Anomalous Hall effect in ferromagnetic disordered metals (original) (raw)
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Physical Review B, 2007
We consider the Anomalous Hall Effect (AHE) in thin disordered ferromagnetic films. Using a microscopic model of electrons in a random potential of identical impurities including spin-orbit coupling, we develop a general formulation for strong, finite range impurity scattering. Explicit calculations are done within a short range but strong impurity scattering to obtain AH conductivities for both the skew scattering and side jump mechanisms. We also evaluate quantum corrections due to interactions and weak localization effects. We show that for arbitrary strength of the impurity scattering, the electron-electron interaction correction to the AH conductivity vanishes exactly due to general symmetry reasons. On the other hand, we find that our explicit evaluation of the weak localization corrections within the strong, short range impurity scattering model can explain the experimentally observed logarithmic temperature dependences in disordered ferromagnetic Fe films.
Intrinsic mechanism of anomalous Hall effect in a twodimensional magnetic system with impurities
physica status solidi (c), 2006
We report some new results on the Anomalous Hall effect induced by the Berry phase in momentum space. Our main calculations are performed within the model of a two-dimensional electron gas with the spin-orbit interaction of Rashba type, taking into account the scattering from impurities. We demonstrate that such an "intrinsic" mechanism can really dominate but there is a competition between the geometric Berry-phaseinduced term σ II xy in the Hall conductivity and the impurity-induced term σ I xy , related to the contribution of the states in the vicinity of the Fermi surface. We also show that the contribution to the Hall conductivity from the electron states close to the Fermi surface has the intrinsic property as well, and it does not vanish in the clean limit. The main effect of the impurity-related contribution is a possible change of sign of the off-diagonal conductivity. The resulting magnitude and sign of the Hall conductivity strongly depend on the electron density in the system.
Physical Review B, 2016
We develop a first-principles procedure for the individual evaluation of the intrinsic, side-jump, and skew-scattering contributions to the anomalous Hall conductivity σxy. This method is based on the different microscopic conductive processes of each origin of σxy in the Kubo-Bastin formula. We also present an approach for implementing this scheme in the tight-binding linear muffin-tin orbital (TB-LMTO) method with the coherent potential approximation (CPA). The validity of this calculation method is demonstrated for disordered FePt and FePd alloys. We find that the estimated value of each origin of σxy exhibits reasonable dependencies on the electron scattering in these disordered alloys.
Reviews of Modern Physics, 2010
We present a review of experimental and theoretical studies of the anomalous Hall effect (AHE), focusing on recent developments that have provided a more complete framework for understanding this subtle phenomenon and have, in many instances, replaced controversy by clarity. Synergy between experimental and theoretical work, both playing a crucial role, has been at the heart of these advances. On the theoretical front, the adoption of Berry-phase concepts has established a link between the AHE and the topological nature of the Hall currents which originate from spin-orbit coupling. On the experimental front, new experimental studies of the AHE in transition metals, transition-metal oxides, spinels, pyrochlores, and metallic dilute magnetic semiconductors, have more clearly established systematic trends. These two developments in concert with first-principles electronic structure calculations, strongly favor the dominance of an intrinsic Berry-phase-related AHE mechanism in metallic ferromagnets with moderate conductivity. The intrinsic AHE can be expressed in terms of Berry-phase curvatures and it is therefore an intrinsic quantum mechanical property of a perfect cyrstal. An extrinsic mechanisms, skew scattering from disorder, tends to dominate the AHE in highly conductive ferromagnets. We review the full modern semiclassical treatment of the AHE which incorporates an anomalous contribution to wavepacket group velocity due to momentum-space Berry curvatures and correctly combines the roles of intrinsic and extrinsic (skew scattering and side-jump) scattering-related mechanisms. In addition, we review more rigorous quantum-mechanical treatments based on the Kubo and Keldysh formalisms, taking into account multiband effects, and demonstrate the equivalence of all three linear response theories in the metallic regime. Building on results from recent experiment and theory, we propose a tentative global view of the AHE which summarizes the roles played by intrinsic and extrinsic contributions in the disorder-strength vs. temperature plane. Finally we discuss outstanding issues and avenues for future investigation.
