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 paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.

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Many-Body Physics with Ultracold Gases

The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented, together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover, the role and the complexity of escape in driven systems exhibiting possibly multiple, metastable stationary nonequilibrium states is identified. At lower temperatures, quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed, thereby providing a description of dissipative escape events at all temperatures. In addition, an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.

Reaction-rate theory: fifty years after Kramers

We describe an ab initio method for calculating the electronic structure, electronic transport, and forces acting on the atoms, for atomic scale systems connected to semi-infinite electrodes and with an applied voltage bias. Our method is based on the density-functional theory (DFT) as implemented in the well tested SIESTA approach (which uses nonlocal norm-conserving pseudopotentials to describe the effect of the core electrons, and linear combination of finite-range numerical atomic orbitals to describe the valence states). We fully deal with the atomistic structure of the whole system, treating both the contact and the electrodes on the same footing. The effect of the finite bias (including self-consistency and the solution of the electrostatic problem) is taken into account using nonequilibrium Green's functions. We relate the nonequilibrium Green's function expressions to the more transparent scheme involving the scattering states. As an illustration, the method is applied to three systems where we are able to compare our results to earlier ab initio DFT calculations or experiments, and we point out differences between this method and existing schemes. The systems considered are: (i) single atom carbon wires connected to aluminum electrodes with extended or finite cross section, (ii) single atom gold wires, and finally (iii) large carbon nanotube systems with point defects.

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Density-functional method for nonequilibrium electron transport

Density functional approximations for the exchange‐correlation energy EDFAxc of an electronic system are often improved by admixing some exact exchange Ex: Exc≊EDFAxc+(1/n)(Ex−EDFAx). This procedure is justified when the error in EDFAxc arises from the λ=0 or exchange end of the coupling‐constant integral ∫10 dλ EDFAxc,λ. We argue that the optimum integer n is approximately the lowest order of Gorling–Levy perturbation theory which provides a realistic description of the coupling‐constant dependence Exc,λ in the range 0≤λ≤1, whence n≊4 for atomization energies of typical molecules. We also propose a continuous generalization of n as an index of correlation strength, and a possible mixing of second‐order perturbation theory with the generalized gradient approximation.

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Rationale for mixing exact exchange with density functional approximations

A strong exchange field, such as produced by ferromagnetically aligned impurities in a metal, will tend to polarize the conduction electron spins. If the metal is a superconductor, this will happen only if the spin-exchange field is sufficiently strong compared to the energy gap. When the field is strong enough to break many electron pairs, the self-consistent gap equation is modified and a new type of depaired superconducting ground state occurs. In the idealization of a spatially uniform exchange field with no scattering, it is found that the depaired state has a spatially dependent complex Gorkov field, corresponding to a nonzero pairing momentum in the BCS model. The presence of the "normal" electrons from the broken pairs reduces the total current to zero, gives the depaired state some spin polarization, and results in almost normal Sommerfeld specific heat and single-electron tunneling characteristics. The nonzero value of the pairing momentum also gives rise to an unusual anisotropic electrodynamic behavior of the superconductor, as well as to a degenerate ground state and low-lying collective excitations, in accordance with Goldstone's theorem. The effects of scattering in an actual superconducting ferromagnetic alloy have not been studied and may interfere with experimental investigation of the theoretical results found in this paper for the idealized model.

