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The dense Kondo behaviour observed in Ce metal, its alloys and compounds is discussed by taking into account spin-orbit coupling and crystal field splitting. Especially, by using an expression for the Kondo temperature under a crystal field, we clarify the reason why the Kondo effect dominates the RKKY interaction.

Wavelength [nm]Photon Energy [eV] Depth from Si Surface [nm] Si depth where integrated amount of light decreases to

Theory of heavy electron is reviewed on the basis of the Fermi liquid theory. The importance of the orbital degeneracy in realizing the heavy electrons is stressed by using the scaling theory on the Kondo temperature. With use of the periodic Anderson Hamiltonian, the expressions for the physical quantities, such as electronic specific heat, magnetic susceptibility, conductivity, relaxation time of nuclear spin and anomalous Hall coefficient are derived. These results explain the essential properties of heavy electrons. For further development the extension to the orbital degenerate case is essential and discussed mainly on the specific heat and the susceptibility. At the end the relation between the Fermi liquid state and spin fluctuation is discussed with use of the orthogonality theorem. § 1. Introduction 141In this paper we discuss the normal state properties of the heavy fermion systems. At the beginning we discuss the reason why the heavy electron system is realized at low temperatures. 1 > In usual rare earth metals the magnetic long range. order, such as helical structure, appears at a temperature around 50 K ,...,300 K~ The magnetic long range order is due to the RKKY (Ruderman-Kittel-Kasuya-Yosida) interaction, ]RKKYSi· Sj, which is proportional to S 2 , S being the magnitude of localized spin. For example, Gd metal with localized spin S=7 /2 orders in the ferromagnetic state below 300 K. This RKKY interaction between Ce (Yb) ions with a single /-electron (hole) is weak because of Si=1/4 compared with Sz 2 =49/4 for Gd. If the magnetic ordering temperature is scaled by S 2 from that of Gd, the critical temperature forCe (Yb) is given by 6 K. If we scale the paramagnetic Curie temperature by the de Gennes factor (g 1 -1) 2 j(j + 1), we obtain 3 K for that of Ce 3 +. These values for the magnetic ordering temperature of Ce system are reasonable compared with observed ones. Moreover, if we take into account the Kondo effect, it lowers further the ordering temperature estimated above.In addition to the low ordering temperature due to small localized spins, the Kondo temperature becomes high owing to the orbital degeneracy, even for the weak coupling of the exchange interaction. Z>-4 > This is the important fact in realizing the heavy electron in the Ce and Yb systems. We shall discuss it in the next section. The other rare earth metals than Ce and Yb have the multiply occupied /-shell. For the /-shell with plural electrons or holes, the Hund's coupling is strong enough to reduce the degree of freedom of angular momentum exchanged by the s-/ exchange.