Interplay of CEF effects and RKKY interaction in Ce- and Yb-based heavy-fermion compounds

We calculate the influence of Crystalline Electric Field (CEF) effects on the indirect Ruderman-Kittel-Kasuya-Yoshida (RKKY) exchange interaction between local 4f moments in Ce- and Yb-compounds. Starting from a periodic Anderson model and neglecting spin-orbit effects among the conduction states, we show that the anisotropy of the CEF ground state manifests itself in the anisotropy of the effective exchange coupling constant J(R, R’) between two moments at sites R and R’ while the interaction between two Kramers doublets is isotropic in pseudo-spin space. We evaluate the exchange constant for various models of the conduction states in tetragonal Ce- and Yb-122 compounds. The influence of spin-orbit interaction among the conduction electrons is discussed.