Spin Correlations and Finite-Size Effects in the One-Dimensional Kondo Box (original) (raw)
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The role of magnetic anisotropy in the Kondo effect
Nature Physics, 2008
In the Kondo effect, a localized magnetic moment is screened by forming a correlated electron system with the surrounding conduction electrons of a non-magnetic host 1 . Spin S = 1/2 Kondo systems have been investigated extensively in theory and experiments, but magnetic atoms often have a larger spin 2 . Larger spins are subject to the influence of magnetocrystalline anisotropy, which describes the dependence of the magnetic moment's energy on the orientation of the spin relative to its surrounding atomic environment 3,4 . Here we demonstrate the decisive role of magnetic anisotropy in the physics of Kondo screening. A scanning tunnelling microscope is used to simultaneously determine the magnitude of the spin, the magnetic anisotropy and the Kondo properties of individual magnetic atoms on a surface. We find that a Kondo resonance emerges for large-spin atoms only when the magnetic anisotropy creates degenerate ground-state levels that are connected by the spin flip of a screening electron. The magnetic anisotropy also determines how the Kondo resonance evolves in a magnetic field: the resonance peak splits at rates that are strongly direction dependent. These rates are well described by the energies of the underlying unscreened spin states.
Physical Review B, 2015
We analyze the spatial correlation structure of the spin density of an electron gas in the vicinity of an antiferromagnetically-coupled Kondo impurity. Our analysis extends to the regime of spinanisotropic couplings, where there are no quantitative results for spatial correlations in the literature. We use an original and numerically exact method, based on a systematic coherent-state expansion of the ground state of the underlying spin-boson Hamiltonian. It has not yet been applied to the computation of observables that are specific to the fermionic Kondo model. We also present an important technical improvement to the method, that obviates the need to discretize modes of the Fermi sea, and allows one to tackle the problem in the thermodynamic limit. As a result, one can obtain excellent spatial resolution over arbitrary length scales, for a relatively low computational cost, a feature that gives the method an advantage over popular techniques such as the Numerical and Density-Matrix Renormalization Groups. We find that the anisotropic Kondo model shows rich universal scaling behavior in the spatial structure of the entanglement cloud. First, SU(2) spinsymmetry is dynamically restored in a finite domain in parameter space in vicinity of the isotropic line, as expected from poor man's scaling. More surprisingly, we are able to obtain in closed analytical form a set of different, yet universal, scaling curves for strong exchange asymmetry, which are parametrized by the longitudinal exchange coupling. Deep inside the cloud, i.e. for distances smaller than the Kondo length, the correlation between the electron spin density and the impurity spin oscillates between ferromagnetic and antiferromagnetic values at the scale of the Fermi wavelength, an effect that is drastically enhanced at strongly anisotropic couplings. Our results also provide further numerical checks and alternative analytical approximations for the Kondo overlaps that were recently computed by Lukyanov, Saleur, Jacobsen, and Vasseur [Phys. Rev. Lett. 114, 080601 (2015)] .
Physical Review B, 2009
A magnetic moment in a metal or in a quantum dot is, at low temperatures, screened by the conduction electrons through the mechanism of the Kondo effect. This gives rise to spin-spin correlations between the magnetic moment and the conduction electrons, which can have a substantial spatial extension. We study this phenomenon, the so-called Kondo cloud, by means of the density matrix renormalization group method for the case of the single-impurity Anderson model. We focus on the question whether the Kondo screening length, typically assumed to be proportional to the inverse Kondo temperature, can be extracted from the spin-spin correlations. For several mechanisms-the gate potential and a magnetic field-which destroy the Kondo effect, we investigate the behavior of the screening cloud induced by these perturbations.
Kondo Effect in the Presence of Magnetic Impurities
Physical Review Letters, 2006
We measure transport through gold grain quantum dots fabricated using electromigration, with magnetic impurities in the leads. A Kondo interaction is observed between dot and leads, but the presence of magnetic impurities results in a gate-dependent zero-bias conductance peak that is split due to a RKKY interaction between the spin of the dot and the static spins of the impurities. A magnetic field restores the single Kondo peak in the case of an antiferromagnetic RKKY interaction. This system provides a new platform to study Kondo and RKKY interactions in metals at the level of a single spin.
Entanglement Probe of Two-Impurity Kondo Physics in a Spin Chain
Physical Review Letters, 2012
We propose that real-space properties of the two-impurity Kondo model can be obtained from an effective spin model where two single-impurity Kondo spin chains are joined via an RKKY interaction between the two impurity spins. We then use a DMRG approach, valid in all ranges of parameters, to study its features using two complementary quantum-entanglement measures, the negativity and the von Neumann entropy. This non-perturbative approach enables us to uncover the precise dependence of the spatial extent ξK of the Kondo screening cloud with the Kondo and RKKY couplings. Our results reveal an exponential suppression of the Kondo temperature TK ∼ 1/ξK with the size of the effective impurity spin in the limit of large ferromagnetic RKKY coupling, a striking display of "Kondo resonance narrowing" in the two-impurity Kondo model. We also show how the antiferromagnetic RKKY interaction produces an effective decoupling of the impurities from the bulk already for intermediate strengths of this interaction, and, furthermore, exhibit how the non-Fermi liquid quantum critical point is signaled in the quantum entanglement between various parts of the system.
