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

This article reviews the current status of lattice-dynamical calculations in crystals, using density-functional perturbation theory, with emphasis on the plane-wave pseudopotential method. Several specialized topics are treated, including the implementation for metals, the calculation of the response to macroscopic electric fields and their relevance to long-wavelength vibrations in polar materials, the response to strain deformations, and higher-order responses. The success of this methodology is demonstrated with a number of applications existing in the literature.

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Phonons and related crystal properties from density-functional perturbation theory

We present a comprehensive, up-to-date compilation of band parameters for the technologically important III–V zinc blende and wurtzite compound semiconductors: GaAs, GaSb, GaP, GaN, AlAs, AlSb, AlP, AlN, InAs, InSb, InP, and InN, along with their ternary and quaternary alloys. Based on a review of the existing literature, complete and consistent parameter sets are given for all materials. Emphasizing the quantities required for band structure calculations, we tabulate the direct and indirect energy gaps, spin-orbit, and crystal-field splittings, alloy bowing parameters, effective masses for electrons, heavy, light, and split-off holes, Luttinger parameters, interband momentum matrix elements, and deformation potentials, including temperature and alloy-composition dependences where available. Heterostructure band offsets are also given, on an absolute scale that allows any material to be aligned relative to any other.

Band parameters for III–V compound semiconductors and their alloys

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

We propose an electron wave analog of the electro‐optic light modulator. The current modulation in the proposed structure arises from spin precession due to the spin‐orbit coupling in narrow‐gap semiconductors, while magnetized contacts are used to preferentially inject and detect specific spin orientations. This structure may exhibit significant current modulation despite multiple modes, elevated temperatures, or a large applied bias.

Electronic analog of the electro‐optic modulator

Spin splitting of subband states in semiconductor heterostructures at B=0 is ascribed to the inversion asymmetry--induced bulk ${\mathrm{k}}^{3}$ term, which dominates in large-gap materials, and to the interface spin-orbit or Rashba term, which becomes important in narrow-gap systems. We show for AlGaAs/GaAs heterostructures how this finite spin splitting at B=0 evolves from the Zeeman splitting for B\ensuremath{\ne}0 and predict a vanishing spin splitting at a finite -magnetic- field ---, which depends on the electron concentration in the inversion layer.

Spin splitting in semiconductor heterostructures for B-->0.

The reduced point symmetry ${\mathit{C}}_{2\mathit{v}}$ of a zinc-blende-based (001) interface allows mixing between heavy- and light-hole states even under normal incidence. We have generalized the envelope function approximation to take into account such a mixing by including off-diagonal terms into boundary conditions for the envelopes. The normal off-diagonal hole reflection from a GaAs/AlAs(001) heterointerface as well as \ensuremath{\Gamma}-point interband matrix elements in GaAs/AlAs multilayered structures have been calculated and the results have been compared with those obtained by pseudopotential and tight-binding calculations. The best fit with the numerical calculations gives for the dimensionless heavy-light hole mixing coefficient values ${\mathit{t}}_{\mathit{l}\mathrm{\ensuremath{-}}\mathit{h}}$=0.9 and 0.32. The theory of exchange splitting of excitonic levels in type II GaAs/AlAs superlattices has been extended to include not only the heavy-light hole mixing but also an admixture of spin-orbit-split states in the heavy-hole wave function. An agreement between theory and experiment for the anisotropic exchange splitting has been achieved for ${\mathit{t}}_{\mathit{l}\mathrm{\ensuremath{-}}\mathit{h}}$=0.5. A tight-binding model has been used to relate the microscopic parameters with coefficients in the boundary conditions for the hole envelope function. The tight-binding model estimation of ${\mathit{t}}_{\mathit{l}\mathrm{\ensuremath{-}}\mathit{h}}$=0.44 is in reasonable agreement with the other estimations of ${\mathit{t}}_{\mathit{l}\mathrm{\ensuremath{-}}\mathit{h}}$. \textcopyright{} 1996 The American Physical Society.

Heavy-light hole mixing at zinc-blende (001) interfaces under normal incidence

Nonparabolicity and warping in the conduction band of GaAs

We investigate theoretically the Zeeman effect on the lowest confined electron in quantum wires and quantum dots. A general relation is established between the symmetry of a low-dimensional system and properties of the electron g factor tensor, ${g}_{\ensuremath{\alpha}\ensuremath{\beta}}.$ The powerful method used earlier to calculate the transverse g factor in quantum wells is extended to one-dimensional (1D) and 0D zinc-blende-based nanostructures and analytical expressions are derived in the frame of Kane's model for the g factors in quantum wells, cylindrical wires, and spherical dots. The role of dimensionality is illustrated on two particular heteropairs, ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ and ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{In}}_{x}\mathrm{A}\mathrm{s}/\mathrm{I}\mathrm{n}\mathrm{P}.$ The efficiency of the developed theoretical concept is demonstrated by calculating the three principal values of the g factor tensor in rectangular quantum wires in dependence on the wire width to establish also the connection with the 2D case.

Electron g factor in one- and zero-dimensional semiconductor nanostructures

Quantum resonances in the valence bands of semiconductors under uniaxial stress provide very detailed information on the band parameters if the experimental data can be analyzed on the basis of an adequate theoretical model. Such a model has been developed for and applied to Ge by Hensel and Suzuki and yielded high-precision band parameters for this material. The theory which is based on the invariant expansion of the valence-band Hamiltonian and makes use of the symmetry of the diamond lattice fails, however, to explain similar experiments for InSb. The reason for this failure is twofold: The reduced symmetry of the zinc-blende lattice makes it necessary to consider inversion-asymmetry-induced contributions to the effective Hamiltonian; the small gap of InSb requires an exact treatment of the couplings between valence band and lowest conduction band. Here we present a theory to overcome these difficulties. An effective Hamiltonian, acting in the eightfold space of the valence band and the lowest conduction band of a zinc-blende-type material, is constructed by invariant expansion. For this purpose the method of invariants is extended to the cross space between valence band and conduction band on the basis of the angular momentum calculus. The Hamiltonian describes the Landau levels of valence and conduction bands under uniaxial stress for magnetic fields (parallel to the stress) along the high-symmetry [001], [111], and [110] directions. Since the Hamiltonian is constructed on group-theoretical grounds, the eigenstates can be classified according to their transformation properties, and selection rules are given for both inter- and intraband transitions.

Ulrich Rössler

Papers

Spin splitting in semiconductor heterostructures for B-->0.

Heavy-light hole mixing at zinc-blende (001) interfaces under normal incidence

Nonparabolicity and warping in the conduction band of GaAs

Electron g factor in one- and zero-dimensional semiconductor nanostructures

Quantum resonances in the valence bands of zinc-blende semiconductors. I. Theoretical aspects