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Effect of intersite band hybridization and on-site correlation on the magnetism of localized-moment systems
Abstract
We study the effect of the conduction-electron density of states on magnetic transition temperatures in metallic systems with localized magnetic moments. We assume the indirect-exchange interaction to originate from s-f mixing of the Anderson type and we perform calculations of the coupling parameters, up to fourth-nearest neighbors, in the formalism of da Silva and Falicov. The density-of-states models are obtained from a two-component band in tight-binding scheme and we include on-site Coulomb correlation. We find that the magnetic energy has a modulated Ruderman-Kittel-Kasuya-Yoshida-like behavior as a function of the number of conduction electrons n. This is, however, dominated by two strong maxima when n is such that the Fermi level lies on a peak of the density of states. In this condition the transition temperature is enhanced by at least 1 order of magnitude with respect to the weaker background. This behavior is found for different values of the virtual excitation energy of the s-f mixing mechanism.
... Actually, the value of J varies following changes either of the interaction distance [11, 12] (e.g. due to the substituent ion having a different radius), or of the band occupancy [18] (e.g. due to nonisovalent substitutions). ...
An interpretation of the Cu-site substitution effects on the critical temperature of La2CuO4-derived superconductors is presented. We argue that the available data on the dependence ofT
c on the amount of Cu-site substitutions indicate that the integrity of the Cu spin lattice is not fundamental to the superconductivity.
A consistent way of systematizing the published data is proposed, by focusing on the interplay of valence fluctuations and
accompanying lattice deformations.
An attempt to find a quantitative relationship between magnetic transition temperature and conduction states properties in metallic materials is presented. The exchange interaction among magnetic moments is assumed to be of the Anderson's s-f type and the conduction states have s-d orbital character. The results are analyzed vs. different amount of s-d hybridization within LCAO scheme.
We investigate the indirect exchange interaction between localized moments via conduction bands. The origin of the exchange is assumed to be the Anderson s-f mixing mechanism appropriate to anomalous rare earth and light actinide systems. The conduction states originate from s-orbitals in a CsCl structure. Hubbard correlation in Hartree-Fock approximation is included. We perform calculations of the coupling constants between localised moments and obtain a characteristic relationship between the conduction electrons density of states and the magnetic transition temperature.
We study a two-band Hamiltonian for hybridized and correlated bands of sc and bcc symmetry, the latter case approximating a two-dimensional band. Magnetic phase diagrams are obtained, showing in the bcc case a region of rapid phase change with filling which is absent in the sc case.
Because of large spatial separation of the Mn atoms in Heusler alloys the Mn 3d states belonging to different atoms do not overlap considerably. Therefore an indirect exchange interaction between Mn atoms should play a crucial role in the ferromagnetism of the systems. To study the nature of the ferromagnetism of various Mn-based semi- and full-Heusler alloys we perform a systematic first-principles calculation of the exchange interactions in these materials. The calculation of the exchange parameters is based on the frozen-magnon approach. The calculations show that the magnetism of the Mn-based Heusler alloys depends strongly on the number of conduction electrons, their spin polarization and the position of the unoccupied Mn 3d states with respect to the Fermi level. Various magnetic phases are obtained depending on the combination of these characteristics. The Anderson's s-d model is used to perform a qualitative analysis of the obtained results. The conditions leading to diverse magnetic behavior are identified. If the spin polarization of the conduction electrons at the Fermi energy is large and the unoccupied Mn 3d states lie well above the Fermi level, an RKKY-type ferromagnetic interaction is dominating. On the other hand, the contribution of the antiferromagnetic superexchange becomes important if unoccupied Mn 3d states lie close to the Fermi energy. The resulting magnetic behavior depends on the competition of these two exchange mechanisms. The calculational results are in good correlation with the conclusions made on the basis of the Anderson s-d model which provides useful framework for the analysis of the results of first-principles calculations and helps to formulate the conditions for high Curie temperature. Comment: 16 pages, 9 figures, 2 tables
The Green-function technique, termed the irreducible Green functions (IGF) method, that is a certain reformulation of the equation-of motion method for double-time temperature dependent Green functions is presented. This method was developed to overcome some ambiguities in terminating the hierarchy of the equations of motion of double-time Green functions and to give a workable technique to systematic way of decoupling. The approach provides a practical method for description of the many-body quasi-particle dynamics of correlated systems on a lattice with complex spectra. Moreover, it provides a very compact and self-consistent way of taking into account the damping effects and finite lifetimes of quasi-particles due to inelastic collisions. In addition, it correctly defines the Generalized Mean Fields, that determine elastic scattering renormalizations and, in general, are not functionals of the mean particle densities only. Although some space is devoted to the formal structure of the method, the emphasis is on its utility. Applications to the lattice fermion models such as Hubbard/Anderson models and to the Heisenberg ferro- and antiferromagnet, which manifest the operational ability of the method are given. It is shown that the IGF method provides a powerful tool for the construction of essentially new dynamical solutions for strongly interacting many-particle systems with complex spectra.
