Many-particle effects in adsorbed magnetic atoms with easy-axis anisotropy: the case of Fe on the CuN/Cu(100) surface

We study the effects of the exchange interaction between an adsorbed magnetic atom with easy-axis magnetic anisotropy and the conduction-band electrons from the substrate. We model the system using an anisotropic Kondo model and we compute the impurity spectral function, which is related to the differential conductance (dI / dV) spectra measured using a scanning tunneling microscope. To make contact with the known experimental results for iron atoms on the CuN/Cu(100) surface (Hirjibehedin et al 2007 Science 317 1199), we calculated the spectral functions in the presence of an external magnetic field of varying strength applied along all three spatial directions. It is possible to establish an upper bound on the coupling constant J : in the range of the magnetic fields for which the experimental results are currently known (up to 7 T), the low-energy features in the calculated spectra agree well with the measured dI / dV spectra if the exchange coupling constant J is at most half as large as that for cobalt atoms on the same surface. We show that for an even higher magnetic field (between 8 and 9 T) applied along the 'hollow direction', the impurity energy states cross, giving rise to a Kondo effect which takes the form of a zero-bias resonance. The coupling strength J could be determined experimentally by performing tunneling spectroscopy in this range of magnetic fields. On the technical side, the paper introduces an approach for calculating the expectation values of global spin operators and all the components of the impurity magnetic susceptibility tensor (including the out-of-diagonal ones) in numerical renormalization group (NRG) calculations with no spin symmetry. An appendix contains a density functional theory (DFT) study of the Co and Fe adsorbates on the CuN/Cu(100) surface: we compare magnetic moments, as well as orbital energies, occupancies, centers and spreads, by calculating the maximally localized Wannier orbitals of the adsorbates.