Chapter 105 Valence-fluctuation and heavy-fermion 4f systems

Abstract

This chapter deals with valence-fluctuation and heavy-fermion 4f systems, such as Ce, Sm, Eu, Tm and Yb alloys and compounds. Sections 1 and 2 summarize the most important physical properties of these systems, based on the main theoretical results achieved so far and on representative data. In the main part (section 3) we summarize neutron scattering data of VF and HF systems. By means of neutrons one can measure the magnetic structure of a system (elastic magnetic scattering) and magnetic and non-magnetic excitations such as relaxational modes (quasi-elastic excitations), magnons, crystal field, and spin-orbit transitions, and phonons. Some of these excitations have been observed in all VF or HF systems. Both VF and HF systems exhibit a quasi-elastic line due to spin fluctuations or the Kondo effect. Both expressions are used synonymously, but in VF systems the quasi-elastic line is quite broad, corresponding to a high characteristic energy, and is fairly temperature independent. Here one speaks in general about spin fluctuations. In HF systems the quasi-elastic line is narrower, temperature dependent, and has, at low temperatures, an halfwidth 1/2 Γ ⋍ k B T N K . A typical quasi-elastic line can be fitted by a Lorentzian and corresponds to a single relaxation time. In most HF compounds the line becomes Q -dependent at low temperatures, indicating spin correlations that at still lower temperatures often lead to magnetic order. These spin correlations, on the other hand, lead already to deviations from the Lorentz shape above the spin-ordering temperature. In VF compounds spin correlations do not play a role, but the high-temperature quasi-elastic line also changes shape and becomes narrower and inelastic at low temperatures. Ce-based HF systems have been investigated by many groups, whereas few data exist for the corresponding VF systems and for Yb-, Sm-, Eu-, and Tm-based VF and HF systems. As a consequence, our survey over Ce-based VF and Yb, Sm, Eu, and Tm systems is rather complete, whereas for Ce-based HF systems we could only select representative examples. Part of this strong research activity on Ce compounds is due to the fact that CeCu 2 Si 2 becomes superconducting, and it is an enormous challenge to find other superconducting HF systems. In addition, one has in these systems a variety of magnetic structures, such as ferromagnetic, antiferromagnetic and spiral order and metamagnetism. In many cases the detection of these structures is hampered by moments that are strongly reduced by the Kondo effect. In addition to the Kondo effect one has in HF systems strong crystal field effects, and the corresponding 4f-levels can be determined by neutron scattering experiments. The interplay between Kondo and CF effects varies from system to system, and the corresponding information is part of the content of this chapter. Since in HF systems the Kondo temperature is typically rather small, one observes at low temperature mainly the properties of the lowest CF level. Valence fluctuations couple to phonons, and our review gives a rather complete survey of the corresponding anomalies. In addition, one has phonon anomalies due to the CF-phonon interaction, since a lattice deformation around an R ion modifies the crystalline electric field. Finally, we mention the spin-orbit interaction, which is