This paper consists of a highly condensed review of the experimental and theoretical studies of heavy-fermion and mixed-valence materials. It points out the applicability and limitations of the various theoretical models. The Fermi liquid models are applicable at low temperatures, and whether one chooses to use the one-band, two-band or the LDA model depends on the amount of detail demanded by the experimental situation. The spin fluctuation model is the model of choice for single impurities as well as dense systems at high temperatures. The electronic polaron model is principally a model for the cross-over regime between Fermi liquid and local moment limits. Whether there is any hope of uniting all theories remains to be resolved. The situation is comparable to the theory of ferromagnetism in local moment systems. At very low temperatures one can understand the experimental results in terms of the spin wave theory. Near the Curie temperature all measurements on the critical phenomena are united by the scaling theory. Between these two Well- understood limits the average properties of the system is best handled by the mean-field theory, which is a rather crude approximation. An exact solution of the Heisenberg Hamiltonian continues to elude us.
As mentioned in the introduction, there is a tendency in literature to classify mixed- valence and heavy-fermion systems as two distinct classes of materials. It is our view that the distinction is artificial, because as fig. 3 clearly shows, there is no gap in the mass spectrum from mixed-valence systems at the lower left corner to heavy-fermion systems at the upper right corner. Other experimental results also demonstrate a lack of clear demarcation between systems in the low-mass end and those in the high-mass end. One can only see a steady decrease in the characteristic energy or temperature
as one traverses up the graph. It is also clear that lanthanide and actinide compounds are evenly distributed in fig. 3, indicating that members of both series can make mixed- valence as well as heavy-fermion compounds provided that the environment is right.
There are differences in detail, however, between lanthanide and actinide compounds.
The lanthanides Ce and Yb have one 4f electron or hole, making it easier to analyze the cross-over from local to itinerant behavior. The actinide systems, on the other hand, have many 5f electrons per atom, and the role of the Hund's rule coupling among the many f electrons has not been studied in a systematic manner. It is hoped that this review will provide impetus for further investigations.
Since the main subject of this review is controversial, we hasten to emphasize that the views presented here are less than objective. The reader has the perfect right to weigh the evidence differently or invoke evidence unknown to this reviewer and reach a radically different point of view. After all, Nature has no respect for human intelligence. It should not surprise us if different interactions may play the dominant role in different, albeit very similar substances. What is also likely is that some new mechanism may be found some day that explains everything or produces more confusion. The only safe conclusion one can draw at this point is that the field is still wide open.
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Handbook on the Physics and Chemistry of Rare Earths Vol. 17 - Lanthanides/Actinides: Physics - I
edited by K.A. Gschneidner, Jr., L. Eyring, G.H. Lander and G.R. Choppin
© 1993 Elsevier Science Publishers B.V. All rights reserved
Chapter 112
T H E O R Y O F C O H E S I O N I N R A R E E A R T H S A N D A C T I N I D E S
BÖRJE JOHANSSON
Condensed Marter Theory Group, Institute of Physics, University of Uppsala, BOX 530, S-75121 Uppsala, Sweden