A canonical transformation of the Schrieffer-Wolff type is applied to the periodic Anderson model. The case of infinitely correlated f-like orbitals is dealt with, and these are described through standard basis operators, including spin degeneracy only. First- and third-order terms in the mixing parameter are eliminated. The resulting Hamiltonian contains terms up to fourth order. These describe several interaction processes including intersite spin and charge correlations, conduction-electron scattering, and excitonic interactions. A detailed analysis of the modified Ruderman-Kittel-Kasuya-Yosida interaction obtained is given. Possible extensions of some of the results to higher orders are discussed. The method provides a way to evaluate the spin and charge susceptibilities of the conduction-electron gas in this model. The possible relevance of these functions to a theory of the phonon spectrum and of magnetic ordering of intermediate-valence systems is mentioned.
A method is presented for computing the mixing parameters in the Anderson model for heavy-rare-earth compounds, based on a linear combination of atomic orbitals fit to a self-consistent band-structure calculation. An appropriate average of these parameters is used in a many-body calculation of the valence-band-x-ray-photoemission and inverse-photoemission spectra of YbP, with the Coulomb integral U as the only adjustable quantity. The calculated inverse-photoemission spectrum agrees qualitatively with room-temperature low-resolution data by Baer et al.
The problem of the highly correlated electron gas V/sub 2/O/sub 3/ consisting of a filled a/sub 1g/ and a quarterly full e/sub g/ band is treated on the basis of a Hartree-Fock calculation with spin and orbit unrestriction. The values of the effective hopping integrals which include covalency effects (due to the overlap of the 2p/sub ..pi../ orbitals of the oxygens with the 3d wave functions of the vanadium atoms) are assessed on the bases of available band-structure calculations and experimental results measuring covalency contributions. For reasonable values of the Hubbard parameters U/sub m/m approx. = 2 eV, U/sub m/n approx. = 1.6 eV, and J/sub m/n approx. = 0.2 eV (the interatomic Coulomb repulsion of electrons on the same orbit (m, m) on different orbits (m, n) and the exchange integral J/sub m/n) it is found that the observed spin structure of V/sub 2/O/sub 3/ together with an antiferromagnetic orbital order gives the lowest Hartree-Fock ground-state energy amongst a large class of solutions which we considered and shows a gap in the density of states of the order of 0.2--0.3 eV. Since this gap appears already in the trigonal phase, we feel confident that the monoclinic distortion in the low-temperature phase is of magnetostrictive origin and not a primary cause of the metal-insulator transition. The peculiar value of 1.2..mu../sub B/ per V atom as observed by neutron scattering is interpreted as a strongly covalency-enhanced moment on the V atom. The atomic limit value of 1..mu../sub B/ due to one magnetic e/sub g/ electron per V atom is reduced to approx. = 0.75..mu../sub B/ in an itinerant picture. The covalency mechanism providing the extra 0.4..mu../sub B/ is known as back-bonding effect and leads at the same time to a negative spin density on the oxygen ions which are therefore no longer diamagnetic. Negative /sup 17/O NMR shift in the insulating antiferromagnetic phase should be able to verify this conjecture.
