Magnetic-field-induced valence transition in rare-earth systems

The magnetic-field-induced valence transition in rare-earth systems has been investigated using the periodic Anderson model supplemented by the Falicov-Kimball term. This model has been solved by first decoupling the Falicov-Kimball term as proposed by Khomskii and Koharjan and then taking the limit of infinite intra-site Coulomb repulsion. The valence transition both in the absence and in the presence of magnetic field as a function of temperature is studied. It has been found that the system makes transition from non-magnetic to magnetic state when the magnetic field increases beyond a critical value H _c. The phase boundary defined in terms of reduced field H _c(T)/H _c(0) and reduced temperature T/T _v (T _v being the valence transition temperature in the absence of field) is almost independent of the position of the localized level. The results are in qualitative agreement with experimental observations in Yb- and Eu-compounds.     

Valence transition in the periodic Anderson model

A very rich phase diagram has recently been found in CeCu₂Si₂ from high pressure experiments where, in particular, a transition between an intermediate valence configuration and an integral valent heavy fermion state has been observed. We show that such a valence transition can be understood in the framework of the periodic Anderson model. In particular, our results show a breakdown of a mixed-valence state which is accompanied by a drastic change in the f occupation in agreement with experiment. This valence transition can possibly be interpreted as a collapse of the large Fermi surface of the heavy fermion state which incorporates not only the conduction electrons but also the localized f electrons. The theoretical approach used in this paper is based on the novel projector-based renormalization method (PRM). With respect to the periodic Anderson model, the method was before only employed in combination with the basic approximations of the well-known slave-boson mean-field theory. In this paper, the PRM treatment is performed in a more sophisticated manner where both mixed as well as integral valent solutions have been obtained. Furthermore, we argue that the presented PRM approach might be a promising starting point to study the competing interactions in CeCu₂Si₂ and related compounds.     

Correlated electrons in the presence of disorder

Several new aspects of the subtle interplay between electronic correlations and disorder are reviewed. First, the dynamical mean-field theory (DMFT) together with the geometrically averaged (“typical”) local density of states is employed to compute the ground state phase diagram of the Anderson-Hubbard model at half-filling. This non-perturbative approach is sensitive to Anderson localization on the one-particle level and hence can detect correlated metallic, Mott insulating and Anderson insulating phases and can also describe the competition between Anderson localization and antiferromagnetism. Second, we investigate the effect of binary alloy disorder on ferromagnetism in materials with f-electrons described by the periodic Anderson model. A drastic enhancement of the Curie temperature T_c caused by an increase of the local f-moments in the presence of disordered conduction electrons is discovered and explained.     

Finite cell calculations on the periodic Anderson Hamiltonian

We report finite cell calculations on the one-dimensional periodic Anderson Hamiltonian. The ground state for two electrons per site is found to be an insulating non-magnetic singlet, which evolves continuously from the noninteracting U = 0 limit to the large U mixed valence and Kondo lattice regimes. The calculations for four sites given energy gaps which agree well with results for the infinite lattice in the few cases where they are known.     

Neuropsychological constraints to human data production on a global scale

High-magnetic-field X-ray absorption spectra (XAS) and its X-ray magnetic circular dichroism (XMCD) at the Yb L_2, 3 edges of YbInCu₄ are calculated around the field-induced valence transition at about 30 T. The calculations are made by using a new theoretical framework with an extended single impurity Anderson model (SIAM) developed recently by the present author. Two parameters in SIAM, the 4f level and the hybridization strength, are taken as different values in low- and high-magnetic-field phases of the field-induced valence transition. The calculated results are compared with recent experimental data measured by Matsuda et al. by utilizing a miniature pulsed magnet up to 40 T. The field-dependence of the calculated XMCD spectra is explained in detail on the basis of the field-dependence of the Yb 4f wavefunctions in the ground state. Some possibilities are discussed on the negative XMCD signal observed experimentally at the L₂ edge.     

Many-body effects in core-level spectroscopy of rare-earth compounds

Many-body effects in core-level photoemission and core-level photoabsorption are discussed for rare-earth systems, especially for Ce and La compounds, both in metallic and insulating forms. Emphasis is put on effects of metallic mixed valency and insulating covalency of 4f electrons on these spectra. For the insulating compound CeO₂, detailed analyses of the 3d core photoemission (3d-XPS) and the 2p core photoabsorption (L₃-XAS) are presented by using the impurity Anderson model with a filled valence band. In order to give a consistent interpretation for 3d-XPS and L₃-XAS, it is shown to be essential to take account of the Coulomb interactions U _fd (between a 4f electron and a photoexcited 5d electron in the L₃-XAS) and -U _dc (between the 5d electron and a core hole), in addition to -U _fc (between the 4f electron and the core hole). Discussions are given on the physical information derived from the analysis, on similarities and differences in spectral features between insulating and metallic systems, and also on some related topics.     

