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 review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. This mapping is exact for models of correlated electrons in the limit of large lattice coordination (or infinite spatial dimensions). It extends the standard mean-field construction from classical statistical mechanics to quantum problems. We discuss the physical ideas underlying this theory and its mathematical derivation. Various analytic and numerical techniques that have been developed recently in order to analyze and solve the dynamical mean-field equations are reviewed and compared to each other. The method can be used for the determination of phase diagrams (by comparing the stability of various types of long-range order), and the calculation of thermodynamic properties, one-particle Green's functions, and response functions. We review in detail the recent progress in understanding the Hubbard model and the Mott metal-insulator transition within this approach, including some comparison to experiments on three-dimensional transition-metal oxides. We present an overview of the rapidly developing field of applications of this method to other systems. The present limitations of the approach, and possible extensions of the formalism are finally discussed. Computer programs for the numerical implementation of this method are also provided with this article.

Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions

Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.

Electronic Structure: Basic Theory and Practical Methods

One of Feynman's early applications of path integrals was to superfluid $^{4}\mathrm{He}$. He showed that the thermodynamic properties of Bose systems are exactly equivalent to those of a peculiar type of interacting classical "ring polymer." Using this mapping, one can generalize Monte Carlo simulation techniques commonly used for classical systems to simulate boson systems. In this review, the author introduces this picture of a boson superfluid and shows how superfluidity and Bose condensation manifest themselves. He shows the excellent agreement between simulations and experimental measurements on liquid and solid helium for such quantities as pair correlations, the superfluid density, the energy, and the momentum distribution. Major aspects of computational techniques developed for a boson superfluid are discussed: the construction of more accurate approximate density matrices to reduce the number of points on the path integral, sampling techniques to move through the space of exchanges and paths quickly, and the construction of estimators for various properties such as the energy, the momentum distribution, the superfluid density, and the exchange frequency in a quantum crystal. Finally the path-integral Monte Carlo method is compared to other quantum Monte Carlo methods.

Path integrals in the theory of condensed helium

High-volume information-processing and communications devices are at present based on semiconductor devices, whereas information-storage devices rely on multilayers of magnetic metals and insulators. Switching within information-processing devices is performed by the controlled motion of small pools of charge, whereas in the magnetic storage devices information storage and retrieval is performed by reorienting magnetic domains (although charge motion is often used for the final stage of readout). Semiconductor spintronics offers a possible direction towards the development of hybrid devices that could perform all three of these operations, logic, communications and storage, within the same materials technology. By taking advantage of spin coherence it also may sidestep some limitations on information manipulation previously thought to be fundamental. This article focuses on advances towards these goals in the past decade, during which experimental progress has been extraordinary.

Challenges for semiconductor spintronics

We report the details of an application of the method of maximum entropy to the extraction of spectral and transport properties from the imaginary-time correlation functions generated from quantum Monte Carlo simulations of the nondegenerate, symmetric, single-impurity Anderson model. We find that these physical properties are approximately universal functions of temperature and frequency when these parameters are scaled by the Kondo temperature. We also found that important details for successful extractions included the generation of statistically independent, Gaussian-distributed data, and a good choice of a default model to represent the state of our prior knowledge about the result in the absence of data. We suggest that our techniques are not restricted to the Hamiltonian and quantum Monte Carlo algorithm used here, but that maximum entropy and these techniques lay the general groundwork for the extraction of dynamical information from imaginary-time data generated by other quantum Monte Carlo simulations.

Quantum Monte Carlo simulations and maximum entropy: Dynamics from imaginary-time data.

We present the results of a theoretical model describing electrical spin injection from a spin-polarized contact into a nonmagnetic semiconductor. The model includes the possibility of interface resistance due, for example, to a tunnel barrier at the contact/semiconductor heterojunction, and shows that such interface resistance can be critical in determining spin injection properties. With no interface resistance spin injection is very weak for contacts with typical metallic resistivities. For higher bulk resistivity contacts, such as doped semiconductors, or for completely spin-polarized contacts, strong spin injection is possible without significant interface resistance. However the spin polarization must be extremely close to complete for contacts with metallic resistivities. A tunnel barrier with spin-dependent interface resistance can greatly enhance spin injection. An insulating tunnel barrier with a spin-polarized contact, and a ferromagnetic insulator tunnel barrier, both have spin-dependent interface resistance, and provide two promising approaches to achieve significant electrical spin injection. The model is consistent with a variety of experimental observations, identifies the basic physics problems that must be addressed to achieve a high degree of spin injection, and suggests systematic strategies to achieve strong spin injection.

Electrical spin injection into semiconductors

An outstanding problem in the simulation of condensed-matter phenomena is how to obtain dynamical information. We consider the numerical analytic continuation of imaginary-time quantum Monte Carlo data to obtain real-frequency spectral functions. This is an extremely ill-posed problem similar to the inversion of a Laplace transform. We suggest an image-reconstruction approach, which has been widely applied to data analysis in experimental research. Specifically, we apply the maximum-entropy method (ME) to the analytic continuation of quantum Monte Carlo data. We report encouraging preliminary results for the Fano-Anderson model of an impurity state in a continuum. The incorporation of additional prior information, such as sum rules and asymptotic behavior, can be expected to significantly improve results. We compare (ME) to alternative methods. We also discuss statistical error propagation for the analytic continuation problem via the likelihood function, which is independent of the choice of image-reconstruction method. This includes the sensitivity of the data to structure in the spectral function, the optimization of Monte Carlo simulations, and how to incorporate covariance in the statistical errors of the Monte Carlo method.

Maximum-entropy method for analytic continuation of quantum Monte Carlo data

We examine non-Boltzmann Monte Carlo algorithms used to study slowly relaxing systems. By adding a simple bookkeeping step to the Metropolis algorithm, we obtain statistical estimators of canonical macrostate probabilities. These estimators enable a natural accumulation of statistics from simulations having different importance weights, enable temperature extrapolation without using energy to define macrostate labels, improve parallelization, and reduce variance. We illustrate with an Ising model example.

https://iopscience.iop.org/article/10.1209/epl/i1999-00257-1/pdf

Canonical transition probabilities for adaptive Metropolis simulation

We present an approximation to the total-energy tight-binding (TB) method based on use of the kernel polynomial method within a truncated subspace. Chebyshev polynomial moments of the Hamiltonian matrix are generated in a stable and efficient manner through recursive matrix-vector multiples. To compute the energy, either the electronic density of states (DOS) or the zero-temperature Fermi function is smeared by convolution with the kernel polynomial, with Jackson damping to minimize Gibbs oscillations while maintaining the positivity of the DOS. These are shown to give approximate lower and upper bounds, respectively, on the exact TB energy, and are averaged to obtain an improved energy estimate. The scaling of the computational work is made linear in the number of atoms by truncating the moment computation at a certain range about each atom. Energy derivatives necessary for molecular dynamics are obtained via a matrix-polynomial derivative relation. The method converges to exact TB as the number of moments and the truncation range are increased. We demonstrate the convergence properties and viability of the method for materials simulations in an examination of defects in silicon. We also discuss the relative importance of truncation range versus number of moments. {copyright} {ital 1996 The American Physical Society.}

R. N. Silver

Papers

Quantum Monte Carlo simulations and maximum entropy: Dynamics from imaginary-time data.

Electrical spin injection into semiconductors

Maximum-entropy method for analytic continuation of quantum Monte Carlo data

Canonical transition probabilities for adaptive Metropolis simulation

Linear-scaling tight binding from a truncated-moment approach.