Screening and interaction of magnetic impurities in Luttinger liquids

The spin and charge correlations induced in the conduction electron sea by the presence of a spin-1=2 magnetic impurity are investigated for one-dimensional electrons. For correlated conduction electrons, the RKKY interaction between magnetic impurities exhibits only a slow algebraic decay with distance. Increasing the exchange coupling between conduction electrons and magnetic impurity leads to a competition between the RKKY interaction and the Kondo effect. For a two-impurity model, we study the influence of the electronic correlations on this competition. Furthermore, the Kondo screening cloud and the local spin susceptibility far away from a magnetic impurity are discussed.     

Dynamics of a tunneling magnetic impurity: Kondo effect induced incoherence

We study how the formation of the Kondo compensation cloud influences the dynamical properties of a magnetic impurity that tunnels between two positions in a metal. The Kondo effect dynamically generates a strong tunneling impurity-conduction electron coupling, changes the temperature dependence of the tunneling rate, and may ultimately result in the destruction of the coherent motion of the particle at zero temperature. We find an interesting two-channel Kondo fixed point as well for a vanishing overlap between the electronic states that screen the magnetic impurity. We propose experiments where the predicted features could be observed.     

Anomalous magnetic splitting of the kondo resonance

The splitting of the Kondo resonance in the density of states of an Anderson impurity in a finite magnetic field is calculated from the exact Bethe-ansatz solution. The result gives an estimate of the electron spectral function for a nonzero magnetic field and the Kondo temperature, with consequences for transport experiments on quantum dots in the Kondo regime. The strong correlations of the Kondo ground state cause a significant low-temperature reduction of the peak splitting. Explicit formulas are found for the shift and broadening of the Kondo peaks. A likely cause of the problems of large- N approaches to spin- 1 / 2 impurities at finite magnetic field is suggested.     

Bipolaron formation in the presence of magnetic impurities

The formation of bipolarons in the presence of magnetic impurities is studied theoretically. We use the extended Hubbard Su–Schrieffer–Heeger (SSH) model with Brazovskii–Kirova and Kondo interaction terms. Parameters are chosen suitably for cis-polyacetylene. A Quantum Monte Carlo (QMC) algorithm is used to study the equilibrium lattice structure and charge distribution as a function of doping level and Kondo exchange integral. The magnetic impurities can have a destructive effect on bipolaron stability, instead favouring the two polaron configuration. However by suitably adjusting the doping level, bipolarons can be stabilized over a wide range of impurity strength.     

Persistent currents in a lattice correlated electron ring with a magnetic impurity

The behavior of charge and spin persistent currents in an integrable lattice ring of strongly correlated electrons with a magnetic impurity is exactly studied. Our results manifest that the oscillations of charge and spin persistent currents are similar to the ones, earlier obtained for integrable continuum models with a magnetic impurity. The difference is due to two (instead of one) Fermi velocities of low-lying excitations. The form of oscillations in the ground state is “saw-tooth”-like, generic for any multi-particle coherent one-dimensional models. The integrable magnetic impurity introduces net charge and spin chiralities in the generic integrable lattice system, which determine the initial phase shifts of charge and spin persistent currents. We show that the magnitude of the charge persistent current in the generic Kondo situation does not depend on the parameters of the magnetic impurity, unlike the (magneto)resistivity of transport currents. Received 30 January 2003 / Received in final form 12 March 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: zvyagin@fy.chalmers.se     

The Kondo effect of a magnetic impurity under the crystalline field

Using the Coqblin-Schrieffer exchange interaction, we investigate the Kondo effect for a magnetic impurity under the crystalline field, as occuring in La or Y alloys containing cerium impurities. The Hamann typet-matrix equation for the conduction electron scattered by a magnetic impurity is derived and solved, using the method of Zittarz and Müller-Hartmann. We find a Kondo type anomaly and a decreased Kondo temperature due to the crystalline field splittings. The resistivity, entropy and specific heat are calculated and they show some characteristic behavior due to the crystalline field splittings.     

Influence of interstitials and non magnetic impurities on the Kondo effect

The influence of interstitials and non magnetic impurities on the anomalous resistivity, thermopower and Kondo temperature of dilute magnetic alloys was investigated generalizing a model proposed by Bohnen and Fischer. Numerical results are given as a function of the distance between the interstitial (or non magnetic impurity) and the magnetic impurity using their scattering phase shifts as parameters. The Kondo anomalies are altered considerably, if the magnetic impurity is very close to the non magnetic scattering potential, e.g. if it is part of an interstitial dumbbell.This work is part of a doctoral thesis of G.Wehr at the Technische Universität München     

