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We consider a magnetic impurity which interacts by hybridization with asystem of strongly correlated conduction electrons. The latter are described bya Hubbard Hamiltonian. By means of a canconical transformation the chargedegrees of freedom of the magnetic impurity are eliminated. The resultingeffective Hamiltonian $H_{\rm eff}$ is investigated and various limiting casesare considered. If the Hubbard interaction $U$ between the conduction electronsis neglected $H_{\rm eff}$ reduces to a form obtained by the Schrieffer-Wolfftransformation, which is essentially the Kondo Hamiltonian. If $U$ is large andthe correlations are strong $H_{\rm eff}$ is changed. One modification concernsthe coefficient of the dominant exchange coupling of the magnetic impurity withthe nearest lattice site. When the system is hole doped, there is also anantiferromagnetic coupling to the nearest neighbors of that site involvingadditionally a hole. Furthermore, it is found that the magnetic impurityattracts a hole. In the case of electron doping, double occupancies arerepelled by the impurity. In contrast to the hole-doped case, we find nomagnetic coupling which additionally involves a doubly occupied site.Comment: 16 pages, Revtex 3.

Interaction of a magnetic impurity with strongly correlated conduction electrons