Many-particle effects in adsorbed magnetic atoms with easy-axis anisotropy: the case of Fe on 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., Science {\bf 317}, 1199 (2007)], 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 7T), 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 even higher magnetic field (between 8 and 9T) 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 paper introduces an approach for calculating the expectation values of global spin operators and all components of the impurity magnetic susceptibility tensor in numerical renormalization group (NRG) calculations with no spin symmetry. An appendix contains a density-functional-theory (DFT) study of the Cu and Fe adsorbates on 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.Comment: 18 pages, 7 figure

Kondo resonance line-shape of magnetic adatoms on decoupling layers

The zero-bias resonance in the dI/dV tunneling spectrum recorded using a scanning tunneling microscope above a spin-1/2 magnetic adatom (such as Ti) adsorbed on a decoupling layer on metal surface can be accurately fitted using the universal spectral function of the Kondo impurity model both at zero field and at finite external magnetic field. Excellent agreement is found both for the asymptotic low-energy part and for the high-energy logarithmic tails of the Kondo resonance. For finite magnetic field, the nonlinear fitting procedure consists in repeatedly solving the impurity model for different Zeeman energies in order to obtain accurate spectral functions which are compared with the experimental dI/dV curves. The experimental results at zero field are sufficiently restraining to enable an unprecedented reliability in the determination of the Kondo temperature, while at finite fields the results are more ambiguous and two different interpretations are proposed

Van Hove singularities in the paramagnetic phase of the Hubbard model: a DMFT study

Using the dynamical mean-field theory (DMFT) we study the paramagnetic phase of the Hubbard model with the density of states (DOS) corresponding to the three-dimensional cubic lattice and the two-dimensional square lattice, as well as a DOS with inverse square root singularity. We show that the electron correlations rapidly smooth out the square-root van Hove singularities (kinks) in the spectral function for the 3D lattice and that the Mott metal-insulator transition (MIT) as well as the magnetic-field-induced MIT differ only little from the well-known results for the Bethe lattice. The consequences of the logarithmic singularity in the DOS for the 2D lattice are more dramatic. At half filling, the divergence pinned at the Fermi level is not washed out, only its integrated weight decreases as the interaction is increased. While the Mott transition is still of the usual kind, the magnetic-field-induced MIT falls into a different universality class as there is no field-induced localization of quasiparticles. In the case of a power-law singularity in the DOS at the Fermi level, the power-law singularity persists in the presence of interaction, albeit with a different exponent, and the effective impurity model in the DMFT turns out to be a pseudo-gap Anderson impurity model with a hybridization function which vanishes at the Fermi level. The system is then a generalized Fermi liquid. At finite doping, regular Fermi liquid behavior is recovered.Comment: 7 pages, 9 figure

Magnetic anisotropy effects on quantum impurities in superconducting host

We study the magnetic anisotropy effects on the localized sub-gap excitations induced by quantum impurities coupled to a superconducting host. We establish the ground-state phase diagrams for single-channel and two-channel high-spin Kondo impurities; they unveil surprising complexity that results from the (multi-stage) Kondo screening in competition with the superconducting correlations and the magnetic anisotropy splitting of the spin multiplets. We discuss the possibility of detecting the Zeeman splitting of the sub-gap states, which would provide an interesting spectroscopic tool for studying the magnetism on the single-atom level. We also study the problem of two impurities coupled by the Heisenberg exchange interaction, and we follow the evolution of the sub-gap states for both antiferromagnetic and ferromagnetic coupling. For sufficiently strong antiferromagnetic coupling, the impurities bind into a singlet state that is non-magnetic, thus the sub-gap states move to the edge of the gap and can no longer be discerned. For ferromagnetic coupling, some excited states remain present inside the gap.Comment: 14 pages, 16 figures (significantly extended version, includes a section on the two-impurity effects