Magnetic correlations between two Kondo impurities with two magnetic configurations: Narrow-band limit - Allub, Roberto Jose (2013)
The lowest excitation energy and the magnetic correlations 〈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 and (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 (Δ), 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 →0, the strong coupling regime takes place and the physics that governs the ground state depends on Δ/V. For V<<−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 <−Δ, with major charge fluctuations between the magnetic configurations, a singlet ground state occurs and antiferromagnetic (AF) correlations between the impurities appear. When φ increases, the decoupling of the impurities proceeds and 〈S1·S2 〉decreases, finally for φ=π/2 the decoupled limit takes place and the model is reduced to two independent ions (〈S1·S2 〉= 0). For a narrow region of Δ/V, when φ increases, the model shows the crossover from singlet (AF) ground state to triplet (F) ground state.