Intermediate Valence Systems Research Articles

Study of intermediate valence by the time-dependent collision approach

An approximation method has been worked out for studying intermediate-valence systems by the time-dependent collision approach of Lal [Phys. Rev. B 27, 2535 (1983)]. A practical expression for the density operator of the intermediate-valence state has been obtained which includes distortion effects which are calculated in terms of the radial wave packets of the ($4f$ or $5d$-band) electrons. Matrix elements of the density operator for the transitions $f\ensuremath{\rightarrow}f$ and $f\ensuremath{\rightarrow}d$ are calculated and normalized properly to yield the value of the $f$-state occupation and the collision-generated hybridization. It is found that this hybridization assumes a maximum value when the $f$-state energy is equal to the Fermi energy. It is also found that the collision-generated hybridization is significantly weaker than the Coulomb interaction between the $4f$ electron and the band electron.

On the stability of ferromagnetism in intermediate valence systems

We study the stability of ferromagnetism in intermediate valence systems which fluctuate between a magnetic (J≠0) and a non-magnetic (J=0) state as e.g. EuO. We consider thes-f model extended by a hybridization term as a good description of the normal valence as well as the intermediate valence phase of such materials. Special attention is devoted to the competing influence ofs-f exchange ands-f hybridization on the Curie temperatureTc. For large gaps between the localizedf-level and the conduction band (normal valence phase!)s-f exchange ands-f hybridization both tend to stabilize magnetism giving rise to an effective exchange interaction betweenf-moments. This effective exchange increases with decreasing gap leading to a substantialTc-enhancement for small gaps. In the intermediate valence phase, however, electronic fluctuations destroy the collective magnetism, and that twofold, namely by reducing the local magnetic moment and by enhancing entropy-influences. The latter leads toTc→0, therewith determining the boundary between the ferromagnetic and paramagnetic phase. A corresponding phase diagramm, in dependence of hybridizationV andf-level positionEf, is derived and discussed.

High-pressure magnetic susceptibility of the intermediate valence system EuPd2Si2

The pressure dependence (0-7 kbar) of the magnetic susceptibility is reported for the intermediate valence system EuPd2Si2 in the temperature interval 77-300K. It is found that the thermally induced valence transition becomes more gradual on application of pressure The characteristic fluctuation temperature Tf, also seems to be pressure dependent.

Existence of the Fermi-liquid behaviour in the theory of intermediate valence

An exact equivalence of the periodic Anderson model and generalized Hubbard model in atomic representation is shown. Energy spectrum of the quasiparticle is calculated by using diagram technique for the Hubbard operators. Conditions of Fermi-surface existence and Fermi-liquid behaviour are obtained in intermediate valence systems.

Raman spectroscopy of intermediate valent (IV) systems: Electron-phonon coupling and charge fluctuation

Raman scattering measurements on intermediate valent rare earth chalcogenides crystallizing in the NaCl structure are reviewed. The experimentally obtained Raman intensities are compared with the theoretically calculated intensities, using a lattice dynamical model in which the electron lattice interaction has been expressed in terms of local intraionic charge deformabilities, with monopolar (breathing Γ1+), dipolar (Γ15−), and quadrupolar (Γ12+) symmetry. Phonon anomalies in SmS, Sm0·75 Y0·25S and YS are described and discussed. Finally, evidence for a new excitation involving 4f charge fluctuations is presented, which is observed as a dispersionless excitation in the acoustic-optic phonon gap in (IV) materials.

On the coexistence of magnetism and intermediate valence

We investigate the possibility of ferromagnetism in intermediate valence systems, which fluctuate between a magnetic ( J ≠ 0) and a nonmagnetic ( J = 0) state (f.i. EuO). We extend the s-f model by a hybridization term and present an exact solution for the atomic limit. We find as main condition for ferromagnetism that the average 4f-occupation n f should exceed a critical value n (c) f. For n f < n ( c) f no magnetic ordering appears. The question whether ferromagnetism or not in intermediate valence systems is not so much influenced by the concrete values of the 4 f − 5 d gap or the hybridization matrix element, but primarily by n (c) f.

Kondo effect of trivalent Tm in Y 0.9Tm 0.1S

The existence of a Kondo effect in a trivalent alloy Y 0.9Tm 0.1 S is shown by the Curie-Weiss behavior of the susceptibility and by a ln T decrease of Δϱ = ϱ alloy - ϱ YS above ∼ 12 K comparable with that observed in TmS. Comparisons are made with the Kondo dilute alloys of the intermediate valent system (Y,Tm)Se.

Theoretical and experimental progress in intermediate valence systems (invited)

Recent experimental measurements such as susceptibility, specific heat, thermopower, and UPS on a wide range of intermetallic intermediate valence systems, e.g. YbCuAl, CeSn3, support a high degree of universality in the properties of such materials which apparently form a unique class of metallic compounds. The ratio χ(0)/γ≂g2μ2B (J+1) (J+1/2)/π2k2B is a good constant for compounds of a given rare earth (though g and J are rare earth dependent). A class of compounds of a given IV rare earth ion shows scaling of properties in terms of an effective temperature, or energy, scale TF, which is strong function of valence. We review the success of theoretical approaches such as perturbation theory, local Fermi liquid theory, the Bethe Ansatz technique, and large-N perturbation theory in understanding these experimental facts. A challenge continues to be the understanding of the ground state, in which lattice periodicity plays a fundamental role, giving rise to ραT2 in some metallic, and a several meV gap in insulating, IV compounds.

