# Theory of substitutionally disordered Heisenberg ferromagnets

28 May 1977-Journal of Physics C: Solid State Physics (IOP Publishing)-Vol. 10, Iss: 10, pp 1741-1750

TL;DR: In this article, the spin-wave spectra of a disordered Heisenberg ferromagnet were derived within a cluster coherent potential approximation in which a cluster of spins consisting of a central spin and the shell of its nearest neighbours was embedded in an effective medium and its scattering was considered with respect to the medium.

Abstract: A calculation of the spin-wave spectra of a disordered Heisenberg ferromagnet in which two species of spins are randomly distributed is presented. The theory is developed within a cluster coherent potential approximation in which a cluster of spins consisting of a central spin and the shell of its Z nearest neighbours is embedded in an effective medium and its scattering is considered with respect to the medium. For simplicity it is assumed that scattering due to the cluster depends only on the number of the different types of atoms constituting the shell rather than on their detailed configurations on the shell. Correlated site and bond disorder, an important feature of the magnetic problem, is handled in a relatively simple manner.

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Bell Labs

^{1}TL;DR: In this paper, a substitutional alloy based on the concept of an effective or coherent potential was introduced, which, when placed on every site of the alloy lattice, will simulate the electronic properties of the actual alloy.

Abstract: We introduce a model of a substitutional alloy based on the concept of an effective or coherent potential which, when placed on every site of the alloy lattice, will simulate the electronic properties of the actual alloy. The coherent potential is necessarily a complex, energy-dependent quantity. We evaluate the model for the simple case of a one-dimensional alloy of $\ensuremath{\delta}$-function potentials. In order to provide a basis for comparison, as well as to see if a simpler scheme will suffice, we also calculate the spectrum of the same alloy using the average $t$-matrix approximation introduced by Beeby. On the basis of these results, we conclude that the average $t$-matrix approximation is not adequate for the description of an actual transition-metal alloy, while the coherent-potential picture will provide a more reasonable facsimile of the density of states in such an alloy.

1,867 citations

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TL;DR: A review of the methods for determining 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") can be found in this paper.

Abstract: 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.

1,213 citations

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TL;DR: In this paper, a single-band model Hamiltonian is used to describe the electronic structure of a three-dimensional disordered binary alloy, and several common theories based on the single-site approximation in a multiple-scattering description are compared with exact results for this Hamiltonian.

Abstract: A single-band model Hamiltonian is used to describe the electronic structure of a three-dimensional disordered binary alloy. Several common theories based on the single-site approximation in a multiple-scattering description are compared with exact results for this Hamiltonian. The coherent-potential theory of Soven and others is shown to be the best of these. Within the appropriate limits, it exhibits dilute-alloy, virtual-crystal, and well separated impurity-band behavior. Hubbard and Onodera's and Toyozawa's simple model density of states is employed in numerical calculations for a wide variety of concentrations and scattering-potential strengths. Explicit results are exhibited for the total density of states, the partial density contributed by each component, and such $k$-dependent properties as the Bloch-wave spectral density and the distribution function. These illustrate the general conclusions as well as the limitations of the quasiparticle description.

1,025 citations

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TL;DR: In this paper, the electronic structure of binary alloys is discussed for a system in which both the atomic energy levels and the hopping integrals are random quantities, and three self-consistent equations are obtained that must be solved simultaneously; these replace the single CPA equation.

Abstract: The electronic structure of binary alloys is discussed for a system in which both the atomic energy levels and the hopping integrals are random quantities. This paper is a detailed study of the generalization of the coherent-potential approximation (CPA) introduced earlier by the present authors. We show that a locator description provides a particularly suitable formalism for setting up this generalized problem and how, with the aid of a simple device, configuration averaging may be performed by the use of established techniques. The approximation used is, as in the case of the usual CPA, a single-site one. Three self-consistent equations are obtained that must be solved simultaneously; these replace the single CPA equation. Numerical results are displayed for a series of alloys, and a discussion of certain aspects of the theory, such as its moment-preserving properties, is also included.

159 citations

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TL;DR: In this article, the authors used a cluster model to describe the excitations near to the defect and compared the predictions of the various theories with the experimental results, showing that the theory is fairly satisfactory for a low concentration of defects and low temperatures.

Abstract: The introduction of a low concentration of defects into a magnetic insulator modifies the spectrum of the magnetic excitations. In general the spectrum consists of a set of impurity modes associated with the defect and its immediate neighbors. Impurity modes that occur outside the band of host excitations are localized in the neighborhood of the defect and at the same time perturb the host band, while modes lying within the band lead to resonant behavior of the excitations of the host. In recent years, optical, neutron scattering, and nuclear magnetic resonance techniques have been used to study mixed crystals of antiferromagnetic transition metal fluorides. Many of the features may be understood by using the molecular field or Ising model for the excitations. An improvement on this form of the theory is to use a cluster model to describe the excitations near to the defect. Some features may however be described only when the excitations of the host are treated adequately; this requires the use of Green's function theories that have been developed for antiferromagnets containing defects. A detailed comparison is presented of the predictions of the various theories with the experimental results. Although the theory is fairly satisfactory for a low concentration of defects and low temperatures, considerable complexities arise in extending it to higher temperatures and large concentrations.

139 citations