Showing papers on "Coherent potential approximation published in 1977"
TL;DR: In this article, a method for solving the CPA equations for a random substitutional alloy crystal potential which consists of nonoverlapping'muffin-tin' potential wells is presented.
Abstract: A method is presented for solving the CPA equations for a random substitutional alloy crystal potential which consists of nonoverlapping 'muffin-tin' potential wells. The case of paramagnetic Ni-Cu alloys is considered.
38 citations
TL;DR: In this paper, the electron correlation in disordered alloys is discussed in the Hubbard model and a single band model is assumed, and the t -approximation and the coherent potential approximation are used.
Abstract: The electron correlation in disordered alloys is discussed in the Hubbard model. A single band model is assumed, and the t -approximation and the coherent potential approximation are used. It is shown that intra-atomic Coulomb interactions are screened by the effect of electron correlation and effective intra-atomic Coulomb interactions at atomic sites are introduced. As an example their numerical estimation is carried out for Pd–Rh alloys. The effective intra-atomic Coulomb interactions are found to be considerably dependent on the concentration of alloys. By taking into account the electron correlation a generalized transverse spin susceptibility for disordered alloys is also calculated.
36 citations
TL;DR: In this article, the angular distribution of photo-emitted electrons from a 001 surface of single crystal Cu 77 Ni 23 random substitutional alloy was studied in terms of calculations based on the Coherent Potential Approximation for non-overlapping muffin tin potentials.
23 citations
TL;DR: In this article, the average density of states and the local density for the paramagnetic and ferromagnetic Ni-Pd, Ni−Pt and Pd-Pt alloys are calculated by the coherent potential approximation by taking account of an off-diagonal randomness.
Abstract: The average density of states and the local density of states for the paramagnetic and ferromagnetic Ni–Pd, Ni–Pt and Pd–Pt alloys are calculated by the coherent potential approximation by taking account of an off-diagonal randomness. The Hubbard model is assumed and the Hartree-Fock approximation is used. It is found that the band-width of these alloys changes nearly linearly with concentration. The peak of the density of states near the Fermi level remains without large distortion by alloying and that of the local density of states is similar to that of each pure metal. The bulk and local magnetic moments, paramagnetic spin susceptibility and low temperature specific heat coefficient are calculated. These results are compared with experiments and qualitative agreements are obtained.
16 citations
TL;DR: In this paper, the residual resistivity of Ni-Fe and Ni-Cr is calculated in the coherent potential approximation to the muffin-tin potential model by use of a new method of computation.
Abstract: The residual resistivity of Ni-Fe and Ni-Cr is calculated in the coherent potential approximation to the muffin-tin potential model by use of a new method of computation.
15 citations
TL;DR: In this article, a single site coherent potential approximation (CPA) including force constant changes in the additive limit (designated the CPA-F) is applied to phonons in Rb/sub 1-c/K/sub c/ alloys.
Abstract: A single-site coherent potential approximation (CPA) including force constant changes in the additive limit (designated the CPA-F) is applied to phonons in Rb/sub 1-c/K/sub c/ alloys. The CPA-F results are in better overall agreement with the neutron scattering measurements of Kamitakahara and Copley than mass-defect CPA results. However, marked discrepancies in the concentration, branch, and wave-vector dependence and in the line shapes remain between CPA-F and experimental neutron scattering cross sections. These discrepancies suggest the need to include multiple scattering from pairs and larger clusters in the theoretical treatment.
15 citations
TL;DR: In this paper, an extension of the usual diagrammatic coherent-potential approximation is considered to account for the presence of disorder both in off-diagonal and inhomogeneous terms, applied to the quenched site-disordered Ising model (S=1/2) above the transition, where the fundamental equation for the correlation function is a generalized random phase approximation.
