Exciton effects in a scaling theory of intermediate valence and Kondo systems

An interplay of the Kondo scattering and exciton effects (d-f Coulomb interaction) in intermediate valence systems and Kondo lattices is demonstrated to lead to an essential change of the scaling behavior in comparison with the standard Anderson model. In particular, a marginal regime can occur where characteristic fluctuation rate is proportional to flow cutoff parameter. In this regime, the “Kondo temperature” itself is strongly temperature-dependent, which may give a key to the interpretation of controversial experimental data for heavy fermions and related systems.     

Kondo universality,energy scales,and intermediate valence in plutonium

On the basis of the concepts of an intermediate-valence (IV) regime, an analysis is carried out of macroscopic properties of the α and δ phases of plutonium, as well as of several model systems based on rare earth elements. Within a single-site approximation (SSA), the characteristic Kondo interaction energy, the f-electron shell occupation number, the effective degeneracy of the ground-state f multiplet, and the crystal field splitting energy are estimated. The ground state in plutonium is considered as a quantum-mechanical superposition of states with different valences. The temperature dependence of the static magnetic susceptibility of δ plutonium is calculated. It is shown that δ plutonium satisfies the Wilson and Kadowaki-Woods universal relations, whereby it can be classified as a Kondo system. At the same time, the problem of the position of plutonium in the general classification of solids, as well as the problem of the temperature dependence of magnetic susceptibility of δ plutonium, remains open. The concept of multiple intermediate valence (MIV) is put forward as a possible means for solving the above problems. The MIV regime is characterized by fluctuations from the basic configuration 3+ to the states 4+ and 2+, which make a fundamental difference between plutonium and 4f electron systems based, say, on samarium.     

Elastic properties of intermediate valence,Kondo and stable valence RAl2 compounds

Measurements of ultrasonic velocities and pressure volume behavior show that, compared to integral valence rare earth dialuminides, the intermediate valence compound, YbAl₂, is mechanically soft and the Kondo compound, CeAl₂, is much less so. These results show that in the case of intermediate valence the degenerate electronic configurations strongly effect the elastic properties while for the Kondo case, where the electronic configurations are nondegenerate, there is little effect.     

Role of the d-f Coulomb interaction in intermediate valence and Kondo systems: a numerical renormalization group study

Using the numerical renormalization group method, the dependences on temperature of the magnetic susceptibility χ(T) and specific heat C(T) are obtained for the single-impurity Anderson model with inclusion of d-f the Coulomb interaction. It is shown that the exciton effects caused by this effect (charge fluctuations) can significantly change the behaviour of C(T) in comparison with the standard Anderson model at moderately low temperatures, whereas the behaviour of χ(T) remains nearly universal. The ground-state and temperature-dependent renormalizations of the effective hybridization parameter and f-level position caused by the d-f interaction are calculated, and satisfactory agreement with the Hartree-Fock approximation is derived.     

Dynamical susceptibility of intermediate valence systems

The transverse susceptibility if magnetic systems described by the Anderson model is calculated evaluating the self energy for the two particle Green function. The results are applied to semiconductors and metals. In the first case a shift in the resonance frequency is obtained as well as a continuum of excitations corresponding to the promotion of electrons from the localized state to the conduction band states. In the metallic case a Korringa relation for the relaxation time in the magnetic limit is obtained. The real and imaginary parts of the self energy are given as functions of the distance from the localized level to the Fermi level.     

Density of states and the problem of Sm valence

Density of states for Sm metal has been calculated in DFT/GGA approximation using the same treatment for f and s-d bands. It is concluded that the 4f electrons of Sm must be considered as valence electrons, not shallow core states. Therefore the 4f-5d transition cannot change the valence of Sm, which may be characterized (if necessary) by the sum of all electrons in the s-d-f valence bands. The possibility of alternative interpretation of UPS spectra of Sm adsorbed films is illustrated by calculations of DOS (density of states) for oxygen-contaminated Sm crystal.     

