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

We review the methods which have been developed over the past several years to determine the behavior of solids whose properties vary randomly at the microscopic level, with principal attention to systems having composition variation on a well-defined structure (random "alloys"). We begin with a survey of the various elementary excitations and put the dynamics of electrons, phonons, magnons, and excitons into one common descriptive Hamiltonian; we then review the use of double-time thermodynamic Green's functions to determine the experimental properties of systems. Next we discuss these aspects of the problem which derive from the statistical specification of the microscopic parameters; we examine what information can and cannot be obtained from averaged Green's functions. The central portion of the review concerns methods for calculating the averaged Green's function to successively better approximation, including various self-consistent methods, and higher-order cluster effects. The last part of the review presents a comparison of theory with the experimental results of a variety of properties---optical, electronic, magnetic, and neutron scattering. An epilogue calls attention to the similarity between these problems and those of other fields where random material heterogeneity has played an essential role.

The theory and properties of randomly disordered crystals and related physical systems

Electrons in disordered systems and the theory of localization

The body of research on (III,Mn)V diluted magnetic semiconductors initiated during the 1990's has concentrated on three major fronts: i) the microscopic origins and fundamental physics of the ferromagnetism that occurs in these systems, ii) the materials science of growth and defects and iii) the development of spintronic devices with new functionalities. This article reviews the current status of the field, concentrating on the first two, more mature research directions. From the fundamental point of view, (Ga,Mn)As and several other (III,Mn)V DMSs are now regarded as textbook examples of a rare class of robust ferromagnets with dilute magnetic moments coupled by delocalized charge carriers. Both local moments and itinerant holes are provided by Mn, which makes the systems particularly favorable for realizing this unusual ordered state. Advances in growth and post-growth treatment techniques have played a central role in the field, often pushing the limits of dilute Mn moment densities and the uniformity and purity of materials far beyond those allowed by equilibrium thermodynamics. In (III,Mn)V compounds, material quality and magnetic properties are intimately connected. In the review we focus on the theoretical understanding of the origins of ferromagnetism and basic structural, magnetic, magneto-transport, and magneto-optical characteristics of simple (III,Mn)V epilayers, with the main emphasis on (Ga,Mn)As. The conclusions we arrive at are based on an extensive literature covering results of complementary ab initio and effective Hamiltonian computational techniques, and on comparisons between theory and experiment.

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Theory of ferromagnetic (III, Mn) V semiconductors

This review summarizes recent first-principles investigations of the electronic structure and magnetism of dilute magnetic semiconductors (DMSs), which are interesting for applications in spintronics. Details of the electronic structure of transition-metal-doped III-V and II-VI semiconductors are described, especially how the electronic structure couples to the magnetic properties of an impurity. In addition, the underlying mechanism of the ferromagnetism in DMSs is investigated from the electronic structure point of view in order to establish a unified picture that explains the chemical trend of the magnetism in DMSs. Recent efforts to fabricate high-TC DMSs require accurate materials design and reliable TC predictions for the DMSs. In this connection, a hybrid method (ab initio calculations of effective exchange interactions coupled to Monte Carlo simulations for the thermal properties) is discussed as a practical method for calculating the Curie temperature of DMSs. The calculated ordering temperatures for various DMS systems are discussed, and the usefulness of the method is demonstrated. Moreover, in order to include all the complexity in the fabrication process of DMSs into advanced materials design, spinodal decomposition in DMSs is simulated and we try to assess the effect of inhomogeneity in them. Finally, recent works on first-principles theory of transport properties of DMSs are reviewed. The discussion is mainly based on electronic structure theory within the local-density approximation to density-functional theory.

First-principles theory of dilute magnetic semiconductors

The success of minimum polarity over rigid band models in describing the electronic structure of NiCu alloys is ascribed to the fact that the random scattering potential is strong enough to produce nearly independent Ni and Cu subbands. Calculations of magnetic properties using a model density of states whose first three moments are exact are in good agreement with experiment and essentially better than previous results.

Minimum Polarity Models in the Theory of Magnetic Properties of NiCu Alloys

The generalized Kadanoff-Baym Ansatz, used to simplify the non-equilibrium Green's functions to the kinetic equation for the density matrix, leads to an incorrect dynamics of a system if the self-energy has a rich energy spectrum. We propose an approximation of the vertex correction which dynamically changes with the density matrix while it benefits from simplicity of stationary propagators. On the molecular bridge between ferromagnetic leads, we demonstrate that this simple vertex fixes the failure of the kinetic equation on a negligible computational cost.

B. Velický

Papers

Minimum Polarity Models in the Theory of Magnetic Properties of NiCu Alloys

Dynamical vertex correction to the generalized Kadanoff-Baym Ansatz