Magnetic susceptibility of mixed valence compounds

Magnetic susceptibility of mixed-valence compounds has been calculated as a function of pressure using Falicov-Kimball model wherein thef-s hybridisation has been taken into account. This model can very well explain the continuous as well as discontinuous transitions from ground states of integral to intermediate valence. Our results for magnetic susceptibility are in qualitative agreement with recent experimental results on some mixed-valence compounds.     

The role of fluctuations in mixed valence compounds

Previous renormalization group results for a simple spinless mixed valence model yielded large intersite ?-electron correlations if extended coherent hybridization mixed valence states are assumed. We simulate these correlations by an ?-level energy distribution and analyze its consequences. It is seen that a relatively small distribution width already smears the coherent hybridization gap leading to a lattice of essentially independent resonant levels.     

Phonons in mixed valence systems

The effect of valence changes due to f?d electronic transitions on phonons is studied. A large electronic density of states at the Fermi-energy in the intermediate valence state causes significant softening of the longitudinal acoustic and optic phonons and large phonon line-widths. These phonon renormalizations due to strong electron-lattice coupling are largest for phonon wavevectors q along the (111)-direction and maximal at the zone-boundary for LO modes and nearly half-way towards the zone-boundary in the case of LA mode. The results agree well with recent neutron scattering data on Sm_0.75Y_0.25S.     

Virtual levels,mixed valence phase and electronic phase transitions in rare earth compounds

We discuss the influence of the Coulomb interaction between localized and conduction electrons on the properties of magnetic impurities in metals and on electronic phase transitions such as the γ—α—α' transitions in Ce and the insulator—metal transition in SmS. Due to excitonic pairing between ?-holes and s-electrons, similar to that in excitonic insulators, the virtual ?-levels in metals may acquire an extra width, which, in contrast to the width in the Anderson model, depends upon the position of the ?-level, the width being the largest when the ?-level crosses the Fermi-level. This effect stabilizes the intermediate valence phase. As a result, in the Falicov model we get either a gradual phase transition (like that found in SmTe), or a first order one, followed by the intermediate valence phase (SmS), or, which is most interesting, two successive jump-like transitions with a mixed valence in between, similar to the γ—α—α' transitions in Ce. The mixed valence phase is described here as a kind of an “excitonic insulator”. The theory also predicts the correct slopes of the phase equilibrium lines for both Ce and SmS.     

A local mixed valence model

We consider a purely electronic model for local valence fluctuations consisting of a spinless localized 4f-level interacting with spinless extended 5d-states. We show that (a) the impurity model is related to the anisotropic Kondo problem, (b) a single 4f-level behaves like a resonant level with temperature-dependent width and (c) these results, when extended to a concentrated system of local incoherent mixed valence levels, are qualitatively in agreement with the main experimental features for mixed valence compounds.     

Magnetic re-entrance in intermediate valence compounds

We explore the possibility of magnetic re-entrance in intermediate valence compounds. Using a simplified Anderson-Lattice model we obtain the pressure-temperature magnetic phase diagram. This diagram shows that for some value of the microscopic parameters the temperature induced two transitions (non-magnetic to magnetically ordered to paramagnetic).We calculate the magnetization and the average occupation number of the localized state. Estimations of the observability of the effect in systems like CeAl₂ are made.     

Phenomenological thermodynamics of mixed valence phenomenon

The fluctuation of valence in some rare-earth (RE) compounds is described in terms of the effective potential seen by the RE ion. The nearly degenerate $\text{4?}{}^{\mathrm{n+1}}\text{(5d6s)}{}^2$ and $\text{4?}{}^{\mathrm{n}}\text{(5d6s)}{}^3$ levels of the RE ion split in energy in the presence of a repulsive potential. The energy separation (ΔE) between these levels is a function of external variables such as temperature, pressure or composition, which change the effective potential seen by the ion. The variation of ΔE with temperature is obtained for four Europium compounds from ¹⁵¹Eu Mössbauer isomer shift data. The temperature dependence of susceptibility is then obtained from the same (ΔE) variation and compared with experimental results. A characteristic temperature (T_υ) is found below and above which (ΔE) behave as ΔE = αT and ΔE = βT+γ respectively.     

Role of correlated hopping in mixed valence phenomena

Role of correlated hopping is studied using extended Falicov–Kimball model in a small cluster. A discontinuous insulator-to-metal transition is observed at a critical f-level energy. Transition is sharper for larger correlated hopping. In the specific heat curves a two-peak structure consisting of a sharp peak followed by a Schottky-type broad peak is exhibited. In a limited parameter region, some heavy-fermion like characteristics have been observed.     

