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

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

Friedel oscillations induced surface magnetic anisotropy

We present detailed numerical studies of the magnetic anisotropy energy of a magnetic impurity near the surface of metallic hosts (Au and Cu), that we describe in terms of a realistic tight-binding surface Green's function technique. We study the case when spin-orbit coupling originates from the d-band of the host material and we also investigate the case of a strong local spin-orbit coupling on the impurity itself. The splitting of the impurity's spin-states is calculated to leading order in the exchange interaction between the impurity and the host atoms using a diagrammatic Green's function technique. The magnetic anisotropy constant is an oscillating function of the separation d from the surface: it asymptotically decays as 1/d2 and its oscillation period is determined by the extremal vectors of the host's Fermi Surface. Our results clearly show that the host-induced magnetic anisotropy energy is by several orders of magnitude smaller than the anisotropy induced by the local mechanism, which provides sufficiently large anisotropy values to explain the size dependence of the Kondo resistance observed experimentally.Comment: 11 pages, 7 figures, submitted to PR

Low Temperature Anomaly in Mesoscopic Kondo Wires

We report the observation of an anomalous magnetoresistance in extremely dilute quasi-one-dimensional AuFe wires at low temperatures, along with a hysteretic background at low fields. The Kondo resistivity does not show the unitarity limit down to the lowest temperature, implying uncompensated spin states. We suggest that the anomalous magnetoresistance may be understood as the interference correction from the accumulation of geometric phase in the conduction electron wave function around the localized impurity spin.Comment: Four pages, five figure

Effect of annealing on electron dephasing in three-dimensional polycrystalline metals

We have studied the effect of thermal annealing on electron dephasing times $\tau_\phi$ in three-dimensional polycrystalline metals. Measurements are performed on as-sputtered and annealed AuPd and Sb thick films, using weak-localization method. In all samples, we find that $\tau_\phi$ possesses an extremely weak temperature dependence as $T \to 0$. Our results show that the effect of annealing is non-universal, and it depends strongly on the amount of disorder quenched in the microstructures during deposition. The observed "saturation" behavior of $\tau_\phi$ cannot be easily explained by magnetic scattering. We suggest that the issue of saturation can be better addressed in three-dimensional, rather than lower-dimensional, structures

Kondo Effect on Mesoscopic Scale (Review)

Following the discovery of the Kondo effect the bulk transport and magnetic behavior of the dilute magnetic alloys have been successfully described. In the last fifteen years new directions have been developed as the study of the systems of reduced dimensions and the artificial atoms so called quantum dots. In this review the first subject is reviewed starting with the scanning tunneling microscope (STM) study of a single magnetic impurity. The next subject is the reduction of the amplitude of the Kondo effect in samples of reduced dimension which was explained by the surface magnetic anisotropy which blocks the motion of the integer spin nearby the surface. The electron dephasing and energy relaxation experiments are discussed with the possible explanation including the surface anisotropy, where the situation in cases of integer and half-integer spins is very different. Finally, the present situation of the theory of dynamical structural defects is briefly presented which may lead to two-channel Kondo behavior.Comment: 8 pages, submitted to the JPSJ Special Issue "Kondo effect -- 40 years after the Discovery

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

Size Dependence In The Disordered Kondo Problem

We study here the role randomly-placed non-magnetic scatterers play on the Kondo effect. We show that spin relaxation effects (with time $\tau_s^o$)in the vertex corrections to the Kondo self-energy lead to an exact cancellation of the singular temperature dependence arising from the diffusion poles. For a thin film of thickness $L$ and a mean-free path $\ell$, disorder provides a correction to the Kondo resistivity of the form $\tau_s^o/(k_FL\ell^2)\ln T$ that explains both the disorder and sample-size depression of the Kondo effect observed by Blachly and Giordano (PRB {\bf 51}, 12537 (1995)).Comment: 11 pages, LaTeX, 2 Postscript figure

The Kondo Box: A Magnetic Impurity in an Ultrasmall Metallic Grain

We study the Kondo effect generated by a single magnetic impurity embedded in an ultrasmall metallic grain, to be called a ``Kondo box''. We find that the Kondo resonance is strongly affected when the mean level spacing in the grain becomes larger than the Kondo temperature, in a way that depends on the parity of the number of electrons on the grain. We show that the single-electron tunneling conductance through such a grain features Kondo-induced Fano-type resonances of measurable size, with an anomalous dependence on temperature and level spacing.Comment: 4 Latex pages, 4 figures, submitted to Phys. Rev. Let