Side-Jump Mechanism for the Hall Effect of Ferromagnets
TL;DR: In this paper, the main Hall-effect mechanism was shown to be the main mechanism for the dc Hall effect for Fe, Ni, and their alloys above 100 K, while asymmetric scattering dominates below 100 K.
Abstract: The center of mass of a wave packet undergoes a discontinuous and finite sideways displacement on scattering by a central potential, in the presence of spin-orbit interaction. This is the main Hall-effect mechanism (${\ensuremath{\rho}}_{H}\ensuremath{\propto}{\ensuremath{\rho}}^{2}$) for Fe, Ni, and their alloys above 100 K, while asymmetric scattering dominates below 100 K. Displacement $\ensuremath{\Delta}y$ per actual collision is calculated by partial waves. In the case of Born expansion, the leading term of $\ensuremath{\Delta}y or \frac{{\ensuremath{\rho}}_{H}}{{\ensuremath{\rho}}^{2}}$ is of zero order in the scattering potential. The magnitude is predicted correctly ($\ensuremath{\Delta}y\ensuremath{\approx}{10}^{\ensuremath{-}10}\ensuremath{-}{10}^{\ensuremath{-}11}$ m) when using the effective spin-orbit Hamiltonian derived by Fivaz from spin-orbit interband mixing. The calculation of ${\ensuremath{\rho}}_{H}$ is extended to arbitrary ${\ensuremath{\omega}}_{c}\ensuremath{\tau}$ for compensated and un-compensated metals. Other nonclassical physical mechanisms proposed by Karplus and Luttinger and by Doniach and by Fivaz are spurious for the dc Hall effect.
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TL;DR: In this paper, a detailed review of the role of the Berry phase effect in various solid state applications is presented. And a requantization method that converts a semiclassical theory to an effective quantum theory is demonstrated.
Abstract: Ever since its discovery, the Berry phase has permeated through all branches of physics. Over the last three decades, it was gradually realized that the Berry phase of the electronic wave function can have a profound effect on material properties and is responsible for a spectrum of phenomena, such as ferroelectricity, orbital magnetism, various (quantum/anomalous/spin) Hall effects, and quantum charge pumping. This progress is summarized in a pedagogical manner in this review. We start with a brief summary of necessary background, followed by a detailed discussion of the Berry phase effect in a variety of solid state applications. A common thread of the review is the semiclassical formulation of electron dynamics, which is a versatile tool in the study of electron dynamics in the presence of electromagnetic fields and more general perturbations. Finally, we demonstrate a re-quantization method that converts a semiclassical theory to an effective quantum theory. It is clear that the Berry phase should be added as a basic ingredient to our understanding of basic material properties.
3,344 citations
Cites background from "Side-Jump Mechanism for the Hall Ef..."
...…to scattering: (i) the skew scattering that refers to the asymmetric scattering amplitude with respect to the scattering angle between the incoming and outgoing electron waves (Smit, 1958), and (ii) the side jump which is a sudden shift of the electron coordinates during scattering (Berger, 1970)....
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...In the past, three mechanisms have been identified: the intrinsic contribution (Karplus and Luttinger, 1954; Luttinger, 1958), and the extrinsic contributions from the skew (Smit, 1958) and side-jump scattering (Berger, 1970)....
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TL;DR: In this paper, a review of experimental and theoretical studies of 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.
Abstract: 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 mechanism, skew scattering from disorder, tends to dominate the AHE in highly conductive ferromagnets. We review the full modern semiclassical treatment of the AHE together with the 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. Finally we discuss outstanding issues and avenues for future investigation.
2,970 citations
Cites background from "Side-Jump Mechanism for the Hall Ef..."
...It is important to note that the above definitions have not relied on identifications of semiclassical processes such as side-jump scattering (Berger, 1970) or skew-scattering from asymmetric contributions to the semiclassical scattering rates (Smit, 1955) identified in earlier theories....
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...The side-jump AHE current was viewed as the product of the side-jump per scattering event and the scattering rate (Berger, 1970)....
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TL;DR: In solid-state materials with strong relativistic spin-orbit coupling, charge currents generate transverse spin currents as discussed by the authors and the associated spin Hall and inverse spin Hall effects distinguish between charge and spin current where electron charge is a conserved quantity but its spin direction is not.
Abstract: In solid-state materials with strong relativistic spin-orbit coupling, charge currents generate transverse spin currents. The associated spin Hall and inverse spin Hall effects distinguish between charge and spin current where electron charge is a conserved quantity but its spin direction is not. This review provides a theoretical and experimental treatment of this subfield of spintronics, beginning with distinct microscopic mechanisms seen in ferromagnets and concluding with a discussion of optical-, transport-, and magnetization-dynamics-based experiments closely linked to the microscopic and phenomenological theories presented.
2,178 citations
IBM1
TL;DR: In this paper, the anisotropic magnetoresistance effect in 3D transition metals and alloys is reviewed, which depends on the orientation of the magnetization with respect to the electric current direction in the material.
Abstract: The anisotropic magnetoresistance effect in 3d transition metals and alloys is reviewed. This effect, found in ferromagnets, depends on the orientation of the magnetization with respect to the electric current direction in the material. At room temperature, the anisotropic resistance in alloys of Ni-Fe and Ni-Co can be greater than 5%. The theoretical basis takes into account spin orbit coupling and d band splitting. Other properties such as permeability, magnetostriction, and Hall voltage have no simple relationship to magnetoresistance. Anisotropic magnetoresistance has an important use as a magnetic field detector for digital recording and magnetic bubbles. Such detectors because of their small size are fabricated using thin film technology. Film studies show that thickness, grain size, and deposition parameters play a significant role in determining the percentage change in magnetoresistance. In general, the change is smaller in films than bulk materials. Several tables and graphs that list bulk and film data are presented.
1,581 citations
TL;DR: In this article, the current status of the field of (III,Mn)V diluted magnetic semiconductors is reviewed, focusing on the first two, more mature research directions: the microscopic origins and fundamental physics of the ferromagnetism that occurs in these systems, and the development of spintronic devices with new functionalities.
Abstract: The body of research on (III,Mn)V diluted magnetic semiconductors initiated during the 1990's has concentrated on three major fronts: i) the microscopic origins and fundamental physics of the ferromagnetism that occurs in these systems, ii) the materials science of growth and defects and iii) the development of spintronic devices with new functionalities. This article reviews the current status of the field, concentrating on the first two, more mature research directions. From the fundamental point of view, (Ga,Mn)As and several other (III,Mn)V DMSs are now regarded as textbook examples of a rare class of robust ferromagnets with dilute magnetic moments coupled by delocalized charge carriers. Both local moments and itinerant holes are provided by Mn, which makes the systems particularly favorable for realizing this unusual ordered state. Advances in growth and post-growth treatment techniques have played a central role in the field, often pushing the limits of dilute Mn moment densities and the uniformity and purity of materials far beyond those allowed by equilibrium thermodynamics. In (III,Mn)V compounds, material quality and magnetic properties are intimately connected. In the review we focus on the theoretical understanding of the origins of ferromagnetism and basic structural, magnetic, magneto-transport, and magneto-optical characteristics of simple (III,Mn)V epilayers, with the main emphasis on (Ga,Mn)As. The conclusions we arrive at are based on an extensive literature covering results of complementary ab initio and effective Hamiltonian computational techniques, and on comparisons between theory and experiment.
1,032 citations