Phonon induced instabilities in intermediate valence compounds

The coupling of 4f electrons and longitudinal optical phonons and its implications on different types of structural phase transitions in intermediate valence compounds is discussed within the framework of the periodic Anderson model. Two types of interactions are considered. First, the usual density type of coupling of 4f electrons and phonons leads to a weakly temperature dependent renormalization of the positionE ₀ of the 4f level with respect to the 5d band. Secondly, phonon induced 4f–5d interband transitions lead to a renormalization of the hybridization energyV of 4f and conduction electrons. For appropriate parameter values the latter effect gives rise to discontinuous changes of the occupation of the 4f state.The tendency towards a ferromagnetic or antiferromagnetic instability is essentially suppressed by the presence of phonons.The dependence of the susceptibility on temperature and onE ₀ is calculated and a jump is found whenever a discontinuous change of the occupation of the 4f state occurs.Work performed within the research program of the Sonderforschungsbereich 125, Aachen-Jülich-Köln     

Defect-induced valence instabilities in rare-earth semiconducting compounds

We investigate a possible mechanism for local valence instabilities in a NaCl-type rare earth compound (semiconducting SmS) containing p-substitutional anionic impurities (A=O, Se, Te, P…) or sulphur vacancies (A=υ). Using group theory analysis we discuss the nature of the defect levels from considering the whole cluster Sm₆A formed by a point defect A and the six neighbouring Sm atoms. Phase diagrams for valence transitions are obtained in terms of the defect potential matrix elements from the competition between the promotion energy of an f electron into the conduction bands and the available band structure energy. Especially, possible solutions are presented for A=O, Se, Te.     

Lattice dynamics in the mixed valence compounds Sm(Y)S,CeSn3 and CePd3

Renormalized phonon energies of typical mixed valence compounds such as Sm(Y)S, CeSn₃ and CePd₃ are calculated. The renormalization is caused by the additional interaction of localized 4f electrons with phonons which can lead to drastic phonon anomalies. These anomalies are found to be completely different for the various systems under consideration.     

Stabilization of mixed valence by polaronic effects

Polaronic effects in mixed valence systems are studied in a simple model of localized d-electrons for arbitrary values of relevant parameters. Variational approach is used which permits one to interpolate between the limit of average static lattice distortion and that of different local distortions for different valence states of an ion. It is shown that the degree of local electron-lattice correlation and polaron narrowing of virtual f-level changes with a position of f-level. Polaronic effects make a valence transition more gradual and stabilize mixed valence phase. At the end some comments on a possibility of Valence Density Waves in mixed valence compounds are made and certain properties of CeAl₂ are tentatively ascribed to them.     

On the static susceptibilities of mixed valence systems

Magnetic and charge susceptibilities of mixed valence systems are investigated at temperatures above their fluctuation temperature. It is pointed out that an important contribution to their “paramagnetic Curie temperatures” is of single ion origin. This contribution is calculated for the various mixed valent rare earth ions. Special attention is paid to Tm-systems.     

Anomalous thermal expansion of intermediate valence compounds

A low temperature anomaly in the thermal expansion is predicted for all rare earth compounds with an intermediate valence. The anomaly is caused by a logarithmic variation of the f-electron self-energy with temperature. The sign of the anomaly depends on the Hund's rule correlations of the rare earth ions and is predicted unequivocally by the theory.     

Theory of valence mixing for rare-earth compounds

A theory for the mixed valence state of rare-earth compounds is presented. It includes the following features: (1) two types of electronic states-localized, highly correlated states and itinerant, non-correlated states; (2) a very strong Coulomb repulsion between localized states in the same site; (3) a Coulomb interaction between localized and itinerant states which drives the phase transition; and (4) hybridization between localized and itinerant states which produces the mixed valence state. It is shown that this model produces (a) at T = 0, a variation in the number of localized electrons which may vary in a smooth or in a discontinuous fashion as a function of pressure or alloying; (b) transitions at finite temperature which terminate in a classical critical point. Qualitative agreement with experiment is an encouraging feature of the model.     

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.     

Magnetism of mixed valence (LaSr) hexaferrites

We propose a theoretical model to account for the recently observed magnetic moment reduction of gadolinium in fullerenes. While this reduction has been observed also for other trivalent rare-earth atoms (Dy³⁺, Er³⁺, Ho³⁺) in fullerenes, and can be ascribed to crystal field effects, the explanation of this phenomena for Gd³⁺ is not straightforward due to the spherical nature of its ground state (S=7/2, L=0). In our model the momentum reduction is the result of a subtle interplay between hybridisation and the spin-orbit interaction.     

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.