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We discuss quantum corrections to the anomalous Hall conductivity in disordered metallic films containing magnetic moments. Within a model of skew scattering we show that Coulomb-anomaly terms vanish identically. The weak-localization contribution is cut off by the phase-breaking effect of skew scattering. In a dense system of magnetic moments, the internal magnetic field may cause a more rapid destruction of phase coherence. Our findings are in agreement with a recent experiment on ferromagnetic amorphous Fe films.PACS numbers: 72.15.Rn, 72.15.Gd Scale-dependent corrections to the transport coefficients of disordered systems have been studied in great detail, both theoretically and experimentally, for the past ten years [1][2][3]. The effects of quantum interference as a function of scale size of a disordered, noninteracting electron system, known as weak localization, were first discussed by Abrahams, Anderson, Licciardello, and Ramakrishnan [4] within the context of a scaling theory of localization. At about the same time, Altshuler and Aronov discovered quantum corrections to the thermodynamic and transport properties of a weakly interacting strongly disordered electron system [5] known as the "Coulomb anomaly." Similar corrections are generated by Cooper-pair fluctuations [1].Whereas weak-localization contributions are well understood by now, the interaction-induced quantum corrections predicted theoretically [1,5] have not yet been confirmed experimentally to the same extent. These latter corrections are caused by two different physical effects, both related to the slowing down of the motion of diffusing electrons in a disordered metal as compared to propagating electrons in a clean metal. First, the dynamically screened Coulomb interaction is enhanced, as the screening is less effective at finite frequency. Second, the probability for two electrons to stay close together is higher, thus increasing the effect even of well-screened, short-ranged interactions. A recent experiment designed to prove the long-range nature of the dynamically screened Coulomb interaction did not confirm these theoretical expectations [6].It is therefore of interest to have a new, independent test of the theory. Such a new probe is the anomalous Hall effect [7,8] shown by disordered metallic films containing localized magnetic moments oriented normal to the film surface. It is well known [8] that magnetic moments in metals may give rise to "skew scattering," i.e., an asymmetry of the scattering with respect to positive and negative scattering angles in the plane perpendicular to the direction of the magnetic moment M. The resulting anomalous Hall conductivity is proportional to the magnetization (or sublattice magnetization) in polarized paramagnetic, ferromagnetic, or antiferromagnetic systems [7,8]. In contrast to the ordinary Hall effect, the anomalous Hall conductivity of, e.g., a saturated ferromagnetic system is independent of an applied external magnetic field. Its microscopic mechanism is quite different from the usual Lore...

Abstract. We consider the formation and the Kondo effect of local magnetic moments in the Anderson-Hubbard model with off-diagonal disorder. The existence of moments at sites weakly coupled to the environment is deduced in effective medium approximation. The distribution of moments is calculated both deep in the metallic phase and near the metal-insulator transition. We discuss the Kondo quenching of the moments and derive a distribution of local Kondo temperatures. Recent experimental studies of metallic samples of doped semiconductors have indicated that localized magnetic moments are formed in the metallic phase as these systems approach the metal-insulator transition [ 1 -71. In fact the contribution of these moments dominates the magnetic and thermodynamic properties at low temperatures. The moments are thought to be intrinsic, i.e formed by the same dopant atoms that form the impurity conduction band, rather than being due to additional magnetic ions. There are two issues involved here: (i) the formation of moments, (ii) the eventual quenching of the moments due to coupling to the environment or among each other at low temperature. According to the conventional picture of moment formation [8], a spindegenerate atomic level of an impurity placed sufficiently below the Fermi energy is split by the Coulomb interaction into two levels. There is a level at the original position involving single occupancy and an upper level above the Fermi energy involving double occupancy. Provided the coupling of the conduction electrons to the local impurity is sufficiently weak, the impurity will be occupied by a single electron to a good approximation, and will hence form a spin + local magnetic moment. In the case of doped semiconductors the levels forming the conduction band and the magnetic impurity belong to the same system of dopant atoms, which therefore may be described by a one-band model. The atomic levels are the same at each dopant site, but the hopping elements are not, as the dopant atoms occupy random lattice sites in the host crystal lattice (we neglect possible short-range order correlation). In the metallic regime, i.e. for sufficiently large doping concentration, an impurity conduction band is formed, the Fermi energy lying in the center of the band, at the position of the atomic levels, for the uncompensated materials. Even though at first sight there appears to be no close similarity with above-described picture of the Anderson magnetic impurity, since

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