Spin-Orbit-Induced Kondo Size Effect in Thin Films with 5/2-spin Impurities

Recently, for spin $S=5/2$ impurities quite different size dependence of the Kondo contribution to the resistivity was found experimentally than for S=2. Therefore previous calculation about the effect of the spin-orbit-induced magnetic anisotropy on the Kondo amplitude of the resistivity is extended to the case of $S=5/2$ impurity spin which differs from the integer spin case as the ground state is degenerated. In this case the Kondo contribution remains finite when the sample size goes to zero and the thickness dependence in the Kondo resistivity is much weaker for Cu(Mn). The behavior of the Kondo coefficient as a function of the thickness depends on the Kondo temperature, that is somewhat stronger for larger $T_K$. Comparing our results with a recent experiment in thin Cu(Mn) films, we find a good agreement.Comment: 8 pages, ReVTeX + 4 figures (Postscript

Shape-induced magnetic anisotropy in dilute magnetic alloys

We extend the theory of the surface-induced magnetic anisotropy to mesoscopic samples with arbitrary geometry. The shape-induced anisotropy of impurity spins in small brick-shaped grains of dilute magnetic alloys is studied in detail. The surface-induced blocking of a magnetic-impurity spin is shown to be very sensitive to geometric parameters of a grain. This implies that the apparent discrepancy between the experimental data of different groups on the size dependence of the Kondo resistivity can result from different microstructure of the used samples. In order to interpret recent experimental data on the anomalous Hall effect in thin polycrystalline Fe doped Au films, we analyse the magnetisation of impurity spins as a function of the impurity position and of the grain shape.Comment: 10 pages, 6 figures, E-mail addresses: [email protected], [email protected], [email protected]

Revised theory of the magnetic surface anisotropy of impurities in metallic mesoscopic samples

In several experiments the magnitude of the contribution of magnetic impurities to the Kondo resistivity shows size dependence in mesoscopic samples. It was suggested ten years ago that magnetic surface anisotropy can be responsible for the size dependence in cases where there is strong spin-orbit interaction in the metallic host. The anisotropy energy has the form $\Delta E=K_d ({\bf n}{\bf S})^2$ where ${\bf n}$ is the vector perpendicular to the plane surface, ${\bf S}$ is the spin of the magnetic impurity and $K_d>0$ is inversely proportional to distance $d$ measured from the surface. It has been realized that in the tedious calculation an unjustified approximation was applied for the hybridizations of the host atom orbitals with the conduction electrons which depend on the position of the host atoms. Namely, the momenta of the electrons were replaced by the Fermi momentum $k_F$. That is reinvestigated considering the $k$-dependence which leads to singular energy integrals and in contrary to the previous result $K_d$ is oscillating like $\sin (2 k_F d)$ and the distance dependence goes like $1/d^3$ in the asymptotic region. As the anisotropy is oscillating, for integer spin the ground state is either a singlet or a doublet depending on distance $d$, but in the case of the doublet there is no direct electron induced transition between those two states at zero temperature. Furthermore, for half-integer ($S > 1/2$) spin it is always a doublet with direct transition only in half of the cases.Comment: 10 pages, 4 figure

Theory of magnetoresistance in films of dilute magnetic alloys

Earlier a magnetic anisotropy for magnetic impurities nearby the surface of non-magnetic host was proposed in order to explain the size dependence of the Kondo effect in dilute magnetic alloys. Recently Giordano has measured the magnetoresistance of dilute Au(Fe) films for different thicknesses well above the Kondo temperature $T_K$. In this way he verified the existence of that anisotropy even for such a case where the Kondo effect is not dominating. For detailed comparison of that suggestion with experiments, the magnetic field dependence of the magnetoresistance is calculated in the lowest approximation, thus in the second order of the exchange coupling. The strength of the anisotropy is very close to earlier estimates deduced from the size dependence of the Kondo resistivity amplitude.Comment: (11 pages, 8 figures, essential changes compared to the old version

Spin-Orbit-Induced Magnetic Anisotropy for Impurities in Metallic Samples I. Surface Anisotropy

