The many theoretical studies of the various magnetic, thermal and magnetoelastic properties for paramagnetic and ferromagnetic transition metals and alloys in the simple itinerant electron model are reviewed. The important amendments to the simple itinerant electron model or Stoner model of magnetism due to the spin wave excitations and spin fluctuations are explained.

https://iopscience.iop.org/article/10.1088/0034-4885/44/4/001/pdf

Itinerant electron magnetism

Over the course of the last 15 years density functional theory (DFT)* has evolved as a conceptually and practically useful method for studying the electronic properties of many-electron systems. In this chapter we present a critical review of the general theory together with some illustrative examples.† More complete discussions of several important areas of application may be found in other chapters of this book.

General Density Functional Theory

Publisher Summary The chapter presents a study on the foundations, achievements, and limitations of density functional methods. Because these methods have their origins in the description of the charge clouds in atoms as a degenerate inhomogeneous electron gas by Thomas and Fermi, the chapter presents a review on the Thomas–Fermi statistical theory. The chapter also discusses Dirac's extension to include exchange. Because the foundations of density functional theory at elevated temperatures are discussed, the chapter includes a brief survey of Thomas–Fermi theory at nonzero temperature. After several of the basic concepts of modern density functional theory, the Hohenberg–Kohn theorem and its principal extensions are discussed. This theorem formally completes the original Thomas–Fermi theory by showing that the ground state of a many-electron system is indeed a unique functional of its electron density. The chapter presents a formal discussion on extensions of the original Hohenberg–Kohn theorem to include (1) spin and relativistic effects and (2) elevated temperatures. In the treatment of calculational procedures, the chapter presents the relation of Slater's transition-state method to density functional theory of excited states. After a justification of single-particle equations, the calculational procedures deals exclusively with local density approximations; therefore a short account of approximate ways in which local density approximations can be transcended is presented. Applications of density functional theory to solids are discussed, the former treating some problems, which fall within the scope of linear response theory.

Density Functional Methods:Theory and Applications

The use of self-consistent band calculations to understand the electronic structure of solids is reviewed. The formal basis for the approach is first examined to emphasise that not all band calculations are applications of the same theory. Similarly the critical points, both fundamental and mundane, of the self-consistency process are examined. Again, the central theme is the idea that perhaps some aspects of the self-consistent calculation are not completely established. On the other hand, band structure technique, while still developing, has been rather well explored. Thus one can examine it from the general point of view of seeing what the various techniques imply about the nature of the band structure problem. Finally, some applications of self-consistent band structure calculations are examined.

http://iopscience.iop.org/article/10.1088/0034-4885/44/2/002/pdf

Self-consistent energy band calculations

Transition metal surfaces are important technologically as good catalysts. Interfaces and superlattices of magnetic transition metals also hold the promise of new device applications. The properties of surfaces and interfaces are determined by the local band structure which is directly related to the magnetisation density. One of the fundamental problems of surface magnetism is, therefore, to determine the ground-state surface perturbation to the magnetisation density. After a somewhat turbulent history, the ground-state surface problem is now well understood. The current status of the theory and detailed results for Fe and Ni surfaces are reviewed in the first part of the article. Experimental methods for magnetic surfaces are also discussed, with particular emphasis on the interpretation of data for Fe and Ni, which is still in some cases controversial. The other two central questions addressed in this review concern the nature of magnetic excitations at surfaces and the way the magnetisation disorders near a surface at finite temperatures.

Magnetism at transition metal surfaces

The spin density functional theory is used to derive a variational principle (lower bound) for the wavevector dependent static transverse ferromagnetic spin susceptibility chi +-(q) for a general exchange-correlation energy functional. This variational principle is a direct consequence of the Hohenberg and Kohn minimum energy theorem for the ground state. The importance of spin rotational invariance is stressed in choosing the trial function so that the variational expression for chi +-(q) has the correct behaviour for small q. Noting the relationship between the spin wave stiffness coefficient D and chi +-(q), a rigorous upper bound for D is derived for general ferromagnetic systems. The relationships between the present general theory for D and recent theories based on the local exchange model are discussed.

http://iopscience.iop.org/article/10.1088/0305-4608/8/7/026/pdf

S H Vosko

Papers

Spin density functional theory for the spin wave stiffness coefficient in ferromagnets