance of dynamical correlations
for the electronic structure of this system. Most importantly, we focused on
the magnetic anisotropy and found that neither LSDA, nor LSDA+U can explain the
measured, high values of the axial and transverse anisotropy parameters.
Instead, the spin excitation energies obtained from our LDA+DMFT approach with
exact diagonalization agree significantly better with experimental data. This
affirms the importance of treating fluctuating magnetic moments through a
realistic many-body treatment when describing this class of nano-magnetic
systems. Moreover, it facilitates insight to the role of the hybridization with
surrounding orbitals.