Superconductivity in a Strong Spin-Exchange Field

1. Introduction.- 2. The Independent-Electron Approximation.- 2.1 Starting Hamiltonian.- 2.2 Basis Functions and Basis Sets.- 2.3 Self-Consistent Field Approximation.- 2.4 Simplified SCF Calculational Schemes.- 2.4.1 Semi-empirical SCF Methods.- 2.4.2 Pseudopotentials.- 2.5 Koopmans' Theorem.- 2.6 Homogeneous Electron Gas.- 2.7 Local Exchange Potential - The Xa Method.- 2.8 Shortcomings of the Independent-Electron Approximation.- 2.9 Unrestricted SCF Approximation.- 3. Density Functional Theory.- 3.1 Thomas-Fermi Method.- 3.2 Hohenberg-Kohn-Sham Theory.- 3.3 Local-Density Approximation.- 3.4 Results for Atoms, Molecules, and Solids.- 3.5 Extensions and Limitations.- 4. Quantum-Chemical Approach to Electron Correlations.- 4.1 Configuration Interactions.- 4.1.1 Local and Localized Orbitals.- 4.1.2 Selection of Double Substitutions.- 4.1.3 Multireference CI.- 4.2 Many-Body Perturbation Theory.- 5. Cumulants, Partitioning, and Projections.- 5.1 Cumulant Representation.- 5.1.1 Ground-State Energy.- 5.1.2 Perturbation Expansion.- 5.2 Projection and Partitioning Techniques.- 5.2.1 Coupled-Electron-Pair Approximations.- 5.2.2 Projections Based on Local Operators.- 5.2.3 Method of Increments.- 5.3 Coupled-Cluster Method.- 5.4 Comparison with Various Trial Wavefunctions.- 5.5 Simplified Correlation Calculations.- 6. Excited States.- 6.1 CI Calculations and Basis Set Requirements.- 6.2 Excitation Energies in Terms of Cumulants.- 6.3 Green's Function Method.- 6.3.1 Perturbation Expansions.- 6.3.2 The Projection Method.- 6.4 Local Operators.- 7. Finite-Temperature Techniques.- 7.1 Approximations for Thermodynamic Quantities.- 7.1.1 Temperature Green's Function.- 7.1.2 The Projection Method for T ? 0.- 7.2 Functional-Integral Method.- 7.2.1 Static Approximation.- 7.3 Monte Carlo Methods.- 7.3.1 Sampling Techniques.- 7.3.2 Ground-State Energy.- 8. Correlations in Atoms and Molecules.- 8.1 Atoms.- 8.2 Hydrocarbon Molecules.- 8.2.1 Analytic Expressions for Correlation-Energy Contributions.- 8.2.2 Simplified Correlation Calculations.- 8.3 Molecules Consisting of First-Row Atoms.- 8.4 Strength of Correlations in Different Bonds.- 8.5 Polymers.- 8.5.1 Polyethylene.- 8.5.2 Polyacetylene.- 8.6 Photoionization Spectra.- 9. Semiconductors and Insulators.- 9.1 Ground-State Correlations.- 9.1.1 Semi-empirical Correlation Calculations.- 9.1.2 Ab Initio Calculations.- 9.2 Excited States.- 9.2.1 Role of Nonlocal Exchange.- 9.2.2 The Energy Gap Problem.- 9.2.3 Hedin's GW Approximation.- 10. Homogeneous Metallic Systems.- 10.1 Fermi-Liquid Approach.- 10.2 Charge Screening and the Random-Phase Approximation.- 10.3 Spin Fluctuations.- 11. Transition Metals.- 11.1 Correlated Ground State.- 11.2 Excited States.- 11.3 Finite Temperatures.- 11.3.1 Single-Site Approximation.- 11.3.2 Two-Sites Approximation.- 11.3.3 Beyond the Static Approximation.- 12. Strongly Correlated Electrons.- 12.1 Molecules.- 12.2 Anderson Hamiltonian.- 12.2.1 Calculation of the Ground-State Energy.- 12.2.2 Excited States.- 12.2.3 Noncrossing Approximation.- 12.3 Effective Exchange Hamiltonian.- 12.3.1 Schrieffer-Wolff Transformation.- 12.3.2 Kondo Divergency.- 12.3.3 Fermi-Liquid Description.- 12.4 Magnetic Impurity in a Lattice of Strongly Correlated Electrons.- 12.5 Hubbard Hamiltonian.- 12.5.1 Ground-State: Gutzwiller's Wavefunction and Spin-Density Wave State.- 12.5.2 Excitation Spectrum.- 12.5.3 The Limits of One Dimension and Infinite Dimensions.- 12.6 The t - J Model.- 12.7 Slave Bosons in the Mean-Field Approximation.- 12.8 Kanamori's t-Matrix Approach.- 13. Heavy-Fermion Systems.- 13.1 The Fermi Surface and Quasiparticle Excitations.- 13.1.1 Large Versus Small Fermi Surface.- 13.2 Model Hamiltonian and Slave Bosons.- 13.3 Application of the Noncrossing Approximation.- 13.4 Variational Wavefunctions.- 13.5 Quasiparticle Interactions.- 13.6 Quasiparticle-Phonon Interactions Based on Strong Correlations.- 14. Superconductivity and the High-Tc Materials.- 14.1 The Superconducting State.- 14.1.1 Pair States.- 14.1.2 BCS Ground State.- 14.1.3 Pair Breaking.- 14.2 Electronic Properties of the High-Tc Materials.- 14.2.1 Electronic Excitations in the Cu-O Planes.- 14.2.2 Calculation of the Spectral Weight by Projection Techniques.- 14.2.3 Size of the Fermi Surface.- 14.3 Other Properties of the Cuprates.- 14.3.1 Loss of Antiferromagnetic Order.- 14.3.2 Optical Conductivity.- 14.3.3 Magnetic Response.- 14.4 Heavy Fermions in Nd2_xCexCuO4.- B. Derivation of Several Relations Involving Cumulants.- C. Projection Method of Mori and Zwanzig.- D. Cross-Over from Weak to Strong Correlations.- E. Derivation of a General Form for ??).- F. Hund's Rule Correlations.- G. Cumulant Representation of Expectation Values and Correlation Functions.- H. Diagrammatic Representation of Certain Expectation Values.- I. Derivation of the Quasiparticle Equation.- J. Coherent-Potential Approximation.- K. Derivation of the NCA Equations.- L. Ground-State Energy of a Heisenberg Antiferromagnet on a Square Lattice.- M. The Lanczos Method.- References.

