Showing papers on "Coherent potential approximation published in 1974"
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
TL;DR: In this paper, the energy spectrum of exciton polaron is studied with the dynamical CPA (coherent potential approximation), which is introduced for inelastic scattering by Einstein phonons at every lattice site.
Abstract: Energy spectrum of exciton polaron is studied with the dynamical CPA (coherent potential approximation), which is introduced for inelastic scattering by Einstein phonons at every lattice site. The coherent potential at energy E is determined by the potentials at energies apart from E by integral times the phonon energy. We determine applicability ranges of the concepts used in the limiting cases; (I) the nearly free exciton for weak coupling, (II) multiple bands of the vibronic excitons for small excitation transfer, and (III) the self-trapped exciton for strong coupling. An ambiguous boundary separating (II) and (III) lies about S ≃6, with S representing the ratio of the energy gain of exciton localization to the phonon energy. The change with increasing excitation transfer for a fixed S is characterized by the sharp crossing of (III) with (I) for \(S{\gtrsim}6\), while by the gradual merging of (II) into (I) for \(S{\lesssim}6\).
93 citations
TL;DR: In this article, analytic properties of the coherent potential approximation (CPA) were derived, and it was shown that the conditional densities of states are always positive and that the iteration scheme, starting from the averaged t-matrix approximation, is always convergent to the CPA.
Abstract: Some analytic properties of the coherent potential approximation (CPA) are derived. As shown recently by Muller-Hartmann (1973), the CPA is analytic: this result is rederived by using a slightly different method. It is then shown that the conditional densities of states are always positive and that the iteration scheme, starting from the averaged t-matrix approximation, is always convergent to the CPA. Finally all these results are extended to the molecular CPA first proposed by Tsukada (1969).
76 citations
TL;DR: In this article, the down-and up-spin Green functions were obtained in the weak s − d interaction limit with the results of the molecular field approximation and in the strong interaction limit, respectively.
Abstract: Electronic structure in magnetic semiconductors is investigated on the basis of the s - d exchange model. The exchange scattering of an electron by localized spins is treated in the coherent potential approximation. Coupled equations for the down- and up- spin Green functions are obtained. These equations agree in the weak s - d interaction limit with the results of the molecular field approximation and in the strong interaction limit with those obtained previously by the present author. The density of states for down- and up- spins is calculated in the paramagnetic and completely ferromagnetic states for various values of interaction strength, by assuming a semi-elliptic form for unperturbed density of states.
56 citations
TL;DR: In this paper, the coherent potential approximation (CPA) has been generalized to describe spin waves in a dilute Heisenberg ferromagnet at T = 0 and the full T matrix of an isolated vacancy in an effective medium is evaluated.
Abstract: The coherent potential approximation (CPA) has been generalized to describe spin waves in a dilute Heisenberg ferromagnet at T=0. The full T matrix of an isolated vacancy in an effective medium is evaluated and the self-energy is obtained selfconsistently. In order to project out the spurious degrees of freedom associated with the fictitious spins on the vacancy sites, a class of pseudopotentials are constructed. The response functions G(k, omega ) and density of states rho ( omega ) for two such pseudopotentials are evaluated in detail. The had core pseudopotential is found to yield the best CPA approximation although it fails near the critical percolation concentration of magnetic sites, as do all the effective medium theories in the face of large fluctuations. The spin-wave stiffness D is calculated and the magnetization and specific heat near T=0. The random phase approximation is used to find Tc, the transition temperature.
53 citations
TL;DR: In this paper, the authors generalize the coherent potential approximation (CPA) for the lattice dynamics of mass-disordered systems to the case of mixed diatomic crystals.
