Valence fluctuation phenomena occur in rare-earth compounds in which the proximity of the 4f level to the Fermi energy leads to instabilities of the charge configuration (valence) and/or of the magnetic moment. The authors review the experimental results observed in the subset of such systems for which the 4f ions form a lattice with identical valence on each site. The discussion includes key thermodynamic experiments, such as susceptibility and lattice constant, and spectroscopic experiments such as XPS and neutron scattering. This is followed by a review of existing theoretical work concerning both the ground states and the isomorphic phase transitions which occur in such compounds; the emphasis is on those aspects which make valence fluctuation phenomena such a challenging many-body problem.

https://iopscience.iop.org/article/10.1088/0034-4885/44/1/001/pdf

Valence fluctuation phenomena

This paper presents an extension of the self-consistent perturbation theory for the Anderson model to periodic valence-fluctuation systems. The extended scheme takes the reciprocal of the number of effective neighbors as a proper expansion parameter for intersite interactions. Self-consistent account is taken of the Kondo effect, the intersite exchange interaction and the intersite coherence. Simple illustration is given how the heavy-fermion behavior emerges in the present framework.

Self-Consistent Perturbation Theory for Valence-Fluctuating Lattice Systems

We study the low-energy states of Kondo alloys as a function of the magnetic impurity concentration per site $x$ and the conduction electron average site occupation ${n}_{c}$. Using two complementary approaches, the mean-field coherent potential approximation and the strong-coupling limit, we identify and characterize two different Fermi-liquid regimes. We propose that both regimes are separated by a Lifshitz transition at $x={n}_{c}$. Indeed, we predict a discontinuity of the number of quasiparticles that are enclosed in the Fermi surface. This feature could provide a scenario for the non-Fermi liquid properties that were recently observed in Kondo alloy systems around $x={n}_{c}$.

https://hal.archives-ouvertes.fr/hal-00834108/document

Lifshitz transition in Kondo alloys.

We have measured the resistance R, magnetoresistance, and magnetization of sintered samples of the compounds Sn
 x
 Eu1.2−x
Mo6S8, where x = 0, 0.12, 0.24, and 0.48. A large resistance anomaly beginning at T ~ 100 K and extending to low temperatures is found in all of the alloys except x = 0.48, which had a high superconducting transition temperature T
c ~ 11.3 K. The resistance anomaly, which appears to be correlated with the depression of T
c, is also correlated with a large negative magnetoresistance at temperatures T ⩽ 12 K. For all samples except x = 0.48, that part of the magnetoresistance attributed to spin-flip scattering is proportional to the square of the magnetization M
2 and is 30–40% of R (0) for some samples. Magnetization measurements are consistent with a spin-7/2 paramagnetic behavior of Eu2+ ions when allowance is made for a concentration of 20–30% nonmagnetic (J = 0) Eu3+ ions as determined from Mossbauer measurements. The experimental results are inconsistent with predictions of dilute magnetic alloy Kondo models. We speculate that the resistance anomaly and suppression of T
c for x ⩽ 0.24 are associated with a semiconductor-like behavior.

Transport anomalies and magnetic properties of Sn x Eu 1.2−x Mo 6 S 8 alloys

At the Fermi level, omega =0, a striking decrease occurs in the density of states of conduction electrons exchange-coupled to randomly distributed magnetic impurity spins in a metal. The mathematical structure of this reduction due to the Kondo effect is studied analytically. A discrete energy level is found embedded at omega =0 in the continuous energy spectrum of one of the component electron Green functions defined in the coherent potential approximation. This is found to play an essential role in producing the dip in the density of states and in determining the induced electron spin polarisation at an impurity site. It is also shown that no Kondo lattice state exists in a periodic magnetic system.

Analytic investigation of the Kondo effect in highly concentrated magnetic alloys

Electronic properties of a highly doped Kondo system are discussed. The method of expressing the s-d exchange interaction in terms of the two kinds of quasi-spins, proposed by one of the authors (Kurata (1970)) for the single-impurity Kondo problem, is extended to this system. A generalised Hartree-Fock approximation is made for the interaction and the coherent potential approximation for configurational average over the sites of randomly distributed impurity spins. The density of states of conduction electrons and electrical resistivity are calculated for various concentrations of impurity spins. A reduction of the density of states due to the Kondo effect is found at the Fermi level.

Y Kurata

Papers

The Kondo effect in highly concentrated magnetic alloys