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

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

A fast KKR CPA method is explained and its convergence properties are examined numerically. It is shown that a step number of N 300, which determines the number of k-points used for the numerical integration in the k-space as well as the number of iteration steps in determining the coherent t-matrix, is sufficient for most purposes, including total-energy calculations. As a typical application the electronic structure of ferromagnetic Ni-Fe systems is calculated in the framework of the KKR CPA combined with the local spin density approximation, which demonstrates the feasibility of the present method.

https://iopscience.iop.org/article/10.1088/0953-8984/1/43/006/pdf

Fast Korringa-Kohn-Rostoker coherent potential approximation and its application to FCC Ni-Fe systems

Itinerant-electron ferromagnetism at finite temperatures is discussed by using the functional-integral method with two fields within the static and saddle-point approximations combined with the single-site approximation; a single atom of a pure metal is regarded as an impurity embedded in the host which is treated by a kind of the alloy-analogy approximation. The amplitude of the local magnetic moment is shown to have a weak temperature dependence and to remain finite even in the paramagnetic state, where the spin susceptibility obeys an approximate Curie-Weiss law. Numerical calculations are made with the use of a simplified model for the density of states of bcc transition metals. Calculated results are discussed with reference to experimental data of iron.

Single-Site Functional-Integral Approach to Itinerant-Electron Ferromagnetism

Magnetic amorphous alloys obtained by rapid quenching of the melt are excellent soft magnetic materials with a wide range of technological applications. They also represent a significant challenge to the scientific understanding of magnetic materials, since most of the existing theories of solids assume lattice periodicity. For these reasons, the magnetic and other properties of amorphous alloys have been very actively studied over the last decade. In recent years increasing attention has been directed to the fundamental understanding of the structural, thermal and magnetic properties of the amorphous alloys. It is not only scientifically but also technologically important to achieve such an understanding, since the amorphous alloys are, in many respects, so different from conventional crystalline magnetic materials. The author attempts to summarise recent progress in research on magnetic amorphous alloys and critically assesses the present level of understanding of this new class of magnetic materials, focusing mostly on the transition-metal-metalloid glasses. He starts with a review of early developments and a discussion on the nature of glasses and glass formation and proceeds to an extensive discussion of their atomic structure, both from the experimental and theoretical points of view.

https://iopscience.iop.org/article/10.1088/0034-4885/47/12/002/pdf

Magnetic amorphous alloys: physics and technological applications

An application of the coherent potential approximation (CPA) to ferromagnetic alloys is discussed on the basis of a nondegenerate tight-binding model. The intraatomic coulomb interaction is taken into account self-consistently within the framework of the Hartree-Fock approximation. Numerical calculations are carried out for the case of Ni 1- x Fe x . The results are in good agreement with the experimental data of the magnetic moments of Ni and Fe in concentrated alloys and also with the data of the electronic specific heat. The instability of the nonmagnetic state at a finite temperature is discussed by calculating the susceptibility in CPA. Possible experiments to check the calculated electronic structure are discussed. An extention to a degenerate (multiband) tight-binding model is also presented.

Junjiro Kanamori

Papers

An Application of the Coherent Potential Approximation to Ferromagnetic Alloys