Kondo Engineering : from Single Kondo Impurity to the Kondo Lattice

In the first step, experiments on a single cerium or ytterbium Kondo impurity reveal the importance of the Kondo temperature by comparison to other type of couplings like the hyperfine interaction, the crystal field and the intersite coupling. The extension to a lattice is discussed. Emphasis is given on the fact that the occupation number n f of the trivalent configuration may be the implicit key variable even for the Kondo lattice. Three (P, H, T) phase diagrams are discussed: CeRu 2 Si 2 , CeRhIn 5 and SmS. In this article we will use the Kondo idea of strong local enhancement of the effective mass m * of the quasiparticle to understand the new features which appear in a Kondo lattice i.e for a regular array of Kondo paramagnetic centers. Thus an attempt will be given to classify the main parameters of a Kondo impurity and then to schematize the problem by simple relations in order to advance in the experiments on this complex quantum matter which is the Kondo lattice. For simplicity, we restrict the discussion mainly to Ce Kondo centers. 1. Kondo impurity : hierarchy between T K and other couplings The new insight into the Kondo effect is that due to the strong coupling with the Fermi sea below some Kondo temperature (T K) the entropy of a single paramagnetic impurity can collaps at T → 0 K without further coupling with the other impurities. One of the important message given by the study of a single Kondo impurity is that the Kondo energy k B T K is the key energy in the comparison of the electronic coupling given by the Fermi sea with other sources of interactions like the electronuclear hyperfine coupling A 1 or the crystal field effect C CF. 2 If k B T K ≤ A or C CF , the angular momentum J of the Kondo paramagnetic center will feel these inner structures, and only after the selection of a reduced effective spin, the Kondo effect will act and governs the low temperature properties. A nice case is the hyperfine coupling between the electronic effective spin J and its nuclear spin I submitted to the combined effect of a magnetic field (H) and the Kondo exchange term (Γ) between J and s the spin of the conduction electron according to the hamiltonian This situation was extensively studied by the nuclear …