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

A scheme that reduces the calculations of ground-state properties of systems of interacting particles exactly to the solution of single-particle Hartree-type equations has obvious advantages. It is not surprising, then, that the density functional formalism, which provides a way of doing this, has received much attention in the past two decades. The quality of the energy surfaces calculated using a simple local-density approximation for exchange and correlation exceeds by far the original expectations. In this work, the authors survey the formalism and some of its applications (in particular to atoms and small molecules) and discuss the reasons for the successes and failures of the local-density approximation and some of its modifications.

The density functional formalism, its applications and prospects

Electronic excitations lie at the origin of most of the commonly measured spectra. However, the first-principles computation of excited states requires a larger effort than ground-state calculations, which can be very efficiently carried out within density-functional theory. On the other hand, two theoretical and computational tools have come to prominence for the description of electronic excitations. One of them, many-body perturbation theory, is based on a set of Green’s-function equations, starting with a one-electron propagator and considering the electron-hole Green’s function for the response. Key ingredients are the electron’s self-energy S and the electron-hole interaction. A good approximation for S is obtained with Hedin’s GW approach, using density-functional theory as a zero-order solution. First-principles GW calculations for real systems have been successfully carried out since the 1980s. Similarly, the electron-hole interaction is well described by the Bethe-Salpeter equation, via a functional derivative of S. An alternative approach to calculating electronic excitations is the time-dependent density-functional theory (TDDFT), which offers the important practical advantage of a dependence on density rather than on multivariable Green’s functions. This approach leads to a screening equation similar to the Bethe-Salpeter one, but with a two-point, rather than a four-point, interaction kernel. At present, the simple adiabatic local-density approximation has given promising results for finite systems, but has significant deficiencies in the description of absorption spectra in solids, leading to wrong excitation energies, the absence of bound excitonic states, and appreciable distortions of the spectral line shapes. The search for improved TDDFT potentials and kernels is hence a subject of increasing interest. It can be addressed within the framework of many-body perturbation theory: in fact, both the Green’s functions and the TDDFT approaches profit from mutual insight. This review compares the theoretical and practical aspects of the two approaches and their specific numerical implementations, and presents an overview of accomplishments and work in progress.

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Electronic excitations: density-functional versus many-body Green's-function approaches

http://cds.cern.ch/record/262851/files/9405029.pdf

Supersymmetry and quantum mechanics

We present a method for calculating the core-level x-ray photoemission (XPS), the $3d\ensuremath{\rightarrow}4f$ x-ray absorption (XAS), the valence photoemission, and the bremsstrahlung isochromat spectra in a slightly modified Anderson impurity model of a Ce compound at zero temperature. Both the spin and orbital degeneracies of the $f$ level are included and the Coulomb interaction between the $f$ electrons is taken into account. The spectra are expressed in terms of a resolvent operator. A many-electron basis set is introduced, and the resolvent is obtained from a matrix inversion. The particular form of the Anderson model allows us to find a small but sufficiently complete basis set, if the degeneracy ${N}_{f}$ of the $f$ level is large. In particular, we consider the limit ${N}_{f}\ensuremath{\rightarrow}\ensuremath{\infty}$, and show that the method is exact for the XPS, XAS, and valence photoemission spectra in this limit. It is also demonstrated that for ${N}_{f}\ensuremath{\gtrsim}6$, the method provides accurate spectra. Analytical results are obtained for the valence photoemission spectrum ${\ensuremath{\rho}}_{v}(\ensuremath{\epsilon})$. The spectrum has a sharp rise close to the Fermi energy ${\ensuremath{\epsilon}}_{F}$, which goes over to a "Kondo peak" in the spin-fluctuation limit. An exact relation between ${\ensuremath{\rho}}_{v}({\ensuremath{\epsilon}}_{F})$ and the $f$-level occupancy ${n}_{f}$ is shown to be satisfied to within 10% for ${N}_{f}\ensuremath{\ge}6$. We discuss how core-level XPS spectra can be used to estimate the $f$-level occupancy ${n}_{f}$ and the coupling $\ensuremath{\Delta}$ between the $f$ level and the conduction states. We find that the values of ${n}_{f}$ and $\ensuremath{\Delta}$ obtained from core-level XPS are basically consistent with the other spectroscopies and the static, $T=0$ susceptibility. It is, therefore, possible to describe these experiments in the Anderson model, using essentially the same set of parameters for all the experiments. Typically, we find ${n}_{f}g0.7$ and $\ensuremath{\Delta}\ensuremath{\sim}0.1$ eV.