Delocalization and wave-packet dynamics in one-dimensional diluted Anderson models

We study the nature of one-electron eigen-states in a one-dimensional diluted Anderson model where every Anderson impurity is diluted by a periodic function f(l). Using renormalization group and transfer matrix techniques, we provide accurate estimates of the extended states which appear in this model, whose number depends on the symmetry of the diluting function f(l). The density of states (DOS) for this model is also numerically obtained and its main features are related to the symmetries of the diluting function f(l). Further, we show that the emergence of extended states promotes a sub-diffusive spread of an initially localized wave-packet.Received: 7 July 2003, Published online: 19 November 2003PACS: 63.50. + x Vibrational states in disordered systems - 63.22. + m Phonons or vibrational states in low-dimensional structures and nanoscale materials - 62.30. + d Mechanical and elastic waves; vibrations     

Magnetic and dynamic properties of the Hubbard model in infinite dimensions

An essentially exact solution of the infinite dimensional Hubbard model is made possible by using a self-consistent mapping of the Hubbard model in this limit to an effective single impurity Anderson model. Solving the latter with quantum Monte Carlo procedures enables us to obtain exact results for the one and two-particle properties of the infinite dimensional Hubbard model. In particular, we find antiferromagnetism and a pseudogap in the single-particle density of states for sufficiently large values of the intrasite Coulomb interaction at half filling. Both the antiferromagnetic phase and the insulating phase above the Néel temperature are found to be quickly suppressed on doping. The latter is replaced by a heavy electron metal with a quasiparticle mass strongly dependent on doping as soon asn<1. At half filling the antiferromagnetic phase boundary agrees surprisingly well in shape and order of magnitude with results for the three dimensional Hubbard model.     

Study of Some Factors Affecting Thermodynamic Properties of the Insulating Phase of the Periodic Anderson Lattice Model

Within the framework of slave-boson mean-field theory, we study the thermodynamic properties of the periodic Anderson lattice model with half-filled conduction band and one 4f electron at each primitive cell and the degeneracy N_d = 2. It is found that after taking into account the direct nearest-neighbor f-f hopping, such a periodic Anderson lattice model can exhibit both an insulating ground state and a heavy-fermion metal ground state depending on the value of the bare f energy level E_f, the hybridization matrix element V, and the direct f-f hopping strength δ. This is unlike the case neglecting the direct f-f hopping, in which such a periodic Anderson lattice model will predict an insulating ground state only.     

Magnetism and superconductivity in the extended periodic Anderson model

The Anderson model for a periodic array of magnetic ions has been extended by a BCS like interaction term for the conduction electrons. This extended model is studied by means of a generalized Hartree-Fock approximation. Five coupled self-consistency equations are considered for situations where ferromagnetic, superconducting, coexistent and normal phases can occur. Which of these phases actually are allowed for a given set of parameters strongly depends upon the band structure (especially upon the type of electrons near the Fermi energy). Whereas for the general case the self-consistency equations have to be solved numerically from the beginning, the situation is much simplified for the symmetric Anderson model (E _o=–U/2). Here, analytical results are obtained which explain the stability of the coexistent phase. We also use the symmetric model for an expansion of the Ginzburg-Landau type in the spatially homogeneous magnetic and superconducting order parameters. The onset of superconductivity and ferromagnetic order is well described within this approximation. However, at low temperatures we find drastically different solutions due to the strong temperature dependence of the expansion coefficients of the free energy. Therefore, it is difficult to obtain the correct transition temperatures within this approximation. These difficulties stem from general problems connected with the derivation of a Ginzburg-Landau theory for several order parameters from a microscopic theory.Work performed within the research program of the Sonderforschungsbereich 125, Aachen-Jülich-Köln     

两种扩展Harper模型的波包动力学

本文通过二次矩M₂(t)和概率分布W_n(t)数值地研究了两种扩展Harper模型的波包动力学,得到了这两种模型中各个相、各条临界线以及三相点的波包扩散情况.对于第一种扩展Harper模型,发现两个金属相中波包是弹道扩散的,在绝缘体相中波包不扩散,而在三相点以及各条临界线上波包是反常扩散的.同时,发现金属相—金属相转变的临界线上的波包动力学行为与金属相—绝缘体相转变的临界线上的相同,但三相点的动力学行为与各临 关键词： 金属绝缘体转变 扩展Harper模型 波包动力学     