Electron correlations in molecules and solids

The present theoretical understanding of various properties of superionic conductors is reviewed. Emphasis is put on their treatment as classical many-particle systems and on the analysis of their dynamic behaviour. Different kinds of approaches pertaining to the low frequency dynamics are considered in detail. They include stochastic models, like hopping or Fokker-Planck models as well as a hydrodynamic theory. The high frequency (phonon-) dynamics and the information obtained from computer simulations is also analysed. As far as possible, the relevance of the different approaches with respect to experiments on specific materials is discussed. Possible directions for future investigations are outlined.

Theoretical models for superionic conductors

Publisher Summary The chapter presents a study on theory of heavy fermion systems In the heavy fermion systems it seems that some of the features of the single Kondo impurity problem appear in an enhanced form simply, because there is at least one magnetic ion per unit cell Therefore, the heavy fermion systems have sometimes been referred to as “lattices of Kondo ions” or “Kondo lattice systems” The chapter presents a discussion on quasiparticle-phonon interactions and presents a demonstration that elastic properties of heavy fermion systems are almost as interesting as the electronic ones Superconducting heavy fermion systems have attracted great interest, because they are considered as possible candidates for unconventional pairing An outstanding experimental finding is the power-law behavior of the low temperature specific heat, thermal conductivity, ultrasonic attenuation, and nuclear magnetic resonance (NMR) relaxation rate in those systems The chapter also presents a figure based on the scenario within which the heavy fermion systems should be viewed It shows the different degrees of electron correlations in solids The heavy fermion systems are the ones, which come closest to the localization limit, in which electron correlations exclude any charge fluctuations within the f shell

Theory of Heavy Fermion Systems

The electronic structure of heavy-fermion compounds arises from the interaction of nearly localized 4f- or 5f-shell electrons (with atomic magnetic moments) with the free-electron-like itinerant conduction-band electrons. In actinide or rare-earth heavy-fermion materials, this interaction yields itinerant electrons having an effective mass about 100 times (or more) the bare electron mass. Moreover, the itinerant electrons in UPd2Al3 are found to be superconducting well below the magnetic ordering temperature of this compound, whereas magnetism generally suppresses superconductivity in conventional metals. Here we report the detection of a dispersive excitation of the ordered f-electron moments, which shows a strong interaction with the heavy superconducting electrons. This 'magnetic exciton' is a localized excitation which moves through the lattice as a result of exchange forces between the magnetic moments. By combining this observation with previous tunnelling measurements on this material, we argue that these magnetic excitons may produce effective interactions between the itinerant electrons, and so be responsible for superconductivity in a manner analogous to the role played by phonons in conventional superconductors.

Peter Fulde

Papers

Superconductivity in a Strong Spin-Exchange Field

Electron correlations in molecules and solids

Theoretical models for superionic conductors

Theory of Heavy Fermion Systems

Strong coupling between local moments and superconducting 'heavy' electrons in UPd2Al3.