The underscreened Kondo effect: a two S=1 impurity model

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The underscreened Kondo effect is studied within a model of two impurities S=1 interacting with the conduction band and via an interimpurity coupling KS₁.S₂. Using a mean-field treatment of the bosonized Hamiltonian, we show that there is no phase transition, but a continuous cross-over versus K from a non Kondo behaviour to an underscreened Kondo one. For a small antiferromagnetic coupling (K>0), a completely asymmetric situation is obtained with one s=1/2 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 RKKY interaction and a local Kondo effect, as observed in Uranium compounds such as UPt₃.