Effect of Spin-Orbit Coupling on Kondo Phenomena in f7-Electron Systems

In order to promote our basic understanding of the Kondo behavior recently observed in europium compounds, we analyze an impurity Anderson model with seven f electrons at an impurity site by employing a numerical renormalization group method. The local part of the model consists of Coulomb interactions among f electrons, spin-orbit coupling lambda, and crystalline electric field (CEF) potentials, while we consider the hybridization V between local f electrons and single-band conduction electrons with a(u) symmetry. For lambda = 0, we observe underscreening Kondo behavior for appropriate values of V, characterized by an entropy change from ln 8 to ln 7, in which one of the seven f electrons is screened by conduction electrons. When lambda is increased, we obtain two types of behavior depending on the value of V. For large V, we find an entropy release of ln 7 at low temperatures, determined by the level splitting energy due to the hybridization. For small V, we also observe an entropy change from ln 8 to ln 2 by the level splitting due to the hybridization, but at low temperatures, ln 2 entropy is found to be released, leading to the Kondo effect. We emphasize that the Kondo behavior for small V is observed for realistic values of lambda on the order of 0.1 eV. We also discuss the effect of CEF potentials and the multipole properties in the Kondo behavior reported in this paper.