Kondo screening in high-spin side-coupled two-impurity clusters

Abstract

We study the system of two magnetic impurities described by a two-impurity Kondo modelwhere only the first impurity couples directly to the conduction band, while thesecond impurity interacts with the first through Heisenberg exchange coupling in a‘side-coupled’ configuration. We consider various choices of the impurity spins (S1<S2,S1 = S2 andS1>S2) and we contrast the regimes where the inter-impurity exchange couplingJ is either lower or higher than the Kondo temperatureTK(0) of the first impurity in the absence of the second. This model is a high-spin generalization of thetwo-impurity model for side-coupled double quantum dots which corresponds to the simplestS1 = S2 = 1/2 case, where the moments are Kondo-screened successively in two stages forJ<TK(0) (the ‘two-stage Kondo effect’). We show that the two-stage Kondo screening occurs generically forS2≥S1. ForS1≥1, the second Kondotemperature TK(2) is notexponentially reduced, as for S1 = 1/2, but is approximately a power-law function of the couplingJ. Furthermore,for S1≥1 all threescales (TK(0), J,TK(2)) explicitly appear in the temperature dependence of the thermodynamic properties. ForS1>S2, there is no second stage of screening forJ<TK(0). However, in theopposite limit J>TK(0) the Kondo screening of the effective spinS1−S2 is found.