Abstract: We generalize the coherent-potential approximation (CPA) for the lattice dynamics of mass-disordered systems to the case of mixed diatomic crystals. Specific results are obtained for a one-dimensional model. We prove that for mass defects on only one sublattice the CPA self-energy is nonzero only on that sublattice. We compare the configuration-averaged density of states calculated by the CPA with computer experiments on several mixed diatomic chains. We compare the CPA dielectric susceptibility for the one-dimensional model with the experimental optical properties of several interesting III-V, II-VI, and I-VII mixed crystals. With some qualifications we conclude that the CPA in one-dimension can explain the switching from one-mode- to two-mode-type behavior observed in some III-V mixed systems and unexplained by previous theories. Finally, we present a one-dimensional CPA phase diagram for the transition from one optic band to two optic bands in the density of states.
40 citations
TL;DR: In this paper, the authors discuss the connection between the usual Bragg-Williams theory and some recent extension of the coherent potential approximation derived to deal with the order-disorder transition in alloys.
Abstract: The authors discuss the connection between the usual Bragg-Williams theory and some recent extension of the coherent potential approximation derived to deal with the order-disorder transition in alloys.
40 citations
TL;DR: In this paper, a new technique for evaluating configurationally averaged properties of disordered systems due to Mookerjee (see abstr. A43969 of 1973) is examined.
Abstract: A new technique for evaluating configurationally averaged properties of disordered systems due to Mookerjee (see abstr. A43969 of 1973) is examined. Attention is focused on the site-diagonal element of the single-particle Green function in the Anderson model of cellular disorder, and single-site coherent potential approximation (CPA) is shown to arise naturally within this new formalism. Generalizations to n site and cluster approximations then follow in a very direct and instructive fashion. Necessary analytic properties of the single-particle Green functions are an immediate corollary of the method. Numerical results are presented for the bimodally disordered tight-binding linear chain.
39 citations
TL;DR: In this paper, the excitation of the diluted Heisenberg antiferromagnet using the coherent potential approximation (CPA) by extending the work of Harris et al. for the ferromagneticnet was studied.
Abstract: The excitation of the diluted Heisenberg antiferromagnet are studied using the coherent potential approximation (CPA) by extending the work of Harris et al. for the ferromagnet. The Green functions of the system are described in terms of an effective medium which is determined self-consistently using the CPA equation to treat the scattering of a vacancy and its neighbours. Results of calculations for the spectral weight function and for the density of states are presented. When compared with previous theories the present work is generally found to be more satisfactory. Comparison is also made with neutron scattering data for (Mn1-xZnx)F2 and excellent agreement is found.
29 citations
TL;DR: In this paper, a continued fraction method for calculating the density of states due to Haydock and others is applied to a commonly used model Hamiltonian for a disordered alloy, which suffers from none of the analytic difficulties which bedevil selfconsistent cluster theory methods based on the coherent potential approximation.
Abstract: A continued fraction method for calculating the density of states due to Haydock and others is applied to a commonly used model Hamiltonian for a disordered alloy. The density of states may be calculated with great ease from this method and suffers from none of the analytic difficulties which bedevil selfconsistent cluster theory methods based on the coherent potential approximation. The density of states has been calculated for a simple cubic crystal and displays in the minority band and sometimes in the majority band) peaks which are related to the levels of isolated clusters containing one, two, three or several minority (or majority) atoms. The method has the virtue also of enabling the Lifshitz condition on the density of states to be satisfied although this is done in a slightly artificial manner.
24 citations
TL;DR: In this article, the authors extended the coherent potential approximation (CPA) for vibrational systems to include force-constant changes as well as mass defects in alloys for which the force constants superimpose linearly.
Abstract: The coherent-potential approximation (CPA) for vibrational systems is extended to include force-constant changes as well as mass defects in alloys for which the force constants superimpose linearly. Such a model is correct at both the low- and high-concentration limits, and may be reasonable for broad concentration ranges in some real systems, for example, in diatomic alloys like mixed alkali halides. Results for one-dimensional systems with nearest-neighbor force constant and mass disorder have the same over-all agreement with exact results as was previously found for CPA calculations for mass defects only. Applications in three dimensions appear to be computationally feasible.