Natural orbitals renormalization group approach to a Kondo singlet

A magnetic impurity embedded in a Fermi sea is collectively screened by a cloud of conduction electrons to form a Kondo singlet below a characteristic energy scale TK, the Kondo temperature, through the mechanism of the Kondo effect. We have reinvestigated the Kondo singlet by means of the newly developed natural orbitals renormalization group(NORG) method. We find that, in the framework of natural orbitals formalism, the Kondo screening mechanism becomes transparent and simple, while the intrinsic structure of a Kondo singlet is clearly resolved. For a single impurity Kondo system in whichever case of either finite size or thermodynamic limit, there exists a single active natural orbital that screens the magnetic impurity dominantly. In the perspective of entanglement, the magnetic impurity is entangled dominantly with the active natural orbital, i.e., the subsystem formed by the active natural orbital and the magnetic impurity basically disentangles from the remaining system. We have also studied the structures of the active natural orbital respectively projected into real space and momentum space. Moreover, the dynamical properties, represented by one-particle Green's functions defined at the active natural orbital, are obtained by the correction vector method. Meanwhile, the well-known Kondo resonance is clearly observed in the spectral function at the active natural orbital. To realize the thermodynamic limit, the Wilson chains with the numerical renormalization group approach are employed.     

Kondo effect in a magnetic field and the magnetoresistivity of kondo alloys

The effect of a magnetic field on the spectral density of a S = 1/2 Kondo impurity is investigated at zero and finite temperatures by using Wilson's numerical renormalization group method. A splitting of the total spectral density is found for fields larger than a critical value H(c)(T = 0) approximately 0.5T(K), where T(K) is the Kondo scale. The splitting correlates with a peak in the magnetoresistivity of dilute magnetic alloys which we calculate and compare with the experiments on CexLa1-xAl2,x = 0.0063. The linear magnetoconductance of quantum dots exhibiting the Kondo effect is also calculated.     

Kondo screening in gapless magnetic alloys

The low-energy physics of a spin- Kondo impurity in a gapless host, in which the density of band states ρ₀(ε)=|ε|^r/(|ε|^r+β^r) vanishes at the Fermi level ε=0, is studied by the Bethe ansatz. It is shown that the growth of the parameter Γ_r=βg^−1/r (where g is an exchange coupling constant) drives the ground state of the system from the Kondo regime with a screened impurity spin to the Anderson regime, where the impurity spin is unscreened. However, in a weak magnetic field H, the impurity spin exceeds its free value, , due to a strong coupling to a band.     

Characterizing a high spin magnetic impurity via Andreev reflection spectroscopy

The ground state properties of a high spin magnetic impurity and its interaction with an electronic spin are probed via Andreev reflection. We see that through the charge and spin conductance one can effectively estimate the interaction strength, the ground state spin and magnetic moment of any high spin magnetic impurity. We show how a high spin magnetic impurity at the junction between a normal metal and superconductor can contribute to superconducting spintronics applications. Particularly, while spin conductance is absent below the gap for Ferromagnet-Insulator-Superconductor junctions we show that in the case of a Normal metal-High spin magnetic impurity-Normal Metal-Insulator-Superconductor (NMNIS) junction it is present. Further, it is seen that pure spin conduction can exist without any accompanying charge conduction in the NMNIS junction.     

Field induced magnetic ordering transition in Kondo insulators

We study the 2D Kondo insulators in a uniform magnetic field using quantum Monte Carlo simulations of the particle-hole symmetric Kondo lattice model and a mean field analysis of the Periodic Anderson model. We find that the field induces a transition to an insulating, antiferromagnetically ordered phase with staggered moment in the plane perpendicular to the field. For fields in excess of the quasi-particle gap, corresponding to a metal in a simple band picture of the periodic Anderson model, we find that the metallic phase is unstable towards the spin density wave type ordering for any finite value of the interaction strength. This can be understood as a consequence of the perfect nesting of the particle and hole Fermi surfaces that emerge as the field closes the gap. We propose a phase diagram and investigate the quasi-particle and charge excitations in the magnetic field. We find good agreement between the mean-field and quantum Monte Carlo results.Received: 17 December 2003, Published online: 8 June 2004PACS: 71.27. + a Strongly correlated electron systems; heavy fermions - 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 71.30. + h Metal-insulator transitions and other electronic transitions - 75.30.Mb Valence fluctuation, Kondo lattice, and heavy-fermion phenomena - 75.30.Fv Spin-density waves     

Screening of magnetic moments in PuAm alloy: local density approximation and dynamical mean field theory study

The puzzling absence of Pu magnetic moments in a PuAm environment is explored using the self-consistent dynamical mean field theory calculations in combination with the local density approximation. We argue that delta-Pu-Am alloys provide an ideal testbed for investigating the screening of moments from the single impurity limit to the dense limit. Several important effects can be studied: volume expansion, shift of the bare Pu on-site f energy level, and the reduction of the hybridization cloud resulting from the collective character of the Kondo effect in the Anderson lattice. These effects compensate each other and result in a coherence scale, which is independent of alloy composition, and is around 800 K.     

Spin correlations and finite-size effects in the one-dimensional kondo box

We analyze the Kondo effect of a magnetic impurity attached to an ultrasmall metallic wire using the density matrix renormalization group. The spatial spin correlation function and the impurity spectral density are computed for system sizes of up to L=511 sites, covering the crossover from Ll{K}, with l{K} the spin screening length. We establish a proportionality between the weight of the Kondo resonance and l{K} as a function of L. This suggests a spectroscopic way of detecting the Kondo cloud.     