Scaling of the anomalous Hall effect in lower conductivity regimes
EPL (Europhysics Letters), 2016
PACS 73.50.-h-Electronic transport phenomena in thin films PACS 73.61.Jc-Amorphous semiconductors; glasses PACS 73.50.Jt-Galvanomagnetic and other magnetotransport effects (including thermomagnetic effects) Abstract-The scaling of the anomalous Hall effect (AHE) was investigated using amorphous and epitaxial FexSi1−x (0.43 <x<0.71) magnetic thin films by varying the longitudinal conductivity (σxx) using two different approaches: modifying the carrier mean free path (l) with chemical or structural disorder while holding the carrier concentration (n h) constant or varying n h and keeping l constant. The anomalous Hall conductivity (σxy), when suitably normalized by magnetization and n h , is shown to be independent of σxx for all samples. This observation suggests a primary dependence on an intrinsic mechanism, unsurprising for the epitaxial high conductivity films where the Berry phase curvature mechanism is expected, but remarkable for the amorphous samples. That the amorphous samples show this scaling indicates a local atomic level description of a Berry phase, resulting in an intrinsic AHE in a system that lacks lattice periodicity.
Spin-Hall conductivity due to Rashba spin-orbit interaction in disordered systems
Physical Review B, 2005
We consider the spin-Hall current in a disordered two-dimensional electron gas in the presence of Rashba spin-orbit interaction. We derive a generalized Kubo-Greenwood formula for the spin-Hall conductivity σ z yx and evaluate it in an systematic way using standard diagrammatic techniques for disordered systems. We find that in the diffusive regime both Boltzmann and the weak localization contributions to σ z yx are of the same order and vanish in the zero frequency limit. We show that the uniform spin current is given by the total time derivative of the magnetization from which we can conclude that the spin current vanishes exactly in the stationary limit. This conclusion is valid for arbitrary spin-independent disorder, external electric field strength, and also for interacting electrons.
Theory of the spin Hall effect, and its inverse, in a ferromagnetic metal near the Curie temperature
Physical Review B, 2012
We give a theory of the inverse spin Hall effect (ISHE) in ferromagnetic metals based on skew scattering via collective spin fluctuations. This extends Kondo's theory of the anomalous Hall effect (AHE) to include short-range spin-spin correlations. We find a relation between the ISHE and the four-spin correlations near the Curie temperature TC. Such four-spin correlations do not contribute to the AHE, which relates to the three-spin correlations. Thus our theory shows an essential difference between the AHE and ISHE, providing an essential complement to Kondo's classic theory of the AHE in metals. We note the relation to skew-scattering mechanisms based on impurity scattering. Our theory can be compared to recent experimental results by Wei et al. [Nat. Commun. 3, 1058] for the ISHE in ferromagnetic alloys.
The effect of disorder within the interaction theory of integer quantized Hall effect
We study effects of disorder on the integer quantized Hall effect within the screening theory, systematically. The disorder potential is analyzed considering the range of the potential fluctuations. Short range part of the single impurity potential is used to define the conductivity tensor elements within the self-consistent Born approximation, whereas the long range part is treated self-consistently at the Hartree level. Using the simple, however, fundamental Thomas-Fermi screening, we find that the long range disorder potential is well screened. While, the short range part is approximately unaffected by screening and is suitable to define the mobility at vanishing magnetic fields. In light of these range dependencies we discuss the extend of the quantized Hall plateaus considering the "mobility" of the wafer and the width of the sample, by re-formulating the Ohm's law at low temperatures and high magnetic fields. We find that, the plateau widths mainly depend on the long range fluctuations of the disorder, whereas the importance of density of states broadening is less pronounced and even is predominantly suppressed. These results are in strong contrast with the conventional single particle pictures. We show that the widths of the quantized Hall plateaus increase with increasing disorder, whereas the level broadening is negligible. This work focuses on the disorder effects on the integer quantized Hall effect within the screening theory. Since the early days of QHE, disorder played a very important role, however, interactions were completely neglected. Here we present our results which also includes interactions in a self-consistent manner and show that even without localization one can obtain the quantized Hall plateaus. We investigated different aspects of the impurity potential and suggested a criterion on mobility at high magnetic fields. We think that our work will shed light on the understanding of the QHE and is interest to condensed matter community.
Physical Review B, 2010
The relativistic nature of the electron motion underlies the intrinsic part of the anomalous Hall effect, believed to dominate in ferromagnetic ͑Ga,Mn͒As. In this paper, we concentrate on the crystal band structure as an important facet to the description of this phenomenon. Using different k · p and tight-binding computational schemes, we capture the strong effect of the bulk inversion asymmetry on the Berry curvature and the anomalous Hall conductivity. At the same time, we find that it does not affect other important characteristics of ͑Ga,Mn͒As, namely, the Curie temperature and uniaxial anisotropy fields. Our results extend the established theories of the anomalous Hall effect in ferromagnetic semiconductors.