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Register a new userSpin-1 two-impurity Kondo problem on a lattice
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We present an extensive study of the two-impurity Kondo problem for spin-1 adatoms on square lattice using an exact canonical transformation to map the problem onto an effective one-dimensional system that can be numerically solved using the density matrix renormalization group method. We provide a simple intuitive picture and identify the different regimes, depending on the distance between the two impurities, Kondo coupling $J_K$, longitudinal anisotropy $D$, and transverse anisotropy $E$. In the isotropic case, two impurities on opposite(same) sublattices have a singlet(triplet) ground state. However, the energy difference between the triplet ground state and the singlet excited state is very small and we expect an effectively four-fold degenerate ground state, i.e., two decoupled impurities. For large enough $J_K$ the impurities are practically uncorrelated forming two independent underscreened states with the conduction electrons, a clear non-perturbative effect. When the impurities are entangled in an RKKY-like state, Kondo correlations persists and the two effects coexist: the impurities are underscreened, and the dangling spin-$1/2$ degrees of freedom are responsible for the inter-impurity entanglement. We analyze the effects of magnetic anisotropy in the development of quasi-classical correlations.
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We study the low-temperature properties of the generalized Anderson impurity model in which two localized configurations, one with two doublets and the other with a triplet, are mixed by two degenerate conduction channels. By using the numerical renormalization group and the non-crossing approximation, we analyze the impurity entropy, its spectral density, and the equilibrium conductance for several values of the model parameters. Marked differences with respect to the conventional one-channel spin $s=1/2$ Anderson model, that can be traced as hallmarks of an impurity spin $S=1$, are found in the Kondo temperature, the width and position of the charge transfer peak, as well as the temperature dependence of the equilibrium conductance. Furthermore, we analyze the rich effects of a single-ion magnetic anisotropy $D$ on the Kondo behavior. In particular, as shown before, for large enough positive $D$ the system behaves as a non-Landau Fermi liquid that cannot be adiabatically connected to a non-interacting system turning off the interactions. For negative $D$ the Kondo effect is strongly suppressed. The model studied is suitable for a comprehensive analysis for recent investigations of a single Ni impurity embedded into an Au chain.
The underscreened Kondo effect is studied within a model of two impurities S=1 interacting with the conduction band and via an interimpurity coupling $Kvec{S_1}.vec{S_2}$. Using a mean-field treatment of the bosonized Hamiltonian, we show that there is no phase transition, but a continuous cross-over versus K from a non Kondo behaviour to an underscreened Kondo one. For a small antiferromagnetic coupling (K>0), a completely asymmetric situation is obtained with one s=${1/2}$ component strongly screened by the Kondo effect and the other one almost free to yield indirect magnetism, which shows finally a possible coexistence between a RKKY interaction and a local Kondo effect, as observed in Uranium compounds such as $UPt_3$.
In the first step, experiments on a single cerium or ytterbium Kondo impurity reveal the importance of the Kondo temperature by comparison to other type of couplings like the hyperfine interaction, the crystal field and the intersite coupling. The extension to a lattice is discussed. Emphasis is given on the fact that the occupation number $n_f$ of the trivalent configuration may be the implicit key variable even for the Kondo lattice. Three $(P, H, T)$ phase diagrams are discussed: CeRu$_2$Si$_2$, CeRhIn$_5$ and SmS.
In a Kondo lattice, the spin exchange coupling between a local spin and the conduction electrons acquires nonlocal contributions due to conduction electron scattering from surrounding local spins and the subsequent RKKY interaction. It leads to a hitherto unrecognized interference of Kondo screening and the RKKY interaction beyond the Doniach scenario. We develop a renormalization group theory for the RKKY-modified Kondo vertex. The Kondo temperature, $T_K(y)$, is suppressed in a universal way, controlled by the antiferromagnetic RKKY coupling parameter $y$. Complete spin screening ceases to exist beyond a critical RKKY strength $y_c$ even in the absence of magnetic ordering. At this breakdown point, $T_K(y)$ remains nonzero and is not defined for larger RKKY couplings, $y>y_c$. The results are in quantitative agreement with STM spectroscopy experiments on tunable two-impurity Kondo systems. The possible implications for quantum critical scenarios in heavy-fermion systems are discussed.
We consider the Kondo effect arising from a hydrogen impurity in graphene. As a first approximation, the strong covalent bond to a carbon atom removes that carbon atom without breaking the $C_{3}$ rotation symmetry, and we only retain the Hubbard interaction on the three nearest neighbors of the removed carbon atom which then behave as magnetic impurities. These three impurity spins are coupled to three conduction channels with definite helicity, two of which support a diverging local density of states (LDOS) $propto 1/ [ | omega | ln ^{2}( Lambda /| omega | ) ] $ near the Dirac point $omega rightarrow 0$ even though the bulk density of states vanishes linearly. We study the resulting 3-impurity multi-channel Kondo model using the numerical renormalization group method. For weak potential scattering, the ground state of the Kondo model is a particle-hole symmetric spin-$1/2$ doublet, with ferromagnetic coupling between the three impurity spins; for moderate potential scattering, the ground state becomes a particle-hole asymmetric spin singlet, with antiferromagnetic coupling between the three impurity spins. This behavior is inherited by the Anderson model containing the hydrogen impurity and all four carbon atoms in its vicinity.
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