On the electrical conductivity of intermediate valence compounds

The electrical resistivity of the hybridized 4f-(5d/6s) system interacting with LA phonons is calculated by applying the memory function method to the periodic Anderson model in Hartree-Fock approximation. We propose a new mechanism to explain in part the anomalous resistivity of mixed valence compounds such as CePd₃. For finite hybridizationV a finite fraction of 4f electrons participates in electrical conduction leading to an essential change of the normald band current. Resistivity and the fraction of 4f electrons increase with increasing value of [V/(E–)]² where (E–) is the distance between the effective positionE of the 4f level and the chemical potential. In typical mixed valence systems [V/(E–)]² is strongly temperature dependent and decreases with increasing temperature. This explains the high temperature resistivity behaviour of CePd₃. For (E–) being small compared to the Debye-temperature the resistivity is enhanced and becomes extremely sensitive to small changes of (E–).Work performed within the research program of the Sonderforschungsbereich 125, Aachen-Jülich-Köln     

Lattice thermal conductivity of skutterudite compounds

A generalized expression is used on the basis of relaxation time approximation to facilitate calculation of lattice thermal conductivity of dielectric materials as well as skutterudite family consists of compounds of the form AB₃. It is assumed that phonon scattering processes are independent and is represented by frequency dependent relaxation times. The contributions of normal three phonon scattering processes are included explicitly as redistribution of phonon momentum between two oscillation branches is considered. Magnitudes of relaxation times are estimated from the experimental data. The result for CoSb₃ is in reasonably good agreement with the experimental result in the temperature range 1–1000°K. It is observed that redistribution of phonon momentum between two oscillation branches leads to a significant suppression of thermal conductivity maximum and it is observed that for unfilled skutterudite the main dominant mechanism at the thermal conductivity maximum is three phonon normal scattering process.     

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.     

Lattice thermal conductivity of II–VI compounds

The lattice thermal conductivity of three II–VI compounds, ZnS, ZnSe, and ZnTe has been analysed on the basis of full Callaway's formalism by considering the scattering of phonons by boundary, point defects, normal, and Umklapp processes. An acceptable agreement with the experimental results is found up to 250 K. From the analysis of the adjustable parameters useful information about the lattice anharmonicity and defects have been obtained.     

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.     

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.     

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     

Phonon anomalies in intermediate valence compounds

Phonon anomalies in the intermediate valence compounds SmS, TmSe and YS were studied extensively using a three-body force rigid shell model. Three-body interactions were used because, due to valence fluctuations, the radii of rare-earth ions change significantly and, therefore, the amount of overlap with neighboring chalcogen ions also changes. Change in the radii of the rare-earth ions results in the deformation of the rare-earth ions, whereas change in the amount of overlap with the neighboring chalcogen ion gives rise to long-range three-body interactions between the transferred charges of the lattice. Both of these changes strongly influence the phonon dispersion curves, particularly along the zone boundary. Results obtained from the model are in agreement with the measured data for phonon dispersion as compared to the results obtained using a three-body rigid ion model. Results for Debye temperature variations and two-phonon IR/Raman spectra for these crystals have also been presented, probably for the first time, but could not be compared with experimental data due to their non-availability.     

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.     

Thermophoresis of sublimating aerosol particles with inhomogeneous thermal conductivity

The theory of thermophoresis of a large solid spherical sublimating aerosol particle with a coordinate-dependent thermal conductivity is elaborated. The expression for the thermophoresis rate is derived and analyzed.     

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     

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.     

Lattice thermal conductivity due to impurities

Phonon conductivity of NaF has been calculated using non-linear theory of heat transfer in solid given by Kazakov and Nagaev and shows good agreement with the measurements of Jackson and Walker in the temperature range 2–10°K.     

Lattice thermal conductivity crossovers in semiconductor nanowires

For binary compound semiconductor nanowires, we find a striking relationship between the nanowire's thermal conductivity kappa(nwire), the bulk material's thermal conductivity kappa(bulk), and the mass ratio of the material's constituent atoms, r, as kappa(bulk)/kappa(nwire) (alpha) (1+1/r)(-3/2). A significant consequence is the presence of crossovers in which a material with higher bulk thermal conductivity than the rest is no longer the best nanowire thermal conductor. We show that this behavior stems from a change in the dominant phonon scattering mechanism with decreasing nanowire size. The results have important implications for nanoscale heat dissipation, thermoelectricity, and thermal conductivity of nanocomposites.     

On the pressure-temperature phase diagram of intermediate valence compounds

The pressure-temperature (P, T) phase diagram of intermediate valence compounds has been calculated on the basis of the periodic Anderson model which was extended to include the interaction of 4f electrons with longitudinal optical phonons. It is shown that the positive slope (dP/dT>0) of the phase boundary between the insulating and the mixed valence phase as observed experimentally in Sm S and many other systems is determined by the behaviour of the electronic density of states of the interacting system as function ofP. Moreover, the observed anomalous thermal contraction in the insulating phase near the phase boundary and the anomalously large thermal expansion in the metallic phase are well described by numerical results for the extended periodic Anderson model.     

Entropy contribution to thermal expansion of rare-earth compounds

The magnetoelastic contribution to the thermal expansion of orthorhombic rare-earth compounds is calculated to second order in perturbation theory. The entropy contribution to the free energy is found and analyzed. The case of higher, tetragonal symmetry is exemplified.     

Possibility of a distortion induced gap in intermediate valence compounds

It is shown that in some stoichiometric intermediate valence compounds a symmetry breaking distortion leading to a hybridization gap in the electronic density of states can exist. We study this possibility for the high pressure phase of SmS and the paramagnetic phase of TmSe.     

Susceptibility of rare earth compounds in the intermediate valence state

The thermodynamic potential of rare earth compounds in a mixed valent state is investigated by perturbation theoretical methods. Two types of contributions must be distinguished, the impurity terms and terms corresponding to interactions between different rare earth sites. For a large class of substances the latter are shown to be of minor importance. The susceptibility of the resulting theory is compared directly with the renormalization group calculations of Krishna-murthy, Wilson and Wilkins and with measured susceptibilities of-Ce, SmB₆, YbAl₃.     

On the absence of magnetic order in intermediate valence compounds

We study the mechanism by which the magnetic order is suppressed in intermediate valence compounds. By a diagrammatic perturbation theory in the hybridization interaction, the effective inter-site exchange interaction is derived for the periodic Anderson model. The result includes the effect of charge fluctuations and is valid for arbitrary position of the local electron level relative to the Fermi level. It is shown that the intersite interaction is destructive to magnetic fluctuations with any wavenumber in the case of intermediate valence.Work supported by the Deutsche Forschungsgemeinschaft through the research program SFB 125 Aachen-Jülich-Köln     

Magnetic susceptibility and specific heat of intermediate valence Tm compounds

We calculate the static magnetic susceptibility and specific heat of a model periodic system, with valence fluctuations between two magnetic configurations, intended to describe intermediate valence Tm compounds.These properties are derived from an expression for the free energy obtained using the coherent potential approximation, which properly takes into account the correlation energy and the configurational entropy.The resulting properties are in reasonable agreement with the experimental data. Unlike the results found in the commonly studied Anderson model, we find divergences in the magnetic susceptibility that indicate the onset of ferromagnetic order for some values of the model parameters.