Electron spectroscopies for Ce compounds in the impurity model

Numerous correlated electron systems exhibit a strongly scale-dependent behavior. Upon lowering the energy scale, collective phenomena, bound states, and new effective degrees of freedom emerge. Typical examples include (i) competing magnetic, charge, and pairing instabilities in two-dimensional electron systems; (ii) the interplay of electronic excitations and order parameter fluctuations near thermal and quantum phase transitions in metals; and (iii) correlation effects such as Luttinger liquid behavior and the Kondo effect showing up in linear and nonequilibrium transport through quantum wires and quantum dots. The functional renormalization group is a flexible and unbiased tool for dealing with such scale-dependent behavior. Its starting point is an exact functional flow equation, which yields the gradual evolution from a microscopic model action to the final effective action as a function of a continuously decreasing energy scale. Expanding in powers of the fields one obtains an exact hierarchy of flow equations for vertex functions. Truncations of this hierarchy have led to powerful new approximation schemes. This review is a comprehensive introduction to the functional renormalization group method for interacting Fermi systems. A self-contained derivation of the exact flow equations is presented and frequently used truncation schemes are described. Reviewing selected applications it is shown how approximations based on the functional renormalization group can be fruitfully used to improve our understanding of correlated fermion systems.

Functional renormalization group approach to correlated fermion systems

We report the core-level x-ray photoelectron spectroscopy spectra of 30 intermetallic compounds of La and Ce. The results are discussed in the light of calculations using the Anderson impurity model of the $4f$ levels and including the degeneracy of the $4f$ levels. The comparison allows us to derive values for the coupling between the $f$ levels and the conduction states $\ensuremath{\Delta}$ and the number of $4f$ electrons ${n}_{f}$. We find $\ensuremath{\Delta}$ to be up to \ensuremath{\sim} 150 meV in some Ce intermetallic compounds, and find ${n}_{f}$ to range from \ensuremath{\sim}0.8-1.1. We cannot reconcile the core-level results with the traditional promotional model in which $\ensuremath{\Delta}$ was assumed to be 10 meV or less and the $f$-electron count could range from 1 down to zero in Ce intermetallic compounds.

Electronic structure of Ce and its intermetallic compounds

A method is presented for calculating the core and valence spectra of a Ce compound in the impurity model at zero temperature. In the sudden limit this method becomes exact for large degeneracy of the $f$ level. In this limit the valence spectrum has an $f$ peak close to the Fermi energy, ${\ensuremath{\epsilon}}_{\mathrm{F}}$, even if the $f$ level is fairly far below ${\ensuremath{\epsilon}}_{\mathrm{F}}$, and usually there is a second $f$ peak at larger binding energy. These results correlate well with recent experiments for many Ce compounds. Both the core and valence spectra provide information about the occupancy of the $f$ level and about its coupling to the conduction band.

Photoemission from Ce Compounds: Exact Model Calculation in the Limit of Large Degeneracy

We give an overview of the use of the impurity Anderson Hamiltonian to describe the spectroscopic and low-energy thermodynamic properties of cerium intermetallics, with emphasis on interpreting 4f photoemission spectra. We show Ce valence-band resonant photoemission, Bremsstrahlung isochromat and 3d X-ray photoemission spectra for CeRu2, CeNi2, CeIr2 and CeAl, and give a complete theoretical analysis of the spectra. We summarize the relation between the large and small energy scale properties. For each system, all the spectra, as well as the static magnetic susceptibility and Kondo temperature, can be described by the model using essentially the same parameters. We also present details of resonant photoemission spectra for five other cerium compounds, CeSi2, CeOs2, CePd3, CeCo2 and CeNi5, and discuss generally the problem of obtaining the experimental 4f spectrum. Alternative theories of 4f photoemission are examined critically and we give applications of the Anderson Hamiltonian theory to CeAl2,...

K. Schönhammer

Papers

Electron spectroscopies for Ce compounds in the impurity model

Functional renormalization group approach to correlated fermion systems

Electronic structure of Ce and its intermetallic compounds

Photoemission from Ce Compounds: Exact Model Calculation in the Limit of Large Degeneracy

Electronic structure of cerium and light rare-earth intermetallics