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.

4+ pages + suppl. material, 5 figures

References in corpus (12)

• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• The numerical renormalization group method for quantum impurity systems
• RKKY in half-filled bipartite lattices: graphene as an example
• Diluted Graphene Antiferromagnet
• Exchange interaction between single magnetic adatoms
• Long-range Kondo signature of a single magnetic impurity
• Quantum criticality in a double quantum-dot system
• Interplay between Kondo effect and Ruderman-Kittel-Kasuya-Yosida interaction
• Spin Correlations and Finite-Size Effects in the One-dimensional Kondo Box
• Block Lanczos density-matrix renormalization group method for general Anderson impurity models: Application to magnetic impurity problems in graphene
• Competition between Kondo screening and indirect magnetic exchange in a quantum box
• Numerical study of finite size effects in the one-dimensional two-impurity Anderson model

Cited by in corpus (6)

• Multiple magnetic impurities on surfaces: Scattering and quasiparticle interference
• Natural Orbitals Renormalization Group Approach to the Two-Impurity Kondo Critical Point
• Spatial structure of correlations around a quantum impurity at the edge of a two-dimensional topological insulator
• Spin-1 two-impurity Kondo problem on a lattice
• Generation of current vortex by spin current in Rashba systems
• Magnetic correlation between two local spins in a quantum spin Hall insulator