The resistivity of the dilute alloys of rare earth metals with yttrium has been measured at low temperatures. The result is in qualitative agreement with the recent theories due to Kondo and others on the s--d or s--f scattering. The effective s--f exchange integrals for various rare-earth solutes have been derived from the analysis of the resistivity data and compared with the reported values in other matrices. The integral for Ce is negative, leading to a resistance minimum, while those for heavier rare earths are positive. The sign of the integral has been discussed in terms of the mixing of conduction electrons with localized 4f electrons. The increase of the residual resistivity due to added rare earths depends upon the number of 4f electrons of the solute in a complicated way and is anomalously large for lighter rare earths such as La, Ce, and Pr.
A method is presented for calculating the core and valence spectra of a Ce compound in the impurity model at zero temperature. In the sudden limit this method becomes exact for large degeneracy of the f level. In this limit the valence spectrum has an f peak close to the Fermi energy, εF, even if the f level is fairly far below εF, and usually there is a second f peak at larger binding energy. These results correlate well with recent experiments for many Ce compounds. Both the core and valence spectra provide information about the occupancy of the f level and about its coupling to the conduction band.
The theory of the effective coupling between conduction electrons and the magnetic (or electric) moments of 3d and 4f ions in metals is reviewed, with emphasis on a systematic treatment of the generalized coupling forms which usually apply for real ions with orbital degrees of freedom. With the help of the irreducible-tensor method, the coupling is expanded in forms consistent with general symmetry requirements, and the effects of intra-ionic level structure of LS or LSJ type are taken into account. Coupling contributions from the direct and exchange parts of the Coulomb interaction between ionic and conduction electrons, and from the Anderson-Clogston-Schrieffer-Wolff virtual-mixing mechanism, are evaluated. The symmetry analysis is performed according to the full rotation group, meaning that the conduction band is represented as a free-electron band and effects of crystal-field splitting are not explicitly considered.
The different effect of cerium and gadolinium impurities on the pressure dependence of the superconducting transition temperature of lanthanum is due to different electronic structures of the rare-earth impurity. The ionic model explains the properties of gadolinium alloys, while the resonant scattering theory explains those of cerium alloys.
The density of states of the spectrum which occurs for different types of elementary excitations in solids, when only next neighbour interactions are taken into account (with Δ being the next neighbour lattice vectors), were computed and are investigated and tabulated for the cubic space groups. Its singularities are discussed with regard to a paper of van Hove [5]. As is detailed in the paper, using the standard approximation of these functions for the calculation of thermodynamic observables proves to be justified only for very low temperatures. In order to facilitate their application for calculations in case of higher temperatures, the exact densities of states are approximated by elementary functions with a relative error of less than 1 per 1000.
We present a method for calculating the core-level x-ray photoemission (XPS), the 3d→4f x-ray absorption (XAS), the valence photoemission, and the bremsstrahlung isochromat spectra in a slightly modified Anderson impurity model of a Ce compound at zero temperature. Both the spin and orbital degeneracies of the f level are included and the Coulomb interaction between the f electrons is taken into account. The spectra are expressed in terms of a resolvent operator. A many-electron basis set is introduced, and the resolvent is obtained from a matrix inversion. The particular form of the Anderson model allows us to find a small but sufficiently complete basis set, if the degeneracy Nf of the f level is large. In particular, we consider the limit Nf→∞, and show that the method is exact for the XPS, XAS, and valence photoemission spectra in this limit. It is also demonstrated that for Nf≳6, the method provides accurate spectra. Analytical results are obtained for the valence photoemission spectrum ρv(ε). The spectrum has a sharp rise close to the Fermi energy εF, which goes over to a "Kondo peak" in the spin-fluctuation limit. An exact relation between ρv(εF) and the f-level occupancy nf is shown to be satisfied to within 10% for Nf≥6. We discuss how core-level XPS spectra can be used to estimate the f-level occupancy nf and the coupling Δ between the f level and the conduction states. We find that the values of nf and Δ obtained from core-level XPS are basically consistent with the other spectroscopies and the static, T=0 susceptibility. It is, therefore, possible to describe these experiments in the Anderson model, using essentially the same set of parameters for all the experiments. Typically, we find nf>0.7 and Δ∼0.1 eV.