TL;DR: In this article, a multiband CPA model was developed for ferromagnetic alloys in order to calculate the spin and orbital-dependent densities of states, and the magnetic moments and populations obtained for the Co-Ni alloys were compared with experiments.
Abstract: A multiband CPA model is developed for ferromagnetic alloys in order to calculate the spin- and orbital-dependent densities of states. The magnetic moments and populations obtained for the Co-Ni alloys are compared with experiments. The good agreement obtained with such different data proves the effectiveness of the method and the reliability of the calculated densities of states, the properties of which are also discussed.
TL;DR: In this article, a theory of superconductivity for transition-metal alloys is presented by using the coherent potential approximation, and expressions for the superconducting order parameter and transition temperature of transition metal alloys A x B 1− x in terms of the parameters characterizing the pure metals are given.
TL;DR: In this paper, the Coherent Potential Approximation (CPA) was applied to substitutional disordered alloys consisting of rare earth metal ions with singlet ground state and non-magnetic components.
Abstract: The Coherent Potential Approximation (CPA) is applied to substitutional disordered alloys consisting of rare earth metal ions with singlet ground state and non-magnetic components. We calculate the dependence of the elementary excitations and the transition temperature on the concentration of impurities.
TL;DR: In this article, a simple method for calculating the magnetic susceptibilities in disordered alloys described in the coherent potential approximation is given, with special attention drawn to the paramagnetic case.
Abstract: A simple method for calculating the magnetic susceptibilities in disordered alloys described in the coherent potential approximation is given. Special attention is drawn here to the paramagnetic case. The equivalence with Fukuyama's (1972 and 1973) results is shown.
TL;DR: In this article, the role of disorder on the three dimensional ordering below the Peierls temperature is discussed. And the reduction in the transition temperature in a disordered one dimensional conductor is calculated using the coherent potential approximation.
TL;DR: In this article, a fine-grained ultraviolet photoelectron spectra have been obtained fron clean surfaces of Ag-Au alloys using 21.22 and 40.81 eV photons.
Abstract: Ultraviolet photoelectron spectra have been obtained fron clean surfaces of Ag-Au alloys using 21.22 and 40.81 eV photons. The spectra, which exhibit fine structure not previously reported, have been successfully interpretated in terms of the coherent potential approximation to the extent that currently available calculations permit.
TL;DR: In this paper, the magnetic properties of Ni-Pt alloys are calculated in the coherent potential approximation and a maximum is found in the low temperature electronic specific heat coefficient for alloys near the critical concentration for ferromagnetism.
TL;DR: In this paper, the Stoner theory for magnetism in itinerant systems has been extended to describe the properties of magnetic transition metal alloys in terms of local electronic spin densities.
Abstract: For many years the properties of magnetic transition metal alloys were analyzed in terms of a rigid band model and the Stoner theory for magnetism in itinerant systems. Recently the introduction of the coherent potential approximation (CPA) has resulted in a description of the band structure of metallic alloys in terms of a local electronic charge density of states. The CPA and related approximations are derived in detail in this article and it is shown how these approximations have been extended to describe the properties of magnetic transition metal alloys in terms of local electronic spin densities. Both the statics and dynamics of itinerant magnetic alloys are discussed and the comparison with experiment is examined in detail. The article is concluded with a description of possible improvements to the CPA for magnetic alloys in particular for local environment effects.
TL;DR: In this paper, the density of states of binary alloys from a calculation using the matrix coherent potential approximation was obtained, even though the quasicrystalline assumption for the off-diagonal elements was not employed.
Abstract: Results are presented for the density of states of binary alloys from a calculation using the matrix coherent potential approximation. A form of the density of states with realistic features was obtained even though the quasicrystalline assumption for the off-diagonal elements was not employed. These features arise solely from the local information about small clusters of atoms. However, it is felt from these results that a proper density of state can only be calculated from information of larger clusters.
