Spintronics, or spin electronics, involves the study of active control and manipulation of spin degrees of freedom in solid-state systems. This article reviews the current status of this subject, including both recent advances and well-established results. The primary focus is on the basic physical principles underlying the generation of carrier spin polarization, spin dynamics, and spin-polarized transport in semiconductors and metals. Spin transport differs from charge transport in that spin is a nonconserved quantity in solids due to spin-orbit and hyperfine coupling. The authors discuss in detail spin decoherence mechanisms in metals and semiconductors. Various theories of spin injection and spin-polarized transport are applied to hybrid structures relevant to spin-based devices and fundamental studies of materials properties. Experimental work is reviewed with the emphasis on projected applications, in which external electric and magnetic fields and illumination by light will be used to control spin and charge dynamics to create new functionalities not feasible or ineffective with conventional electronics.

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Spintronics: Fundamentals and applications

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.

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Berry phase effects on electronic properties

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.

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Anomalous hall effect

A revolution in electronics is in view, with the contemporary evolution of the two novel disciplines of spintronics and molecular electronics. A fundamental link between these two fields can be established using molecular magnetic materials and, in particular, single-molecule magnets. Here, we review the first progress in the resulting field, molecular spintronics, which will enable the manipulation of spin and charges in electronic devices containing one or more molecules. We discuss the advantages over more conventional materials, and the potential applications in information storage and processing. We also outline current challenges in the field, and propose convenient schemes to overcome them.

Molecular spintronics using single-molecule magnets

Electrons have a charge and a spin, but until recently these were considered separately. In classical electronics, charges are moved by electric fields to transmit information and are stored in a capacitor to save it. In magnetic recording, magnetic fields have been used to read or write the information stored on the magnetization, which 'measures' the local orientation of spins in ferromagnets. The picture started to change in 1988, when the discovery of giant magnetoresistance opened the way to efficient control of charge transport through magnetization. The recent expansion of hard-disk recording owes much to this development. We are starting to see a new paradigm where magnetization dynamics and charge currents act on each other in nanostructured artificial materials. Ultimately, 'spin currents' could even replace charge currents for the transfer and treatment of information, allowing faster, low-energy operations: spin electronics is on its way.

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The emergence of spin electronics in data storage

A perturbative theory of magnetocrystalline anisotropy and orbital moment in itinerant ferromagnets is presented that clearly outlines the close connection between these two quantities. The theory is used to study the magnetocrystalline anisotropy in transition-metal monolayers. The importance of the crystal-field energy and of the filling of the valence band is emphasized. For the first time the orbital contribution to the magnetization in monolayers is estimated; it is shown that it may produce an anisotropy in the magnetization of the order of 0.1\ensuremath{\mu}B per atom.

Tight-binding approach to the orbital magnetic moment and magnetocrystalline anisotropy of transition-metal monolayers

We have derived the expression of the Ruderman-Kittel-Kasuya-Yosida coupling between two ferromagnetic layers separated by a nonmagnetic spacer, for arbitrary crystal structure and Fermi surface. For the first time, quantitative predictions of the interlayer coupling for Cu, Ag, and Au spacers are given. The results are in good agreement with recent experimental data for fcc Co/Cu and Fe/Cu systems.

Oscillatory coupling between ferromagnetic layers separated by a nonmagnetic metal spacer.

The long-range ordered surface alloy Bi/Ag(111) is found to exhibit a giant spin splitting of its surface electronic structure due to spin-orbit coupling, as is determined by angle-resolved photoelectron spectroscopy. First-principles electronic structure calculations fully confirm the experimental findings. The effect is brought about by a strong in-plane gradient of the crystal potential in the surface layer, in interplay with the structural asymmetry due to the surface-potential barrier. As a result, the spin polarization of the surface states is considerably rotated out of the surface plane.

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Giant spin splitting through surface alloying.

A theory of interlayer exchange coupling is presented. A detailed and comprehensive discussion of the various aspects of the problem is given. The interlayer exchange coupling is described in terms of quantum interferences due to confinement in ultrathin layers. This approach provides both a physically transparent picture of the coupling mechanism, and a suitable scheme for discussing the case of a realistic system. This is illustrated for the Co/Cu/Co(001) system. The cases of metallic and insulating spacers are treated in a unified manner by introducing the concept of the complex Fermi surface.

Theory of interlayer magnetic coupling

We discuss the anomalous Hall effect in a two-dimensional electron gas subject to a spatially varying magnetization. This topological Hall effect does not require any spin-orbit coupling and arises solely from Berry phase acquired by an electron moving in a smoothly varying magnetization. We propose an experiment with a structure containing 2D electrons or holes of diluted magnetic semiconductor subject to the stray field of a lattice of magnetic nanocylinders. The striking behavior predicted for such a system (of which all relevant parameters are well known) allows one to observe unambiguously the topological Hall effect and to distinguish it from other mechanisms.

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Patrick Bruno

Papers

Tight-binding approach to the orbital magnetic moment and magnetocrystalline anisotropy of transition-metal monolayers

Oscillatory coupling between ferromagnetic layers separated by a nonmagnetic metal spacer.

Giant spin splitting through surface alloying.

Theory of interlayer magnetic coupling

Topological Hall effect and Berry phase in magnetic nanostructures.