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

We show that the quantum spin Hall (QSH) effect, a state of matter with topological properties distinct from those of conventional insulators, can be realized in mercury telluride–cadmium telluride semiconductor quantum wells. When the thickness of the quantum well is varied, the electronic state changes from a normal to an “inverted” type at a critical thickness d c . We show that this transition is a topological quantum phase transition between a conventional insulating phase and a phase exhibiting the QSH effect with a single pair of helical edge states. We also discuss methods for experimental detection of the QSH effect.

Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells

Recent theory predicted that the quantum spin Hall effect, a fundamentally new quantum state of matter that exists at zero external magnetic field, may be realized in HgTe/(Hg,Cd)Te quantum wells. We fabricated such sample structures with low density and high mobility in which we could tune, through an external gate voltage, the carrier conduction from n-type to p-type, passing through an insulating regime. For thin quantum wells with well width d 6.3 nanometers), the nominally insulating regime showed a plateau of residual conductance close to 2e(2)/h, where e is the electron charge and h is Planck's constant. The residual conductance was independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance was destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, d = 6.3 nanometers, was also independently determined from the magnetic field-induced insulator-to-metal transition. These observations provide experimental evidence of the quantum spin Hall effect.

Quantum Spin Hall Insulator State in HgTe Quantum Wells

Topological insulators are materials with a bulk excitation gap generated by the spin-orbit interaction that are different from conventional insulators. This distinction is characterized by ${Z}_{2}$ topological invariants, which characterize the ground state. In two dimensions, there is a single ${Z}_{2}$ invariant that distinguishes the ordinary insulator from the quantum spin-Hall phase. In three dimensions, there are four ${Z}_{2}$ invariants that distinguish the ordinary insulator from ``weak'' and ``strong'' topological insulators. These phases are characterized by the presence of gapless surface (or edge) states. In the two-dimensional quantum spin-Hall phase and the three-dimensional strong topological insulator, these states are robust and are insensitive to weak disorder and interactions. In this paper, we show that the presence of inversion symmetry greatly simplifies the problem of evaluating the ${Z}_{2}$ invariants. We show that the invariants can be determined from the knowledge of the parity of the occupied Bloch wave functions at the time-reversal invariant points in the Brillouin zone. Using this approach, we predict a number of specific materials that are strong topological insulators, including the semiconducting alloy ${\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x}$ as well as $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Sn}$ and HgTe under uniaxial strain. This paper also includes an expanded discussion of our formulation of the topological insulators in both two and three dimensions, as well as implications for experiments.

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Topological insulators with inversion symmetry

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

Electrically induced electron-spin polarization near the edges of a semiconductor channel was detected and imaged with the use of Kerr rotation microscopy The polarization is out-of-plane and has opposite sign for the two edges, consistent with the predictions of the spin Hall effect Measurements of unstrained gallium arsenide and strained indium gallium arsenide samples reveal that strain modifies spin accumulation at zero magnetic field A weak dependence on crystal orientation for the strained samples suggests that the mechanism is the extrinsic spin Hall effect

https://science.sciencemag.org/content/sci/306/5703/1910.full.pdf

Observation of the spin Hall effect in semiconductors.

Reducing the heat generated in traditional electronics is a chief motivation for the development of spin-based electronics, called spintronics. Spin-based transistors that do not strictly rely on the raising or lowering of electrostatic barriers can overcome scaling limits in charge-based transistors. Spin transport in semiconductors might also lead to dissipation-less information transfer with pure spin currents. Despite these thermodynamic advantages, little experimental literature exists on the thermal aspects of spin transport in solids. A recent and surprising exception was the discovery of the spin-Seebeck effect, reported as a measurement of a redistribution of spins along the length of a sample of permalloy (NiFe) induced by a temperature gradient. This macroscopic spatial distribution of spins is, surprisingly, many orders of magnitude larger than the spin diffusion length, which has generated strong interest in the thermal aspects of spin transport. Here, the spin-Seebeck effect is observed in a ferromagnetic semiconductor, GaMnAs, which allows flexible design of the magnetization directions, a larger spin polarization, and measurements across the magnetic phase transition. This effect is observed even in the absence of longitudinal charge transport. The spatial distribution of spin currents is maintained across electrical breaks, highlighting the local nature of this thermally driven effect.

Observation of the spin-Seebeck effect in a ferromagnetic semiconductor

A consequence of relativity is that in the presence of an electric field, the spin and momentum states of an electron can be coupled; this is known as spin–orbit coupling. Such an interaction opens a pathway to the manipulation of electron spins within non-magnetic semiconductors, in the absence of applied magnetic fields. This interaction has implications for spin-based quantum information processing1 and spintronics2,3, forming the basis of various device proposals4,5,6,7,8. For example, the concept of spin field-effect transistors4,5 is based on spin precession due to the spin–orbit coupling. Most studies, however, focus on non-spin-selective electrical measurements in quantum structures. Here we report the direct measurement of coherent electron spin precession in zero magnetic field as the electrons drift in response to an applied electric field. We use ultrafast optical techniques to spatiotemporally resolve spin dynamics in strained gallium arsenide and indium gallium arsenide epitaxial layers. Unexpectedly, we observe spin splitting in these simple structures arising from strain in the semiconductor films. The observed effect provides a flexible approach for enabling electrical control over electron spins using strain engineering. Moreover, we exploit this strain-induced field to electrically drive spin resonance with Rabi frequencies of up to ∼30 MHz.

http://www.nanoclub.rwth-aachen.de/Kato_Nature_2004_.pdf

Coherent spin manipulation without magnetic fields in strained semiconductors

Spatial imaging of the spin Hall effect and current-induced polarization in two-dimensional electron gases

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The polarization of conduction electron spins due to an electrical current is observed in strained nonmagnetic semiconductors using static and time-resolved Faraday rotation. The density, lifetime, and orientation rate of the electrically polarized spins are characterized by a combination of optical and electrical methods. In addition, the dynamics of the current-induced spins are investigated by utilizing electrical pulses generated from a photoconductive switch. These results demonstrate the possibility of a spin source for semiconductor spintronic devices without the use of magnetic materials.

Roberto C. Myers

Papers

Observation of the spin Hall effect in semiconductors.

Observation of the spin-Seebeck effect in a ferromagnetic semiconductor

Coherent spin manipulation without magnetic fields in strained semiconductors

Spatial imaging of the spin Hall effect and current-induced polarization in two-dimensional electron gases

Current-induced spin polarization in strained semiconductors.