A theoretical concept is presented for the screening of several magnetic moments locally exchange coupled to conduction electrons in a metallic nanostructure. We consider a quantum confined multi-impurity Kondo model which exhibits the competition between finite-size effects, RKKY interactions, and Kondo physics. In the limit of weak coupling, Kondo correlations are cut by the finite system size; perturbation theory can then be used to derive the low-energy effective model, which is of generalized central-spin form. The theory successfully predicts the degeneracy, total spin, and spin correlations of the ground state, and allows the number of screening channels to be identified. This is demonstrated for a two-impurity model on a finite one-dimensional ring. Density-matrix renormalization-group calculations confirm the physical picture at weak coupling. The nontrivial crossovers to RKKY and strong-coupling regimes are also studied. The numerical renormalization group, tailored to treat finite systems, is used to examine the crossover to the thermodynamic limit.

• Received 13 August 2015
• Revised 2 September 2015

DOI:https://doi.org/10.1103/PhysRevB.92.155104