A systematic investigation of certain electronic properties of the rare-earth metals is reported. Calculations are performed within the framework of the renormalized-atom method in which Hartree-Fock free-atom solutions, with electronic configurations appropriate to the metal, are initially computed; the wave functions are then renormalized to the Wigner-Seitz sphere and used to construct l-dependent Hartree-Fock-Wigner-Seitz crystal potentials. The following results are obtained: (i) Recent spectral information together with the free-atom solutions permits us to estimate the change in neutral-atom correlation energy associated with changing the 4f electron count; contrary to expectation, we find that correlation effects are more significant in a configuration with one fewer 4f and one more 5d electron. (ii) Band extrema and Fermi levels are placed. (iii) The positions of occupied and unoccupied 4f levels are estimated in both a one-electron approach and a multielectron method taking screening and relaxation effects into account in a definite way. The one-electron approximation for the 4f levels fails badly in reproducing the results of recent photoemission experiments, while the multielectron calculations are in surprisingly good accord with experiment. The effective Coulomb-interaction energy between two 4f electrons at the same site, the familiar U, is reduced from the single-particle value of approximately 27 eV to about 7 eV with the inclusion of multielectron effects. (iv) Hartree-Fock values for the 4s- and 5s-shell exchange splittings are compared with soft-x-ray photoemission studies of the rare-earth fluorides and oxides; the calculated 4s splittings are roughly twice as large as experiment while, unexpectedly, the 5s results are in almost precise agreement.
Ground state properties of the divalent rare earth metals Eu and Yb at ambient and high pressures are investigated by calculating their band structures and total energies using the linearized muffin-tin orbital method. To monitor the strengths of the 4f interactions in the local density approximation the hybridization of the 4f electrons is either fully included (itinerant model) or completely neglected (localized model). The effects of spin-polarization are also included for Eu. Divalent to trivalent valence transitions under pressure are discussed and compared with recent X-ray absorption experiments. For Yb, the structural stability of its fcc, bcc and hcp phases is investigated and results are presented.
The conditions necessary in metals for the presence or absence of localized moments on solute ions containing inner shell electrons are analyzed. A self-consistent Hartree-Fock treatment shows that there is a sharp transition between the magnetic state and the nonmagnetic state, depending on the density of states of free electrons, the $s$-${}d$ admixture matrix elements, and the Coulomb correlation integral in the $d$ shell; that in the magnetic state the $d$ polarization can be reduced rather severely to nonintegral values, without appreciable free electron polarization because of a compensation effect; and that in the nonmagnetic state the virtual localized $d$ level tends to lie near the Fermi surface. It is emphasized that the condition for the magnetic state depends on the Coulomb (i.e., exchange self-energy) integral, and that the usual type of exchange alone is not large enough in $d$-shell ions to allow magnetic moments to be present. We show that the susceptibility and specific heat due to the inner shell electrons show strongly contrasting behavior even in the nonmagnetic state. A calculation including degenerate $d$ orbitals and $d$-${}d$ exchange shows that the orbital angular momentum can be quenched, even when localized spin moments exist, and even on an isolated magnetic atom, by kinetic energy effects.