Dynamical susceptibilities of intermediate valence compounds

Relaxation rates of magnetic moment and charge are discussed for systems showing intermediate valence. The periodic Anderson model and a more realistic model with periodic 4f shells are investigated by the use of the Mori formalism. It is shown that the relaxation of the 4f moment and the charge above the spin fluctuation temperature is dominated by the second order process with respect to the hybridization interaction and is nearly independent of temperature. The moment relaxation rate is significantly larger than that in the integral valent case where the fourth order Korringa process is dominant. The theory can explain the anomalously large width and the momentum independent nature of the quasi-elastic component of the neutron scattering on intermediate valence compounds.Work performed under the research program SFB 125 Aachen-Jülich-KölnOn leave of absence from the Department of Applied Physics, Tohoku University, Sendai 980, Japan     

Theory of substitutional alloys of intermediate valence systems: Concentration and temperature dependence of the static magnetic susceptibility

The effect of alloying in intermediate valence compounds is studied within an extended version of the Anderson model which takes into account substitutional disorder of the rare earth ions. In particular, we concentrate on modifications of the conduction band, describe them by an effective shift in the Fermi energy, and consider its influence on the mixed valence behaviour. By applying the alloy analog approximation to the manyparticle Hamiltonian describing the local magnetic 4f shells, the complete effective Hamiltonian is that of a ternary alloy. This problem is solved within the coherent potential approximation and the static magnetic susceptibility is calculated as a function of temperature and disorder. Depending on the shift of the Fermi energy with respect to the 4f levels, qualitatively different behaviour is obtained which corresponds very well with magnetic measurements on different Yb alloys. The model yields an inverse proportionality between the susceptibility atT=0 and the temperatureT _M of the susceptibility maximum as functions of the disorder.Work performed within the research program of the Sonderfor-schungsbereich 125 Aachen-Jülich-Köln     

Pseudogap and symmetry of superconducting order parameter in cuprates

The phase diagram, nature of the normal state pseudogap, type of the Fermi surface, and behavior of the superconducting gap in various cuprates are discussed in terms of a correlated state with valence bonds. The variational correlated state, which is a band analogue of the Anderson (RVB) states, is constructed using local unitary transformations. Formation of valence bonds causes attraction between holes in the d-channel and corresponding superconductivity compatible with antiferromagnetic spin order. Our calculations indicate that there is a fairly wide range of doping with antiferromagnetic order in isolated CuO₂ planes. The shape of the Fermi surface and phase transition curve are sensitive to the value and sign of the hopping interaction t′ between diagonal neighboring sites. In underdoped samples, the dielectrization of various sections of the Fermi boundary, depending on the sign of t′, gives rise to a pseudogap detected in photoemission spectra for various quasimomentum directions. In particular, in bismuth-and yttrium-based ceramics (t′>0), the transition from the normal state of overdoped samples to the pseudogap state of underdoped samples corresponds to the onset of dielectrization on the Brillouin zone boundary near k=(0,π) and transition from “large” to “small” Fermi surfaces. The hypothesis about s-wave superconductivity of La-and Nd-based ceramics has been revised: a situation is predicted when, notwithstanding the d-wave symmetry of the superconducting order parameter, the excitation energy on the Fermi surface does not vanish at all points of the phase space owing to the dielectrization of the Fermi boundary at k _x=± k _y. The model with orthorhombic distortions and two peaks on the curve of T _c versus doping is discussed in connection with experimental data for the yttrium-based ceramic. Zh. éksp. Teor. Fiz. 115, 649–674 (February 1999)     

Magnons coherent transmission and heat transport at ultrathin insulating ferromagnetic nanojunctions

A model calculation is presented for the magnons coherent transmission and corresponding heat transport at insulating magnetic nanojunctions. The system consists of a ferromagnetically ordered ultrathin insulating junction between two semi-infinite ferromagnetically ordered leads with ideally flat crystal interfaces. The ground state of the system is depicted by an exchange Hamiltonian neglecting smaller dipolar and anisotropy terms. The spin dynamics are analyzed using the equations of motion for the spin precession displacements, valid in the limit of low temperatures compared to an order-disorder transition temperature characteristic of the system. The coherent transmission and reflection spectra at the nanojunction boundary are calculated in the Landauer-Buttiker formalism using the matching theory, for all the magnons in the lead bulk, at arbitrary angles of incidence on the boundary, and for variable temperatures. The model calculations yield the thermal conductivity κ _m due to the magnons coherent transmission between the two leads maintained at slightly different temperatures. The model is general, and is applied in particular to the Fe/Gd/Fe system to calculate the coherent transmission of magnons and their thermal conductivity at the junction boundary, for different thicknesses of the Gd junction and its corresponding magnetic order. The calculated results elucidate the comparison between the heat transport from magnons with that in parallel channels from electrons and phonons, at the nanojunction boundary.     