Valence fluctuations between two magnetic configurations: An exactly solvable model

We propose an exactly solvable Hamiltonian that describes intermediate valence systems fluctuating between two magnetic configurations. It consists of a set of localized, highly correlated states hybridized through a conduction band. From it, we derive the spectral density of localized states, valence, static and dynamic magnetic susceptibilities and charge power spectrum. We also describe the results for specific heat and magnetic field dependence of electrical conductivity. We briefly discuss its relevance to the understanding of intermediate valence Tm compounds.

Magnetic susceptibility and NMR measurements in EuNi 2P 2, an intermediate valence system

Magnetic susceptibility and 31P Knight shift measurements establish the presence of Eu ions in the fluctuating valence state in EuNi 2P 2.

On the Phonon Contribution to the Electrical Resistivity of Intermediate Valence Systems

AbstractThe electrical resistivity of an electron–phonon system with two hybridized tight‐binding electron bands is calculated. The electron–electron interaction is taken into account in the Hartree‐Fock approximation leading to an occupation dependent narrowing of the bands. The influence of the effective band width on the resistivity is discussed.

Fourth-order effective Hamiltonian for the Anderson lattice

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.

Pressure dependence of the specific heat of YbCuAl

Abstract The low-temperature specific heat of the intermediate-valence compound YbCuAl has been determined under pressures up to 10 kbar. It is found that the electronic specific heat coefficient increases dramatically. The T 3 term seems to increase, too, which is anomalous as compared to the behaviour of simple metals. These results are discussed within a local Fermi-liquid model for intermediate-valence systems.

Theory of Spin Fluctuations in Tm Compounds

We calculate the spin and charge dynamical susceptibilities of an intermediate-valence system fluctuating between two magnetic configurations. Our results can explain the most important features of the neutron-scattering spectra of TmSe. We show that the energy of the inelastic peak found experimentally is connected with the energy of charge fluctuations.

Magnetic diffuse and small-angle scattering

Magnetic neutron scattering is one of the most valuable tools in exploring magnetism. For disordered magnetic systems, in addition to Bragg scattering, diffuse and small-angle scattering give information. Experimental techniques of the two last mentioned methods are described. They succeeded in a microscopic explanation of magnetic alloys with paramagnetic, spin-glass, ferromagnetic and antiferromagnetic character. Typical examples will be discussed in detail. Non-frozen local magnetic moments show quasi-elastic scattering, the half-width of which is a characteristic for the relaxation processes. By diffuse inelastic neutron scattering the temperature dependence and concentration dependence of such relaxation processes have been studied for classical paramagnetic, Kondo- and intermediate-valence systems. An additional impact to the field is to be expected from new developments of polarization analysis techniques.

A local Fermi liquid theory of intermediate valence systems

A non-interacting local Fermi liquid theory applicable to Ce, Sm, Eu and Yb metallic intermediate valence materials is presented. The induced density of states of a given rare earth ion is taken as the Lorentzian appropriate for a rare earth ion impurity, for which the justification is tentatively discussed. The degeneracy of the resonance is that of the magnetic configuration of the ion. The results are applied to the f occupation, susceptibility and specific heat. A relationship existing in the literature between the zero temperature susceptibility and linear coefficient of specific heat follows exactly from the present very simple theory. The results are compared with a range of experimental data.

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.

On the local polaron model and its applications to intermediate valence systems

The local polaron problem in which a local electronic resonance in a wide conduction band is coupled to a local phonon mode is considered. Earlier work is extended by a more complete treatment of the case where a finite Fermi level is present which is important for intermediate valence materials. The authors demonstrate by variational and perturbational methods that there can be a renormalisation of the level width by a factor exp(-n), where n is the number of phonons in the polaron cloud. They discuss the conditions for this renormalisation to occur and in particular establish the importance of the closeness of the resonance to the Fermi level. The physical basis for the conditions and the relationship to the problem where only a single electron is present, where renormalisation only occurs if the level lies at the bottom of the band, are brought out. Renormalisation due to electron-hole pairs is also discussed. The authors suggest that in a lattice of resonances, renormalisation should lead to suppression of intersite scattering. The implications for intermediate valence systems are discussed.

CPA alloy analog treatment of the disordered extended Anderson model

In connection with quasi-ternary intermediate valence systems like Yb1−xYxCuAl we study the disordered extended Anderson model. The alloy problem is treated within the CPA-alloy analog approximation. The temperature dependence of the static magnetic susceptibility for various values of x is in good qualitative agreement with experiments.

A variational method for the three-site, six-electron intermediate valence model

Describes the application of the variational method to the three-site problem, and shows that the agreement between variational and exact ground state energy is remarkably close, for a wide range of choice of Hamiltonian parameters. As it appears unlikely that exact solutions will be found for realistic intermediate valence systems the indications are that the variational method has considerable potential. Also, the form of the variational wavefunction is conceptually simple.