Ferromagnetic Kondo Effect at Nanocontacts
2009
Magnetic impurities bridging nanocontacts and break junctions of nearly magnetic metals may lead to permanent moments, analogous to the giant moments well known in the bulk case. A numerical renormalization group (NRG) study shows that, contrary to mean field based expectations, a permanent moment never arises within an Anderson model, which invariably leads to strong Kondo screening. By including in the model an additional ferromagnetic exchange coupling between leads and impurity, the NRG may instead stabilize a permanent moment through a ferromagnetic Kondo effect. The resulting state is a rotationally invariant spin, which differs profoundly from mean field. A sign inversion of the zero-bias anomaly and other spectroscopic signatures of the switch from regular to ferromagnetic Kondo are outlined.
The Kondo effect in the presence of magnetic impurities
2006
We measure transport through gold grain quantum dots fabricated using electromigration, with magnetic impurities in the leads. A Kondo interaction is observed between dot and leads, but the presence of magnetic impurities results in a gate-dependent zero-bias conductance peak that is split due to an RKKY interaction (I) between the spin of the dot and the static spins of the impurities. Both ferromagnetic and anti- ferromagnetic interactions have been observed in different samples. A magnetic field restores the single Kondo peak in the case of an anti-ferromagnetic RKKY interaction, whereas the splitting is enhanced in the case of ferromagnetic interaction. A gate electrode can change the relative interaction strength TK/I. This system provides a new platform to study Kondo and RKKY interactions in metals at the level of a single spin.
Numerical analysis of the spatial range of the Kondo effect
Physical Review B, 2010
The spatial length of the Kondo screening is still a controversial issue related to Kondo physics. While renormalization group and Bethe Anzats solutions have provided detailed information about the thermodynamics of magnetic impurities, they are insufficient to study the effect on the surrounding electrons, i.e., the spatial range of the correlations created by the Kondo effect between the localized magnetic moment and the conduction electrons. The objective of this work is to present a quantitative way of measuring the extension of these correlations by studying their effect directly on the local density of states (LDOS) at arbitrary distances from the impurity. The numerical techniques used, the Embedded Cluster Approximation, the Finite U Slave Bosons, and Numerical Renormalization Group, calculate the Green functions in real space. With this information, one can calculate how the local density of states away from the impurity is modified by its presence, below and above the Kondo temperature, and then estimate the range of the disturbances in the non-interacting Fermi sea due to the Kondo effect, and how it changes with the Kondo temperature TK. The results obtained agree with results obtained through spin-spin correlations, showing that the LDOS captures the phenomenology of the Kondo cloud as well. To the best of our knowledge, it is the first time that the LDOS is used to estimate the extension of the Kondo cloud.
Physical Review Letters, 2004
We investigate the effects of spin-polarized leads on the Kondo physics of a quantum dot using the numerical renormalization group method. Our study demonstrates in an unambiguous way that the Kondo effect is not necessarily suppressed by the lead polarization: While the Kondo effect is quenched for the asymmetric Anderson model, it survives even for finite polarizations in the regime where charge fluctuations are negligible. We propose the linear tunneling magnetoresistance as an experimental signature of these behaviors. We also report on the influence of spin-flip processes. PACS numbers: 72.15.Qm, 72.25.Mk, 73.63.Kv Introduction.-Magnetic impurities embedded in metallic hosts cause anomalous resonant scattering of conduction band electrons. At the same time, the localized magnetic moments are screened at low temperature by the itinerant electron spins. This is the celebrated Kondo effect [1], which has been recently revived in mesoscopic physics . Ever since the theoretical predictions and the experimental demonstrations [5], the Kondo effect in phase-coherent systems such as quantum dots (QD's) has stimulated great interest in this field. The remarkable success behind this is the fine tunability of the parameter space (impurity level and hybridization couplings). The controlled manipulation in mesoscopic systems has not only allowed to test various aspects of the Kondo effect, which is a hard task in bulk solids, but also has posed further exciting questions. For example, when the spin-degeneracy of the impurity level is lifted by an external magnetic field, the Kondo peak in the density of states (DOS) of the dot is expected to split [6]. However, new experiments [7] and theoretical studies suggest that the situation is more subtle.
Electron spin resonance in Kondo systems
Physical Review B, 2008
We calculate the dynamical spin response of Kondo impurity and Kondo lattice systems within a semiphenomenological Fermi liquid description, at low temperatures T < TK , the Kondo temperature, and low magnetic fields B ≪ kBTK /gµB. Fermi liquid parameters are determined by comparison (i) with microscopic theory (numerical renormalization group) for the impurity model and (ii) with experiment for the lattice model. We find in the impurity case that the true impurity spin resonance has a width of the order of TK and disappears altogether if the g-factors of impurity spin and conduction electron spin are equal. However, there is an impurity-induced resonance contribution at the conduction electron resonance. The latter is broadened by spin lattice relaxation and is usually unobservable. In contrast, for the Anderson lattice in the Kondo regime we find a sharp ESR resonance line only slightly shifted from the local resonance and broadened by spin lattice relaxation, the latter significantly reduced by both the effects of heavy fermion physics and ferromagnetic fluctuations. We conjecture that our findings explain the sharp ESR-lines recently observed in several heavy fermion compounds.