RKKY interaction between Ce ions inCexLa1−xB6

Abstract

Ce ions in (Ce{sub x}La{sub 1-x})B{sub 6} have a {Gamma}{sub 8} ground multiplet, which is fourfold degenerate and has orbital and spin content. The interaction between Ce ions is of the Ruderman-Kittel-Kasuya-Yosida (RKKY) type, which competes with the Kondo screening. The conduction states of the compound are described by three approximately ellipsoidal pockets centered at the X points of the cubic lattice. The RKKY interaction is calculated considering the interference of the three pockets. The interaction strength strongly depends on the relative position of the ions, as well as on the relative orientation of the line joining two ions to the cubic crystalline field axis. The sixteen states of a pair of Ce ions are split by the RKKY interaction into a singlet, a triplet, and a twelvefold degenerate level. The ground state is always either a singlet or a triplet, depending on the sign of the interaction. Using the exact Bethe ansatz solution of a model for a pair of interacting impurities with {Gamma}{sub 8} ground multiplet, we calculate the occupation of the levels, the magnetic-field susceptibility, the specific-heat {gamma} coefficient, and the Wilson ratio for the ground state as a function of the ratio of the RKKY couplingmore » strength to the Kondo temperature along the main crystallographic directions. As a consequence of the RKKY splitting a pair of impurities always has a quadrupolar moment. The implication of the interactions on the quadrupolar order of CeB{sub 6} is also discussed.« less