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Magnetic impurities embedded in a metal interact via an effectiveRuderman-Kittel-Kasuya-Yosida (RKKY) coupling mediated by the conductionelectrons, which is commonly assumed to be long ranged, with an algebraic decayin the inter-impurity distance. However, they can also form a Kondo screenedstate that is oblivious to the presence of other impurities. The competitionbetween these effects leads to a critical distance above which Kondo effectdominates, translating into a finite range for the RKKY interaction. We studythis mechanism on the square and cubic lattices by introducing an exact mappingonto an effective one-dimensional problem that we can solve with the densitymatrix renormalization group method (DMRG). We show a clear departure from theconventional RKKY theory, that can be attributed to the dimensionality anddifferent densities of states. In particular, for dimension d>1, Kondo physicsdominates even at short distances, while the ferromagnetic RKKY state isenergetically unfavorable.

Kondo versus indirect exchange: the role of the lattice and the actual range of RKKY interactions in real materials