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

Abstract

Magnetic impurities embedded in a metal interact via an effective Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling mediated by the conduction electrons, which is commonly assumed to be long ranged, with an algebraic decay in the inter-impurity distance. However, they can also form a Kondo screened state that is oblivious to the presence of other impurities. The competition between these effects leads to a critical distance above which Kondo effect dominates, translating into a finite range for the RKKY interaction. We study this mechanism on the square and cubic lattices by introducing an exact mapping onto an effective one-dimensional problem that we can solve with the density matrix renormalization group method (DMRG). We show a clear departure from the conventional RKKY theory, that can be attributed to the dimensionality and different densities of states. In particular, for dimension d>1, Kondo physics dominates even at short distances, while the ferromagnetic RKKY state is energetically unfavorable.

arXiv comment4+ pages + suppl. material, 5 figures

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• Strongly correlated multi-impurity models: The crossover from a single-impurity problem to lattice models
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• Efficient tensor network simulation of multi-emitter non-Markovian systems
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