Phonon frequency shift and effect of correlation on the electron-phonon interaction in heavy fermion systems

The electron-phonon interaction in the periodic Anderson model (PAM) is considered. The PAM incorporates the effect of onsite Coulomb interaction (U) between f-electrons. The influence of Coulomb correlation U on the phonon response of the system is studied by evaluating the phonon spectral function for various parameters of the model. The numerical evaluation of the spectral function is carried out in the long wavelength limit at finite temperatures keeping only linear terms in U. The observed behaviour is found to agree well with the general features obtained experimentally for some heavy fermion (HF) systems.     

Mixed valencies: Structure of phase diagrams,lattice properties and the consequences of electron hole symmetry

Symmetry properties and phonon phenomena of mixed valence compounds are discussed within the framework of the periodic Anderson model which was extended to include the interaction of 4f electrons with longitudinal optical phonons. The temperature anomaly in the thermal expansion found in CeSn₃ (positive thermal expansion coefficient) and YbCuAl (negative) is correctly described. Within the model the anomaly is a consequence of the particle hole symmetry of the underlying Hamiltonian. Moreover, the theory gives the positive slope of the phase boundary in the pressure-temperature phase diagram (dP/dT>0), for example for Ce, and predicts a negative slope (dP/dT<0) for Yb compounds.Furthermore, the quite unusual low temperature features of the pressure-temperature phase diagram have been calculated. It is found that the lattice vibrational contribution renormalizes the two essential parameters of the periodic Anderson model. The hybridization energyV ₀ of 4f and 5d–6s states is changed to =V ₀–a–b ² whereas the energy of the 4f stateE ₀ with respect to the 5d band becomes =E ₀–a–b ²., being proportional to the lattice constant, is determined by minimizing the Gibbs free energy, while ² is proportional to the mean square displacement of the rare earth ions. The strong temperature dependence of and ² determines the behaviour of the phase boundary and for large enough coefficientsb andb the phase boundary terminates at two critical points. An argument is given why the unusual low temperature features are more expressed in dirty mixed valence compounds as Sm_1–x Gd _x S than in the pure compound SmS. Furthermore, the theory predicts a quite unusual behaviour of the plasma-like phonon mode in the mixed valence phase: It softens at the critical temperature and at an intermediate temperature.Work performed within the program of the Sonderforschungsbereich 125, Aachen-Jülich-Köln     

An Ising ferromagnet with discontinuous long-range order

An infinite one-dimensional Ising ferromagnetM with long-range interactions is constructed and proved to have the following properties. (1)M has an order-disorder phase transition at a finite temperature. (2) Any Ising ferromagnet of the same structure asM, but with interactions tending to zero with distance more rapidly than those ofM, cannot have a phase-transition. (3) The long-range-order parameter (thermal average of the spin-spin correlation at infinite distance) jumps discontinuously from zero in the disordered phase to a finite value in the ordered phase. All three properties have been conjectured by Anderson and Thouless to hold for a particular Ising ferromagnet which is relevant to the theory of the Kondo effect. AlthoughM is not identical to Anderson's model, the results proved forM support the validity of the physical arguments of Anderson and Thouless.     

Self-consistent alloy treatment of the periodic anderson model: Susceptibility and specific heat of intermediate valence compounds

To describe the electronic properties of mixed valence compounds we study the periodic Anderson model within the frame of the alloy analog approximation. In this approach the model Hamiltonian is replaced by the sum of two single-particle alloy Hamiltonians the parameters of which have to be determined self-consistently. The alloy problem is solved within the coherent potential approximation. In contrast to other treatments of the periodic Anderson model this approximation scheme is exact in both trivially solvable limits of vanishing hybridization and Coulomb repulsion, respectively. For model parameters corresponding to a mixed valence situation only nonmagnetic solutions of the self-consistency equations exist. After discussing the limit of small hybridization analytically we numerically calculate the magnetic susceptibility and the electronic specific heat as a function of temperature for realistic values of the hybridization and Coulomb repulsion. The results are in very good qualitative agreement with experimental data.Work performed within the research program of the Sonderforschungsbereich 125 Aachen/Jülich/Köln     

Symmetry of the superconducting order parameter in frustrated systems determined by the spatial anisotropy of spin correlations

We study the resonating valence bond theory of the Hubbard-Heisenberg model on the half-filled anisotropic triangular lattice. Varying the frustration changes the wave vector of maximum spin correlation in the Mott insulating phase. This, in turn, changes the symmetry of the superconducting state that occurs at the boundary of the Mott insulating phase. We propose that this physics is realized in several families of quasi-two-dimensional organic superconductors.