Dynamical magnetic susceptibility of intermediate valence Tm systems

We calculate the inelastic part of the magnetic neutron scattering cros section of a periodic model for valence fluctuations between two magnetic configurations. The calculations is restricted to the paramagnetic pahse where the coherent potential approximation is used.The resulting frequency (ω), wave vector (q) and temperature dependence agrees qualitatively with the experimental results in TmSe.We find that even for parameters for which there is no gap in the total density of states, an inelastic peak is present with a similar q dependence as the experimentally observed one.We discuss the effects of sample composition and compare the results with those corresponding to the impurity version of the model and the experimental results in dilute systems.     

On the stability of ferromagnetism in intermediate valence systems

It is known that the deformations of the electronic charge density induced by lattice displacements play an important role in lattice dynamics. The multipole expansion of these deformations around the positions of both the cation and the anion leads to a rather general type of deformable shell model. This cluster deformation model can be applied not only to ionic crystals but also to a large variety of other materials like mixed-valence compounds. Taking TiN as an example, it is shown that the model is able to describe the very pronounced phonon anomalies in superconducting transitionmetal compounds and to reproduce the measured phonon dispersion curves within the experimental errors.     

Effect of the d-f coulomb correlation on the valence transition of intermediate valence systems

The d-f Coulomb repulsion, G, is treated by means of a real space decimation procedure on a Bethe lattice. The valence is calculated as a function of the relative position of the f-level with respect to the conduction band. No discontinuous transitions are found.     

Polaronic effects on interconfigurational fluctuation lifetimes in intermediate valence systems

It is shown that in systems exhibiting intermediate valence polaronic effects can lead to significant reductions in interconfiguration fluctuation frequency and to a shift in the electronic excitation spectrum. Numerical estimates for SmS give a shift in good accord with recent experiments and indicate a non-negligible lifetime enhancement factor.     

From mixed valence to the Kondo lattice regime

Many heavy fermion materials are known to cross over from the Kondo lattice regime to the mixed valence regime or vice versa as a function of pressure or doping. We study this crossover theoretically by employing the periodic Anderson model within the framework of the dynamical mean field theory. Changes occurring in the dynamics and transport across this crossover are highlighted. As the valence is decreased (increased) relative to the Kondo lattice regime, the Kondo resonance broadens significantly, while the lower (upper) Hubbard band moves closer to the Fermi level. The resistivity develops a two peak structure in the mixed valence regime: a low temperature coherence peak and a high temperature 'Hubbard band' peak. These two peaks merge, yielding a broad shallow maximum upon decreasing the valence further. The optical conductivity likewise exhibits an unusual absorption feature (shoulder) in the deep mid-infrared region, which grows in intensity with decreasing valence. The involvement of the Hubbard bands in dc transport and of the effective f-level in the optical conductivity are shown to be responsible for the anomalous transport properties. A two-band hybridization-gap model, which neglects incoherent effects due to many-body scattering, commonly employed to understand the optical response in these materials is shown to be inadequate, especially in the mixed valence regime. Comparison of theory with experiment carried out for (a) dc resistivities of CeRhIn(5), Ce(2)Ni(3)Si(5), CeFeGe(3) and YbIr(2)Si(2), (b) pressure dependent resistivity of YbInAu(2) and CeCu(6), and (c) optical conductivity measurements in YbIr(2)Si(2) yields excellent agreement.     

Influence of the electron damping on the properties of intermediate valence systems

The influence of conduction electron damping on the possibility of excitonic coupling in the intermediate valence systems is considered. The scattering by the internal degrees of freedom of f?-shells is shown to be the main mechanism for this damping. It is shown that both the excitonic energy gap and the damping are proportional to s-f? Coulomb integral, so the scattering considered prevents s- and f?-electrons from anomalous coupling. The growth of the resistivity near the point of valence change can be understood as the manifestation of this scattering.     

