Magnetic correlations between two Kondo impurities with two magnetic configurations: Narrow-band limit

The lowest excitation energy and the magnetic correlations 〈S1·S2〉〈S1·S2〉 between two magnetic impurities are analyzed within the two-magnetic-impurity model Hamiltonian. The model includes two magnetic ions that can exist in two valence states and a band of conduction electrons. The two localized states represent the ground states of the ionic configurations (5f)n(5f)n and (5f)n+1(5f)n+1, assumed to be a doublet and a triplet, respectively. In the zero band-width limit, three parameters characterize this model: the energy difference between the magnetic configurations (ΔΔ), the localized-extended-state hybridization energy (V  ), and the relationship between the Fermi wavelength and the distance r→ between the magnetic ions (ϕ=k→F·r→). For ϕ→0ϕ→0, the strong coupling regime takes place and the physics that governs the ground state depends on Δ/VΔ/V. For V⪡−ΔV⪡−Δ, the highest spin configuration is favored, and the model shows a triplet ground state and the coexistence of strong ferromagnetic (F) correlations between the impurities with the Kondo physics of two magnetic impurities. For V<−ΔV<−Δ, with major charge fluctuations between the magnetic configurations, a singlet ground state occurs and antiferromagnetic (AF) correlations between the impurities appear. When ϕϕ increases, the decoupling of the impurities proceeds and 〈S1·S2〉〈S1·S2〉 decreases, finally for ϕ=π/2ϕ=π/2 the decoupled limit takes place and the model is reduced to two independent ions (〈S1·S2〉=0〈S1·S2〉=0). For a narrow region of Δ/VΔ/V, when ϕϕ increases, the model shows the crossover from singlet (AF) ground state to triplet (F) ground state.