Theory of inelastic scattering from magnetic impurities

We use the numerical renormalization group method to calculate the single-particle matrix elements T of the many-body T matrix of the conduction electrons scattered by a magnetic impurity at T=0 temperature. Since T determines both the total and the elastic, spin-diagonal scattering cross sections, we are able to compute the full energy, spin, and magnetic field dependence of the inelastic scattering cross section sigma(inel)(omega). We find an almost linear frequency dependence of sigma(inel)(omega) below the Kondo temperature T(K), which crosses over to a omega(2) behavior only at extremely low energies. Our method can be generalized to other quantum impurity models.     

Exotic Kondo effects in metals: Magnetic ions in a crystalline electric field and tunnelling centres

The ordinary single-channel Kondo model consists of one or more spin-½ local moments interacting antiferromagnetically with conduction electrons in a metal. This model has provided a paradigm for understanding many phenomena of strongly correlated electronic materials, ranging from the formation of heavyfermion Fermi liquids to the mapping of a one-band model in the cuprate superconductors. The simplest extension of this ordinary Kondo model in metals which yields exotic non-Fermi-liquid physics is the multichannel Kondo impurity model in which the conduction electrons are given an extra quantum label known as the channel or flavour index. In the overcompensated regime of this model, nonFermi-liquid physics is possible, in contrast with the single-channel model. We overview here the multichannel Kondo impurity model candidates most extensively studied for explaining real materials, specifically the two-level system Kondo model relevant for metallic glasses, nanoscale devices and some doped semiconductors, and the quadrupolar and magnetic two-channel Kondo models developed for rare-earth and actinide ions with crystal-field splittings in metals. We provide an extensive justification for the derivation of the theoretical models, noting that, whenever the local impurity degree of freedom is non-magnetic, a two-channel Kondo model must follow by virtue of the magnetic spin degeneracy of the conduction electrons. We carefully delineate all energy and symmetry restrictions on the applicability of these models. We describe the various methods used to study these models along with their results and limitations (multiplicative renormalization group, numerical renormalization group, non-crossing approximation, conformal field theory and Abelian bosonization), all of which provide differing and useful views of the physics. We pay particular attention to the role that scale invariance plays in all these theoretical approaches. We point out in each case how various perturbing fields (magnetic, crystalline electric, electric field gradients and uniaxial stress) may destabilize the non-Fermi-liquid fixed point. We then provide an extensive discussion of the experimental evidence for the relevance of the two-level system Kondo model to metallic glasses and nanoscale devices, and of the quadrupolar and magnetic two-channel models to a number of heavyfermion-based alloys and compounds. We close with a discussion of the extension of the single-impurity models which comprise the main focus of this review to other systems (Coulomb blockade), multiple impurities and lattice models. In the latter case, we provide an overview of the relevance of the two-channel Kondo lattice model to non-Fermi-liquid behaviour and exotic superconductivity in heavy-fermion compounds and to the theoretical possibility of odd-frequency superconductivity, which is realized (for the first time) in the limit of infinite spatial dimensions for this model.     

Finite-size effect and Kondo screening effect in an A-B ring with a quantum dot

The properties of the ground state of a closed dot－ring system with a magnetic flux in the Kondo regime are studied theoretically by means of a one-impurity Anderson Hamiltonian. The Hamiltonian is solved by means of the slave-boson mean-field theory. It is shown that at T=0, a suppressed Kondo effect exists in this system even when the mean level spacing of electrons in the ring is larger than the bulk Kondo temperature. The physical quantities depend sensitively on both the parity of the system and the size of the ring; the rich physical behaviour can be attributed to the coexistence of both the finite-size effect and the Kondo screening effect. It is also possible to detect the Kondo screening cloud by measuring the persistent current or the zero field impurity susceptibility χ_{imp} directly in future experiments.     

Density of states in the magnetic ground state of the Friedel-Anderson impurity

By applying a magnetic field whose Zeeman energy exceeds the Kondo energy by an order of magnitude the ground state of the Friedel-Anderson impurity is a magnetic state. In recent years the author introduced the FAIR (Friedel Artificially Inserted Resonance) method to investigate the impurity properties. Within this FAIR approach the full excitation spectrum and the composition of the excitations is calculated and numerically evaluated. From the excitation spectrum the electron density of states is calculated. Majority and minority d-resonances are obtained. The width of the resonances is about twice as wide as the mean field theory predicts. This broadening reduces the height of the resonance curve and therefore the density of states by a factor of two. This yields an intuitive understanding for a previous result of the FAIR approach that it requires a much larger Coulomb interaction for the formation of a magnetic moment than the mean field theory.     

Spin correlation in dilute magnetic alloys

The correlation of a magnetic impurity spin with the spin density of the conduction electrons in a dilute magnetic alloy is calculated non-perturbationally on the basis of the Nagaoka theory. It is shown that there are anomalies due to the Kondo effect in the long range behaviour of this correlation which contradicts the bound state interpretation of the Kondo effect. The most interesting detail is the appearance of a non-oscillating contribution to the correlation.