Abstract: An extension of the usual diagrammatic coherent-potential approximation is considered to account for the presence of disorder both in off-diagonal and inhomogeneous terms. The method is applied to the quenched site-disordered Ising model (S=1/2) above the transition, where the fundamental equation for the correlation function is a generalized random-phase approximation. The results for the initial slope of the critical temperature and the critical concentration are presented for the simple cubic lattice with nearest-neighbour interactions, and they are in reasonable agreement with the values derived by other methods. The differences are studied and a discussion is presented to show that, near the critical concentration, terms not considered in the coherent-potential approximation are as important as the terms included. The application of this method to other models is also briefly discussed and, in the particular case of the Heisenberg model, it is shown that the method reproduces the basic results derived by Harris et al. (1974) using an effective-medium approach.
15 citations
TL;DR: In this article, a review is given of various methods for calculating the electronic and magnetic structure of ferromagnetic transition-metal alloys based on the coherent potential approximation and its extension.
Abstract: A review is given of certain methods for calculating the electronic and magnetic structure of ferromagnetic transition-metal alloys based on the coherent potential approximation and its extension. Three subjects are discussed in detail. (1) The response of the alloys to an external magnetic field is calculated on the basis of the single-site CPA combined with the Hartree-Fock approximation for fcc Ni-Fe, bcc Fe-Ni and Fe-Co alloys. (2) A method of treatening the effect of the nearest-neighbor composition on the basis of an extension of CPA is discussed. The dependence of the Fe atomic magnetic moment and other quantities on the nearest neighbor composition in bcc Fe-Co and Fe-V alloys is calculated as an example of the applications of this method. (3) A method of carrying out the single-site CPA for the muffin-tin potential model is proposed. Some preliminary results are presented.
15 citations
TL;DR: In this article, a quantum formulation of the electrical conductivity of a disordered alloy is made in the coherentpotential approximation (CPA), which is applicable to the case where the one-electron Hamiltonian depends additively on the configurations of individual sites.
Abstract: A quantum formulation of the electrical conductivity of a disordered alloy is made in the coherent-potential approximation (CPA). The formalism is applicable to the case where the one-electron Hamiltonian (or its suitably renormalized form) depends additively on the configurations of individual sites. The configurational average of the vertex function which involves the random one-electron current operator is evaluated in the CPA by introducing the effective (or coherent) current operator, which is periodic but energy-dependent. It is shown that the case where the vertex correction to the vertex function vanishes is rather exceptional but that the kernel of the integral equation determining the vertex correction can be written in the separable type in the CPA. The correspondence between the present theory and the semiclassical Boltzmann theory is investigated in detail.
14 citations
TL;DR: In this article, a coherent potential approximation (CPA) treatment of positron annihilation in an alloy is presented, where simple formulae for the spatial and the momentum distributions of the positrons are derived.
Abstract: A coherent potential approximation (CPA) treatment of positron annihilation in an alloy is presented. Simple formulae for the spatial and the momentum distributions of the positrons are derived. Numerical computations are performed to illustrate the effects of the smearing of the positron momentum distribution and of the electron Fermi momentum of the annihilation photon momentum distribution.
14 citations
TL;DR: In this paper, the Hall conductivity is formulated within the CPA for the tight-binding model Hamiltonian, and the effect of the off-diagonal disorder on the hall conductivity was investigated for a binary alloy with a simple cubic lattice.
Abstract: The Hall conductivity is formulated within the CPA for the tight-binding model Hamiltonian. Particular care is taken for gauge invariance of the formulation. The present formalism is applicable to the case with off-diagonal disorder in addition to diagonal disorder, and the effect of the off-diagonal disorder on the Hall conductivity is investigated for the model considered by Shiba (1971) and that by Blackman et al. (1971). It is shown that the vertex correction to the Hall conductivity vanishes for these models provided that the lattice has the inversion symmetry. For a numerical application of the present formalism a binary alloy with a simple cubic lattice is investigated.
TL;DR: In this paper, the electronic densities of states of bulk and cleaved binary alloys are determined through a tight-binding model, using a continued fraction technique and a computer simulation on clusters of several thousands of atoms.
