Underscreened Kondo effect: A two impurity model

The underscreened Kondo effect is studied within a model of two impurities (Formula presented) interacting with the conduction band and via an interimpurity coupling (Formula presented). Using a mean-field treatment of the bosonized Hamiltonian, we show that there is no phase transition, but a continuous crossover versus (Formula presented) from a non-Kondo behavior to an underscreened Kondo one. For a small antiferromagnetic coupling (Formula presented), a completely asymmetric situation is obtained with one (Formula presented)(Formula presented) component strongly screened by the Kondo effect and the other one almost free to yield indirect magnetism, which shows finally a possible coexistence between a Ruderman-Kittel-Kasuya-Yosida interaction and a local Kondo effect, as observed in Uranium compounds such as (Formula presented).