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

TL;DR

This paper investigates how lattice structure and dimensionality influence the competition between Kondo screening and RKKY interactions in magnetic impurities, revealing that Kondo physics often dominates in higher dimensions contrary to traditional RKKY assumptions.

Contribution

The study introduces an exact mapping to a one-dimensional problem solved with DMRG, showing deviations from conventional RKKY theory due to dimensionality and density of states effects.

Findings

Kondo effect dominates at short distances in dimensions greater than one.

RKKY interactions are finite-range and can be overshadowed by Kondo screening.

Dimensionality significantly alters the balance between Kondo and RKKY interactions.

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.