The conduction electron density of states nearby single magnetic impurities, as measured recently by scanning tunneling microscopy (STM), is calculated, taking into account tunneling into conduction electron states only. The Kondo effect induces a narrow Fano resonance in the conduction electron density of states, while scattering off the d-level generates a weakly energy dependent Friedel oscillation. The line shape varies with the distance between STM tip and impurity, in qualitative agreement with experiments, but is very sensitive to details of the band structure. For a Co impurity the experimentally observed width and shift of the Kondo resonance are in accordance with those obtained from a combination of band structure and strongly correlated calculations. [3] surfaces by measuring the I-V characteristics of the tunneling current through the tip of a scanning tunneling microscope (STM) placed close to the surface and at a small distance R from the magnetic atom (see Fig. 1 (inset)).Although the Kondo resonance, formed in the local conduction electron density of states (LDOS) at the Fermi energy ε F due to resonant spin flip scattering, has been known for a long time [5], the precise line shape was not studied earlier because of the limited spatial resolution available in experiments. Wide tunnel junctions, which were proposed as measurement devices [6], probe the averaged DOS rather than the LDOS. Such experiments exhibited a giant zero bias resistance peak [7,8] or a weak conductance peak, the latter induced by assisted tunneling through impurities in the tunnel barrier [9,10].In the present Letter we present a detailed microscopic study of the Kondo line shape as measured by STM in the vicinity of a single magnetic ion. We assume that the STM current is predominantly due to tunneling into the conduction LDOS, i.e. we neglect direct tunneling into the d-or f-level of a Co or Ce ion. This assumption is justified, because the d-or f-level is localized deeply in the atomic core, and is sufficient to explain the experimental findings as seen below. When a discrete (single-particle) level is coupled to the conduction electron sea (bare DOS ρ 0 ) via a hybridization V , there is a twofold effect: (1) the discrete level is broadened and (2) the continuous conduction LDOS becomes modified. The resulting line shape in the LDOS is called Fano resonance, in reminiscence of the first study of this problem in the context of atomic physics [4]. Here we generalize this problem to the interacting case, i.e. when the discrete level arises from a many-body effect, like the Kondo resonance. It is shown that the many-body correlation effects and the consecutive Fano line shape in the conduction LDOS may be understood in separate steps, thus greatly simplifying the theoretical treatment as compared to other studies [2,11].For concreteness we focus on a Co atom on Au and use the Anderson model [12] with a fivefold orbital degeneracy of the d-level ε d < 0, m = 1 . . . 5,whereis the kinetic energy of the conduction electrons, ...

We demonstrate the artificial construction of magnetic atom chains on a conventional superconductor as a Majorana platform.

In order to study spin-wave excitations of itinerant ferromagnets a relativistic first-principles method based on the adiabatic approach is presented. The derivatives of the free energy up to second order with respect of the polar and azimuthal angles are derived within the framework of the magnetic force theorem and the fully relativistic Korringa-Kohn-Rostoker method. Exchange and spin-orbit coupling are thus incorporated on equal footing in the Hamiltonian. Furthermore, a detailed comparison to classical spin Hamiltonians is given and it is shown that the magnetocrystalline anisotropy energy contains contributions from both the on-site anisotropy and the off-site exchange coupling terms. The method is applied to an Fe monolayer on Cu͑001͒ and Au͑001͒ surfaces and for a Co monolayer on Cu͑001͒. The calculations provide with the gap at zero wave number due to the spin-orbit coupling and uniaxial anisotropy energies in good agreement with the results of the band energy difference method. It is pointed out that the terms in the spin-wave Hamiltonian related to the mixed partial derivatives of the free energy, absent within a nonrelativistic description, introduce an asymmetry in the magnon spectrum with respect to two in-plane easy axes. Moreover, in the case of an in-plane magnetized system the long-wavelength magnons are elliptically polarized due to the difference of the second-order uniaxial and fourth-order in-plane magnetic anisotropy.

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