Motivated by the recent measurements of Kondo resistivity in thin films and wires, where the Kondo amplitude is suppressed for thinner samples, the surface anisotropy for magnetic impurities is studied. That anisotropy is developed in those cases where in addition to the exchange interaction with the impurity there is strong spin-orbit interaction for conduction electrons around the impurity in the ballistic region. The asymmetry in the neighborhood of the magnetic impurity exhibits the anisotropy axis $n$ which, in the case of a plane surface, is perpendicular to the surface. The anisotropy energy is $\Delta E=K_d (nS)^2$ for spin $S$, and the anisotropy constant $K_d$ is inversionally proportional to distance $d$ measured from the surface and $K_d>0$. Thus at low temperature the spin is frozen in a singlet or doublet of lowest energy. The influence of that anisotropy on the electrical resistivity is the subject of the following paper (part II).Comment: 28 pages, RevTeX (using epsfig), 8 eps figures included, submitted to PR

Microscopic theory for quantum mirages in quantum corrals

Scanning tunneling microscopy permits to image the Kondo resonance of a single magnetic atom adsorbed on a metallic surface. When the magnetic impurity is placed at the focus of an elliptical quantum corral, a Kondo resonance has been recently observed both on top of the impurity and on top of the focus where no magnetic impurity is present. This projection of the Kondo resonance to a remote point on the surface is referred to as quantum mirage. We present a quantum mechanical theory for the quantum mirage inside an ideal quantum corral and predict that the mirage will occur in corrals with shapes other than elliptical

Energy relaxation due to magnetic impurities in mesoscopic wires: Logarithmic approach

The transport in mesoscopic wires with large applied bias voltage has recently attracted great interest by measuring the energy distribution of the electrons at a given point of the wire, in Saclay. In the diffusive limit with negligible energy relaxation that shows two sharp steps at the Fermi energies of the two contacts, which are broadened due to the energy relaxation. In some of the experiments the broadening is reflecting an anomalous energy relaxation rate proportional to $E^{-2}$ instead of $E^{-3/2}$ valid for Coulomb electron-electron interaction, where $E$ is the energy transfer. Later it has been suggested that such relaxation rate can be due to electron-electron interaction mediated by Kondo impurities. In the present paper the latter is systematically studied in the logarithmic approximation valid above the Kondo temperature. In the case of large applied bias voltage Kondo resonances are formed at the steps of the distribution function and they are narrowed by increasing the bias. An additional Korringa energy broadening occurs for the spins which smears the Kondo resonances, and the renormalized coupling can be replaced by a smooth but essentially enhanced average coupling (factor of 8-10). Thus the experimental data can be described by formulas without logarithmic Kondo corrections, but with enhanced coupling. In certain regions of large bias, that averaged coupling depends weakly on the bias. In those cases the distribution function depends only on the ratio of the electron energy and the bias, showing scaling behavior. The impurity concentrations estimated from those experiments and other dephasing experiments can be very different, and a possible explanation considering the surface spin anisotropy due to strong spin-orbit interaction is the subject of our earlier paper.Comment: 12 pages, RevTex

Spin-Orbit-Induced Magnetic Anisotropy for Impurities in Metallic Samples II. Finite Size Dependence in the Kondo Resistivity

The electrical resistivity including the Kondo resistivity increase at low temperature is calculated for thin films of dilute magnetic alloys. Assuming that in the non-magnetic host the spin-orbit interaction is strong like in Au and Cu, the magnetic impurities have a surface anisotropy calculated in part I. That anisotropy hinders the motion of the spin. Including that anisotropy the effective electron-impurity coupling is calculated by using the second order renormalization group equations. The amplitude of the Kondo resistivity contribution is reduced as the position of the impurity approaches the surface but the increase occurs approximately at the bulk Kondo temperature. Different proximity effects observed by Giordano are also explained qualitatively where the films of magnetic alloys are covered by pure second films with different mean free path. The theory explains the experimental results in those cases where a considerable amount of impurities is at the surface inside the ballistic region.Comment: 39 pages, RevTeX (using epsfig), 15 eps figures included, submitted to PR

Many-body theory of the quantum mirage

In recent scanning tunneling microscopy experiments, confinement in an elliptical corral has been used to project the Kondo effect from one focus to the other one. I solve the Anderson model at arbitrary temperatures, for an impurity hybridized with eigenstates of an elliptical corral, each of which has a resonant level width delta. This width is crucial. If delta < 20 meV, the Kondo peak disappears, while if delta > 80 meV, the mirage disappears. For particular conditions, a stronger mirage with the impurity out of the foci is predicted.Comment: 5 pages, 5 figures. Some clarifications of the method added, and a reference included to show that the hybridization of the impurity with bulk states can be neglecte