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 review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Ne\'el model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed-matter systems.

Spin glasses: Experimental facts, theoretical concepts, and open questions

Band structure of indium antimonide

Character tables for the "group of the wave vector" at certain points of symmetry in the Brillouin zone are given. The additional degeneracies due to time reversal symmetry are indicated. The form of energy vs wave vector at these points of symmetry is derived. A possible reason for the complications which may make a simple effective mass concept invalid for some crystals of this type structure will be presented.

Spin-Orbit Coupling Effects in Zinc Blende Structures

The NMR signals of isotopically or chemically dilute nuclear spins S in solids can be enhanced by repeatedly transferring polarization from a more abundant species I of high abundance (usually protons) to which they are coupled. The gain in power sensitivity as compared with conventional observation of the rare spins approaches NII(I+1)γI2/NSS(S+1)γS2, or ∼ 103 for S = 13C, I = 1H in organic solids. The transfer of polarization is accomplished by any of a number of double resonance methods. High‐frequency resolution of the S ‐spin signal is obtained by decoupling of the abundant spins. The experimental requirements of the technique are discussed and a brief comparison of its sensitivity with other procedures is made. Representative applications and experimental results are mentioned.

Proton‐enhanced NMR of dilute spins in solids

A calculation is given of the indirect exchange ${\mathrm{I}}_{i}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{I}}_{j}$ type coupling of nuclear magnetic moments in a metal by means of the hyperfine interaction with the conduction electrons. The interaction appears to account qualitatively for the broad nuclear spin resonance lines observed in natural metallic silver. It is expected that the interaction may sharpen the resonances in pure isotopic specimens. The line shape of the minority isotope in a binary mixture may tend to be Gaussian, while that of the majority isotope may tend to be Lorentzian, if the indirect exchange interaction is dominant.

Indirect exchange coupling of nuclear magnetic moments by conduction electrons

An experimental and theoretical discussion is given of the results of cyclotron resonance experiments on charge carriers in silicon and germanium single crystals near 4\ifmmode^\circ\else\textdegree\fi{}K. A description is given of the light-modulation technique which gives good signal-to-noise ratios. Experiments with circularly polarized microwave radiation are described. A complete study of anisotropy effects is reported. The electron energy surfaces in germanium near the band edge are prolate spheroids oriented along $〈111〉$ axes with longitudinal mass parameter ${m}_{l}=(1.58\ifmmode\pm\else\textpm\fi{}0.04)m$ and transverse mass parameter ${m}_{t}=(0.082\ifmmode\pm\else\textpm\fi{}0.001)m$. The electron energy surfaces in silicon are prolate spheroids oriented along $〈100〉$ axes with ${m}_{l}=(0.97\ifmmode\pm\else\textpm\fi{}0.02)m$; ${m}_{t}=(0.19\ifmmode\pm\else\textpm\fi{}0.01)m$. The energy surfaces for holes in both germanium and silicon have the form $E(k)=A{k}^{2}\ifmmode\pm\else\textpm\fi{}{[{B}^{2}{k}^{4}+{C}^{2}({{k}_{x}}^{2}{{k}_{y}}^{2}+{{k}_{y}}^{2}{{k}_{z}}^{2}+{{k}_{z}}^{2}{{k}_{x}}^{2})]}^{\frac{1}{2}}.$ We find, for germanium, $A=\ensuremath{-}(13.0\ifmmode\pm\else\textpm\fi{}0.2)(\frac{{\ensuremath{\hbar}}^{2}}{2m})$, $|B|=(8.9\ifmmode\pm\else\textpm\fi{}0.1)(\frac{{\ensuremath{\hbar}}^{2}}{2m})$, $|C|=(10.3\ifmmode\pm\else\textpm\fi{}0.2)(\frac{{\ensuremath{\hbar}}^{2}}{2m})$; and for silicon, $A=\ensuremath{-}(4.1\ifmmode\pm\else\textpm\fi{}0.2)(\frac{{\ensuremath{\hbar}}^{2}}{2m})$, $|B|=(1.6\ifmmode\pm\else\textpm\fi{}0.2)(\frac{{\ensuremath{\hbar}}^{2}}{2m})$, $|C|=(3.3\ifmmode\pm\else\textpm\fi{}0.5)(\frac{{\ensuremath{\hbar}}^{2}}{2m})$. A discussion of possible systematic errors in these constants is given in the paper.

Cyclotron Resonance of Electrons and Holes in Silicon and Germanium Crystals

The molecular field treatment of the magnetic properties of ferrites given by N\'eel is extended to take into account the antiferromagnetic exchange interactions within the two magnetic sublattices. On further subdividing the two lattices, we show that the ground state may, (1) have an antiparallel arrangement of the spins on the two sites; or (2) consist of a triangular arrangement of the spins on the sublattices; or (3) have antiferromagnetism in each of the two sites separately. We also show that transitions between various configurations may occur in the same substance at different temperatures, without the assumption of temperature-dependent interactions. Neutron diffraction experiments and specific heat measurements are suggested for the detection of the predicted arrangements.

Antiferromagnetic Arrangements in Ferrites

An antiferroelectric state is defined as one in which lines of ions in the crystal are spontaneously polarized, but with neighboring lines polarized in antiparallel directions. In simple cubic lattices the antiferroelectric state is likely to be more stable than the ferroelectric state. The dielectric constant above and below the antiferroelectric curie point is investigated for both first- and second-order transitions. In either case the dielectric constant need not be very high; but if the transition is second order, $\ensuremath{\epsilon}$ is continuous across the Curie point. The antiferroelectric state will not be piezoelectric. The thermal anomaly near the Curie point will be of the same nature and magnitude as in ferroelectrics. A susceptibility variation of the form $\frac{C}{(T+\ensuremath{\theta})}$ as found in strontium titanate is not indicative of antiferroelectricity, unlike the corresponding situation in antiferromagnetism.

Theory of Antiferroelectric Crystals

A field-theoretical treatment is given of the magnetoelastic coupling of magnons and phonons in a ferromagnetic crystal. The effects of the coupling are large when the wavelengths and frequencies of the two fields are equal. If the two transverse phonon states of a given wave vector are degenerate, then the rotatory dispersion of the phonons will be large. The possibility exists of creating nonreciprocal acoustic elements, such as acoustic gyrators. At simultaneous resonance the phonon attenuation is expected to be large. The possibility of magnetostrictive transducers at microwave frequencies is discussed. A calculation is given of the damping by eddy currents of spin waves in a metal.

C. Kittel

Papers

Indirect exchange coupling of nuclear magnetic moments by conduction electrons

Cyclotron Resonance of Electrons and Holes in Silicon and Germanium Crystals

Antiferromagnetic Arrangements in Ferrites

Theory of Antiferroelectric Crystals

Interaction of Spin Waves and Ultrasonic Waves in Ferromagnetic Crystals