A two-band model for intermediate valence compounds

The change of valence as a function of pressure in intermediate valence rare-earth compounds is computed in a two hybridized band model: a conduction band and a 4f-band, being V the hybridization parameter. A Coulomb interaction G between 4f and conduction electrons is also included. For different values of G/V we obtain first or second order transitions from a semiconductor to a metallic state.     

Density of prelocalized states in mesoscopic NS systems

The semiclassical theory of the proximity effect predicts the formation of a gap E _g ～?D/L ² in the excitation spectrum of a diffusive contact between a normal metal and a superconductor (NS). Mesoscopic fluctuations lead to the emergence of states localized anomalously in the normal metal and weakly linked with the superconducting bank, creating a nonzero density of states for energies lower than E _g . In this review, the behavior of the density of quasiparticle states below a quasi-classical gap is considered for various geometries of the NS system (special attention is paid to SNS junctions) and for the problem of a superconductor with a low concentration of magnetic impurities, in which a similar effect is observed. Analysis is mainly carried out on the basis of a fully microscopic method of the supermatrix σ model; in this method, a nonzero density of states emerges due to instanton configurations with broken supersymmetry. In addition, the results of an alternative approach proceeding from the idea of universality of the spectra of random Hamiltonians with the given symmetry are reviewed. In situations studied using both methods, the results are identical. They include the exact expression for the mean density of states of an NS system in the vicinity of E _g . In the framework of 1D and 2D σ models, the subgap density of states is determined with an exponential accuracy. The contacts with a poor transparency of the NS interface are also considered. It is shown that the number of subgap states in the case of low transparency is much greater than unity.

     

Concentrated Kondo systems

This review considers the experimental and theoretical studies of concentrated Kondo systems (CKS), Kondo lattices, substitutional solid solutions and their transition from Kondo impurity to Kondo lattice, and ‘intermediate valence compounds’ which are, in fact, high T _K CKS (T _K is the Kondo temperature). The anomalous low temperature properties of CKS are related to the formation of the narrow (～k _B T _K) high-amplitude Abrikosov-Suhl resonance E _R in the vicinity of the Fermi level E _F. This resonance is situated exactly at E _F in low T _K CKS with T _K < Δ_CF and near E _F in high T _K CKS with T _K > Δ_CF (Δ_CF is the crystal field splitting). In low T _K ‘j=1/2’ CKS the condition E _R=E _F leads to an increase of the density of states at E _F, which is large enough to induce heavy fermion superconductivity in CeCu₂Si₂, UBe₁₃. We demonstrate that the transition from low T _K (E _R=E _F) to high T _K CKS (E _R≠E _F) might be what was formerly considered as a ‘Kondo-lattice-intermediate valence state’ transition. It appears that in many cases the essentially non-integer valence state of the rare-earth elements in metallic compounds is thermodynamically unstable with respect to a transition to an almost integer valence state, because it realizes the maximum gain in free energy from the Kondo condensation.     

Kondo resonance for orbitally degenerate systems

Formation of the Kondo state in the general two-band Anderson model has been investigated within the numerical renormalization group calculations. The Abrikosov-Suhl resonance is essentially asymmetric for the model with one electron per impurity (quarter filling case) in contrast with the one-band case. An external magnetic (pseudomagnetic) field breaking spin (orbital) degeneracy leads to asymmetric splitting and essential broadening of the many-body resonance. Unlike the standard Anderson model, the "spin-up" Kondo peak is pinned against the Fermi level, but not suppressed by the magnetic field.     

Multiple intermediate valence in plutonium

On the basis of the concepts of an intermediate-valence (IV) regime, an empirical model is proposed that quantitatively describes the magnetic susceptibility, specific heat, and effective atomic volume of the low-temperature α phase and the gallium or aluminum-stabilized face-centered cubic (fcc) δ phase of plutonium metal. The results of the paper allow one to estimate the entropy change associated with the α → δ structural phase transition, the value of this change being very close to the experimental value. According to the model, both phases of plutonium are systems with multiple intermediate valence, whose ground state is a many-particle Kondo singlet, and fluctuations occur between 5f electron configurations with integer valences of 3+, 4+, and 2+.