Abstract: Electronic densities of states of bulk and cleaved binary alloys are determined through a tight-binding model, using a continued fraction technique and a computer simulation on clusters of several thousands of atoms. Results are presented for nondegenerate bands and simple and face centred cubic lattices. They are compared with the coherent potential approximation (CPA) and Bethe-Peierls approximation (BPA). The method can deal with cleaved binary alloys and also non-homogeneous alloys, and an example of a cleaved alloy with surface segregation is given. The surface density of states is shown to be strongly sensitive to the composition of the first layer and this could be an important factor in studying surface segregation.
TL;DR: In this paper, the dynamics of a two-component Ising model with randomness during both in the transverse field and the Ising coupling is treated within the single-site coherent potential approximation (CPA).
Abstract: The dynamics of a two-component Ising model in a transverse field (IMTF) with randomness during both in the transverse field and the Ising coupling is treated within the single-site coherent potential approximation (CPA). The authors deal primarily with the polarized phase; they replace the fluctuating longitudinal component of the molecular field by two effective parameters, one for each species, which are determined self-consistently. The CPA spectra of the collective spin excitations are found analytically in the dilute case using a Hubbard model density for the Ising interaction, and are also calculated numerically for the general two-component IMTF. It is shown that the static susceptibility cannot diverge within the single site CPA. Characterizing the phase transition by the softening of the lowest mode in the spectrum. The stability conditions for the polarized phase at T=O are then determined.
TL;DR: In this paper, a simple formulation of the Stoner model is explained and the dependence on the magnetization of a molecular field coefficient is assumed so as to fit the observed temperature variations of the magnetisation for Ni, Co and Fe.
Abstract: A simple formulation of the Stoner model is explained. The dependence on the magnetization of a molecular field coefficient is assumed so as to fit the observed temperature variations of the magnetization for Ni, Co and Fe. Previous and new numerical results on the temperature dependences of the paramagnetic susceptibility and electronic specific heat and the temperature and magnetic field dependences of the high-field spin susceptibility obtained for Ni, Co and Fe and some alloys in the Stoner model are reviewed. The calculated results on the high-field spin susceptibility for Fe alloys and Ni-Cu alloys in the rigid band model and in the coherent potential approximation are also shown. A new estimation of the magnetic energy for Ni and Fe is compared with the values of kBTC. A strong dependence on the magnetization of the molecular field coefficient assumed for Fe and Co is discussed.
TL;DR: In this article, the quantum transport theory formulated in the coherentpotential approximation in the first paper of this series (1977) is applied to a model random alloy, which is much simplified and yet retains some general essential features of a long-range non-local potential.
Abstract: For pt.III see ibid., vol.10, p.2141 (1977). The quantum transport theory formulated in the coherent-potential approximation in the first paper of this series (1977) is applied to a model random alloy, which is much simplified and yet retains some general essential features of a long-range non-local potential. The effects of the vertex correction and the non-locality of the potential on the conductivity are investigated numerically and the features of them are discussed in detail.
TL;DR: A theory of the thermodynamic properties (spin correlation functions, susceptibility and specific heat) in the paramagnetic phase of Ising systems with various forms of random bond arrangement is developed in this article.
Abstract: A theory of the thermodynamic properties (spin correlation functions, susceptibility and specific heat) in the paramagnetic phase of Ising systems with various forms of random bond arrangement is developed. It represents an extension of the random phase approximation (RPA). The difference equation for the spin correlation functions which has random coefficients is solved using the coherent potential approximation (CPA), and the various parameters calculated self-consistently. Results for the quenched dilute bond case are in good agreement with other theories. For a truncated Gaussian distribution of bond strengths it is found that the transition temperature and other properties are fairly universal functions of the mean square of the distribution. The transition to a ferromagnetic phase disappears when the concentration of negative exchange bonds becomes large enough, apparently because of spin glass formation. Results for various binary distributions are also given.
TL;DR: In this paper, the charge and spin structure factors in random binary alloys have been examined in the framework of the Coherent Potential Approximation (CPA) and the spin structure factor shows a characteristic feature, due to the disorder, which in transition metal alloys is expected to give a more contracted neutron form factor.