TL;DR: In this article, a self-consistent theory for phonons in mixed crystals is proposed, taking into account both mass and force-constant changes, and the force-constraint changes are included approximately and treated within a separable kernel approximation.
Abstract: A self-consistent theory has been proposed for phonons in mixed crystals, taking into account both mass and force-constant changes. The force-constant changes are included approximately and treated within a separable kernel approximation. In the limiting cases the theory reproduced the well known results of the low-concentration theories and the mass-disordered coherent potential approximation theory.
TL;DR: In this article, a theory for strong-coupling superconducting transition-metal alloys is developed, where the configurational dependence of the self-energy part is discussed and, in analogy to McMillan, an expression forTc is derived for a single band as well as for anΓ′25-band.
Abstract: Within the coherent potential approximation (CPA) a theory for strong-coupling superconducting transition-metal alloys is developed. The configurational dependence of the selfenergy-part is discussed and, in analogy to McMillan, an expression forTc is derived for a singles band as well as for anΓ′25-band. The electron-phonon coupling constantλ occuring in this expression depends explicitly on: the average component density of states,NA(0) andNB(0), the electron-phonon matrix elements of the components, the difference of the atomic energy levels,δ, and the phonon Green's function at zero frequency. In the limit of the pure metal this expression reduces to that developed by Appel and Kohn. It is shown that the change of the phonon density of states in an alloy due to the atomic mass differences — which is very complicated — does not influence the value ofλ.
TL;DR: In this article, a cluster theory of a dilute antiferromagnet which simultaneously takes into account the fluctuations in the longitudinal and transverse part of the exchange interaction is proposed, which allows to describe the dependence of the line shapes of the spin excitation spectrum on the nonmagnetic atom concentration and the wave vector.
Abstract: A cluster theory of a dilute antiferromagnet which simultaneously takes into account the fluctuations in the longitudinal and transverse part of the exchange interaction is proposed. The present theory allows to describe the dependence of the line shapes of the spin excitation spectrum on the nonmagnetic atom concentration and the wave vector. A comparison with experimental results indicates that the predictions of the theory are valid in a wide range of concentrations when the long-range order persists. It is pointed out that the coherent wave approximation accounts for the gross behaviour of the spin excitation spectrum. It is demonstrated that the results of the cluster theory are close to those of the coherent potential approximation, but more transparent and more suitable for comparison with experiment.
[Russian Text Ignored.]
TL;DR: In this paper, a single-site coherent potential approximation is derived which determines the distribution function, characterizing this alloy model self-consistently by the Green's function, and a static approximation is introduced which is shown to be equivalent to the replacement of the Hubbard model by an alloy model.
Abstract: Starting from the functional-differential equation for the self-energy, a static approximation is introduced which is shown to be equivalent to the replacement of the Hubbard model by an alloy model. By means of the single-site coherent potential approximation an equation is derived which determines the distribution function, characterizing this alloy model self-consistently by the Green's function. The procedure avoids shortcomings of other methods, as ad-hoc assumptions on the distribution function or non-unique decompositions of the interaction term.
Ausgehend von der Funktional-Differentialgleichung der Selbstenergie wird eine statische Approximation eingefuhrt, die der Ersetzung des Hubbard-Modells durch ein Legierungs-modell aquivalent ist. Mit Hilfe der Einzentren-Coherent-Potential-Approximation wird eine Gleichung fur die das Legierungsmodell charakterisierende Verteilungsfunktion abgeleitet, durch die diese Verteilungsfunktion selbstkonsistent aus der Greenschen Funktion bestimmt wird. Dag Verfahren vermeidet Nachteile anderer Methoden, wie ad hoc-An-nahmen uber die Verteilungsfunktion oder nicht eindeutige Zerlegungen des Wechselwirkungsausdrucks.
TL;DR: In this article, the diagram-based methods of electron theory elaborated by Yonezawa for substitutional alloys have been applied to translationally disordered systems with short-range correlations (e.g., liquid metals).