Absence of quantum corrections to the anomalous Hall conductivity

Abstract

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...

Anomalous Hall effect in granular ferromagnetic metals and effects of weak localization

“…For well-conducting samples, the behavior could be well explained by the WL theory 13,15 of the AHE in two-dimensional homogeneously disordered samples. For more resistive samples, however, noticeable deviations from the theoretical predictions were observed.…”

“…Weak localization (WL) effects were studied in Refs. 13,14,15 and it was demonstrated that WL correction to AH conductivity is nonzero 13,14,15 for skewscattering and vanishes 14,15 for side-jump mechanism. The logarithmic temperature dependence of the AH resistivity and the absence of such for the AH conductivity observed in amorphous iron films 16 were initially attributed to the Coulomb interactions 13 and later interpreted 15 in terms of the WL corrections for the side-jump mechanism.…”

“…The Coulomb interaction correction to the AH conductivity has been shown to vanish for both skew-scattering and side-jump mechanisms 13,14 . Weak localization (WL) effects were studied in Refs.…”

Quantized Anomalous Hall Effect in Two-Dimensional Ferromagnets: Quantum Hall Effect in Metals

“…The situation is similar here for the quantized AHE system. In the thin film of Fe, ln T -dependence of σ xx is observed while not for σ xy [20], which is explained by the quantum Coulomb correction combined with the skew scattering mechanism [21].…”

Anomalous Hall effect in epitaxialL10-Mn1.5Ga films with variable chemical ordering

“…This experimental observation of negligible skew scattering caused by weak localization are also supported by the early theoretical work. 25,[29][30] The discrepancies and puzzlingly large n in Figs. 3(a) and (b) should be attributed to their unreasonable presupposition α 0 =α L =α p =α m , i.e.…”