TL;DR: In this paper, the volume paramagnetostriction of disordered alloys is calculated in the itinerant electron model by assuming transfer energys and the number of d -electrons to vary with volume change.
Abstract: The volume paramagnetostriction of disordered alloys is calculated in the itinerant electron model. By assuming transfer energys and the number of d -electrons to vary with volume change, a general expression for the volume dependence of spin paramagnetic susceptibility is derived from the results for the spin paramagnetic susceptibility of a disordered binary alloy which is obtained in the coherent potential approximation and the t -approximation for the electron correlation. Numerical estimations of the spin paramagnetic susceptibility and its volume dependence are given for Pd–Rh, Ni–Rh and Pi–Ni alloys and a good agreement with experiments is obtained. It is found that a volume dependence of the transfer energy or the bandwidth has a main effect on the volume paramagnetostriction.
TL;DR: In this paper, a simple decoupling scheme is proposed and analyzed for the problem of the electron propagation in magnetic semiconductors treated in the s-d model in most important cases, the method is shown to reduce to the Kubo form of the coherent potential approximation.
Abstract: A simple decoupling scheme is suggested and analyzed for the problem of the electron propagation in magnetic semiconductors treated in the s-d model In most important cases, the method is shown to reduce to the Kubo form of the coherent potential approximation It is then used to assess the role of higher order effects in the red shift of the optical absorption edge
TL;DR: In this article, the coherent-potential approximation on the basis of the effective medium approach is reformulated on a diagrammatic expansion and resummation approach due to Yonezawa (1968).
Abstract: For pt.I see ibid., vol.10, p.211 (1977). Quantum transport theory formulated in the previous paper in the coherent-potential approximation on the basis of the effective-medium approach is reformulated on the basis of the diagrammatic expansion and resummation approach due to Yonezawa (1968). It is shown that the new formulation is equivalent to the previous one.
TL;DR: In this paper, the coherent potential approximation has been generalized to incorporate the effects of the local environments in the electronic properties of disordered alloys, and the results for total and local densities of states on an atom in a simple cubic alloy for an s band are in close agreement with the existing exact results.
TL;DR: In this paper, it was shown that the quantum transport theory in the coherentpotential approximation is consistent with the Ward identity and a similar identity and that this consistency is essential to obtaining the correct result in that reduction.
Abstract: For pt.II see ibid., vol.10, p.2131 (1977). It is shown that, when a random substitutional alloy has a small carrier density, a large cancellation occurs between two terms of its electrical conductivity in the quantum transport theory. This cancellation must be treated carefully when the reduction of some quantum transport theory to the Boltzmann transport theory is made in the weak-scattering or the dilute limit. It is shown that the quantum transport theory in the coherent-potential approximation is consistent with the Ward identity and a similar identity and that this consistency is essential to obtaining the correct result in that reduction.
TL;DR: In this paper, a general equation for the coherent potential for binary alloys with completely degenerate electron bands is derived in the alloy analogy approximation with the inclusion of the intra-atomic Coulomb and exchange interactions.
Abstract: A general equation for the coherent potential for binary alloys with completely degenerate electron bands is derived in the alloy analogy approximation with the inclusion of the intra-atomic Coulomb and exchange interactions. Special important cases of pure metals with strong Coulomb interaction and the Hasegawa-Kanamori's alloys as well as the alloys with strong Coulomb correlation are discussed briefly.
TL;DR: In this article, the dynamical properties of the S = 1/2 Heisenberg ferromagnet were studied using an extension of the RPA method, where the effect of temperature is represented by a fixed array of up and down spins, including short-range-order effects.
Abstract: The dynamical properties of the S=1/2 Heisenberg ferromagnet are studied using an extension of the RPA method. The effect of temperature is represented by a fixed array of up and down spins, including short-range-order effects. The spin wave excitations are calculated in this disordered array using the coherent-potential approximation (CPA) for a system of potentials due to the appropriate distribution of bonds. A relation between the number of reversed spins and temperature is derived from self consistency. The method gives a satisfactory approximation overall to the spin wave response at T
TL;DR: In this paper, it was proved that there is no antiferromagnetic solution to the Hubbard model for a half-filled band, within the alloy analogy and the coherent potential approximation.
TL;DR: In this article, the authors present a theoretical model able to describe the occurrence of localized magnetism in disordered systems such as B1−xAc, where A and B are two transition elements and Ac is an actinide impurity.
Abstract: We present a theoretical model able to describe the occurrence of localized magnetism in disordered systems such as A
x
B1−x
Ac, where A and B are two transition elements and Ac is an actinide impurity. The disordered host is treated within the coherent potential approximation (CPA); thed level of the actinide impurity creates a Slater-Koster-liked scattering potential and thef states of the actinide impurity are broadened by thed–f hybridization. The occurrence of magnetic-nonmagnetic transitions as a function ofx is discussed within the Hartree-Fock approximation. In the limiting casesx=0 andx=1, this model improves the previous theories for the magnetism of an actinide impurity in a pure transition host and in the general case it permits some predictions, especially for the system Pd
x
Th1−x
Pu.
TL;DR: In this article, temperature variation of spin susceptibility for Ni-Pt alloys is calculated in the band model, and the densities of states for alloys are calculated by the coherent potential approximation with off-diagonal randomness.
TL;DR: In this paper, the librons in mixtures of ortho- and para-hydrogen are studied using the coherent potential approximation (CPA) by extending their previous work.
Abstract: The librons in mixtures of ortho- and para-hydrogen are studied using the coherent potential approximation (CPA) by extending our previous work. The orientations of ortho-molecules in the vicinity of para-hydrogen defects are determined self-consistently and the influence of the tipping effect on the harmonic coupling parameters is calculated. Further effects of the libron anharmonicities are taken into account by fitting the harmonic coupling parameters to the anharmonick=0 frequencies of Coll and Harris for the pure solid. Numerical results for the overall density of states and the density of states of the threek=0 modes are presented for various concentrations. When compared with corresponding results in the averaget-matrix the present work is generally found to be more satisfactory. We show however, that a clear understanding of the modes in hydrogen mixtures requires an improved treatment of the concentration dependence of the cubic anharmonicities and hence an extension of the CPA to anharmonic systems.
TL;DR: In this article, the volume of a solid solution has a characteristic behavior in its concentration dependence due to the effect of electron correlations, and the volume has a cusp at the concentration which gives the just half-filled valence band, if correlations are sufficiently strong.
Abstract: The volume of a solid solution is shown to have a characteristic behavior in its concentration dependence due to the effect of electron correlations. The volume has a cusp at the concentration which gives the just half-filled valence band, if correlations are sufficiently strong. For the purpose of an illustration, calculations are practised with the use of the coherent potential approximation on the Hubbard model.
TL;DR: In this article, the electrical resistivity of a binary antiferromagnetic alloy due to the scattering on spin disorder and on the static potential of a random distribution of different atoms over the lattice is calculated in the coherent potential approximation.
Abstract: The electrical resistivity of a binary antiferromagnetic alloy due to the scattering on spin disorder and on the static potential of a random distribution of different atoms over the lattice is calculated in the coherent potential approximation. The concentration dependences of the contributions to the resistivity due to the spin disorder and elastic scattering as well as of the interference term caused by differences of the atomic levels and exchange constants of the components are obtained. If the Fermi energy is far from the spectrum gap arising with the transition to the antiferromagnetic state, the resistivity of alloys decreases while the magnetization of the sublattices increases. A more complicated behaviour of the resistivity versus magnetization takes place in those alloys in which the Fermi energy is near the spectrum gap. In this case an increase of elastic and spin contributions to the resistivity is possible with antiferromagnetic ordering. This increase of some contributions to the resistivity may be a reason for such anomalies as the maximum or minimum of the total resistivity in the region of the Neel point.
[Russian Text Ignored].