Single Magnetic Impurity Research Articles

A local view of the Kondo effect: Scanning tunneling spectroscopy

The fascinating many-body physics involved in the interaction of a single magnetic impurity with the conduction electrons of its nonmagnetic metallic host is reflected in unconventional phenomena in magnetism, transport properties and the specific heat. Characteristic low-energy excitations, termed the Kondo resonance, are generally believed to be responsible for this striking behaviour. However, in spite of an intense research for over more than 30 years, a direct spectroscopic observation of the Kondo resonance on individual magnetic adatoms withstood experimental efforts hitherto. The development of low-temperature scanning tunneling microscopes (STM) operating under ultrahigh vacuum (UHV) conditions has provided new opportunities for investigating locally the electronic structure at surfaces. At low temperatures, due to the reduced broadening of the Fermi level of the STM tip and the sample, rather high energy resolution (≤ 1 meV) in scanning tunneling spectroscopy (STS) is achievable. Moreover, the absence of diffusion together with the spatial resolution of the STM enables detailed studies of electronic states on and near single adsorbed atoms and other nanoscale structures. Recently, for the first time, two such STS/STM experiments spatially resolved the electronic properties of individual magnetic adatoms displaying the Kondo effect. In particular, the observed Fano lineshape of the Kondo resonance reveals unambiguously the details of the quantum mechanical interference between the localized orbital and the conduction electrons on an atomic length scale [1,2]. This achievement of the detection of individual magnetic atoms with atomic resolution opens new perspectives for probing magnetic nanostructures.

Kondo Box: A Magnetic Impurity in an Ultrasmall Metallic Grain

We study the Kondo effect generated by a single magnetic impurity embedded in an ultrasmall metallic grain, to be called a ``Kondo box''. We find that the Kondo resonance is strongly affected when the mean level spacing in the grain becomes larger than the Kondo temperature, in a way that depends on the parity of the number of electrons on the grain. We show that the single-electron tunneling conductance through such a grain features Kondo-induced Fano-type resonances of measurable size, with an anomalous dependence on temperature and level spacing.

Scalar-potential effect in an integrable Kondo model

To study the impurity potential effect to the Kondo problem in a Luttinger liquid, we propose an integrable model of two interacting half-chains coupled with a single magnetic impurity ferromagnetically. It is shown that the scalar potential effectively reconciles the spin dynamics at low temperatures. Generally, there is a competition between the Kondo coupling $J$ and the impurity potential $V$. When the ferromagnetic Kondo coupling dominates over the impurity potential ($V<|SJ|$), the Furusaki-Nagaosa many-body singlet can be perfectly realized. However, when the impurity potential dominates over the Kondo coupling ($V\geq |SJ|$), the fixed point predicted by Furusaki and Nagaosa is unstable and the system must flow to a weak coupling fixed point. It is also found that the effective moment of the impurity measured from the susceptibility is considerably enlarged by the impurity potential. In addition, some quantum phase transitions driven by the impurity potential are found and the anomaly residual entropy is discussed.

Kondo Scattering Observed at a Single Magnetic Impurity

Electron scattering of isolated Ce adatoms on Ag(111) surfaces was studied with a low-temperature scanning tunneling microscope. Tunneling spectra obtained on and near Ce reveal a characteristic dip around the Fermi energy which is absent for nonmagnetic Ag adatoms. This feature is detected over a few atomic diameters around Ce atoms at the surface. The transition matrix element from the localized $f$ electron to the tunnel-current carrying continuum states bears a strong resemblance to discrete autoionized states. We interpret the dip spectrum as a Fano interference for the limit where the $f$ orbital has a very small matrix element.

Kondo Physics Seen in a Quantum Dot

A quantum dot, as its name implies, is a minuscule region of metallic or semiconductor material whose dimensions can be as small as a few tens of nanometers on a side. It has been likened to an artificial atom because it carries a discrete charge and quantized electronic energy levels (see the article by Marc Kastner in PHYSICS TODAY, January 1993, page 24). That analogy has now been taken a step further with the demonstration that a quantum dot interacts with nearby metallic leads in much the same way that a single magnetic impurity interacts with a surrounding metallic substance—in the phenomenon known as the Kondo effect.

Local Electronic Structure of a Single Magnetic Impurity in a Superconductor

The electronic structure near a single classical magnetic impurity in a superconductor is determined using a fully self-consistent Koster-Slater algorithm. Localized excited states are found within the energy gap which are half electron and half hole. Within a jellium model we find the new result that the spatial structure of the positive-frequency (electron-like) spectral weight (or local density of states), can differ strongly from that of the negative frequency (hole-like) spectral weight. The effect of the impurity on the continuum states above the energy gap is calculated with good spectral resolution for the first time. This is also the first three-dimensional self-consistent calculation for a strong magnetic impurity potential.

Spin dynamics studies of single Fe and Ni impurity in bcc iron (abstract)

Spin dynamics based on a quasiclassical approximation1 is used to study a single Fe or Ni magnetic impurity in ferromagnetic bcc iron. The optimization of the magnetic structure of the impurity includes quantum effects such as spatial spin inhomogeneity and different orbital contributions. The Pauli equation for noncollinear magnetic configuration is solved for each impurity. When rotated from ferromagnetic ordering, Fe and Ni impurities show different behavior. The Fe moment remains almost unchanged through a rotation of 0.6π radians and drops to zero when the rotation is increased to 0.72π radians. This behavior is primarily due to the interplay of more localized eg states and itinerant t2g states. On the other hand, the Ni moment drops continuously with rotation, going to zero at 0.5π radians. The different degrees of localization of Ni and Fe moments are analyzed in terms of different spatial anisotropy of magnetization density. The inhomogeneous spin space configurations are presented and analyzed using corresponding space dependent exchange integrals.

Strong-coupling limit of the Kondo problem.

We examine the low-temperature properties of a single magnetic impurity in a metal, for an arbitrary ratio of the Kondo coupling to the bandwidth, and arbitrary band filling, using the slave-boson technique. For sufficiently strong coupling, we find that true bound states of conduction electrons and the magnetic impurity appear. Then, the corrections to \ensuremath{\chi} and \ensuremath{\gamma} take small negative values. In the regime where the conduction band is nearly empty, we find a zero-temperature phase transition between a singlet binding phase and a free-local-moment phase.

Green-function theory for a single magnetic impurity near the surface of an antiferromagnet.

Green-function theory for a single magnetic impurity near the surface of an antiferromagnet.

Surface and bulk spin waves in antiferromagnetic perovskites and their interaction with defects near surfaces

The effect of a single magnetic impurity on the excitation spectrum of a semi-infinite Heisenberg antiferromagnet is studied by Green-function methods. The influence of bulk and surface spin waves on the impurity-mode energies is determined, and the theory is applied to perovskite-structure antiferromagnets.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Spin-wave theory of impurity states in a Heisenberg ferromagnet with planar anisotropy

The linear spin-wave theory of a single magnetic impurity in a Heisenberg ferromagnet with planar single-ion anisotropy is presented. The impurity-host exchange is assumed to be ferromagnetic or antiferromagnetic and the ground state of the host taken to be the classical aligned state. The calculation consists of deriving the double-time thermodynamic Green function from the corresponding equation of motion. From the poles of the Green functions the criteria for the impurity modes are obtained and calculations of their energies as functions of various perturbation parameters and for various values of the anisotropy given.

On the Theory of a Heisenberg Impurity Ferromagnet

AbstractUsing the resolvent method a complete solution of the Wolfram‐Callaway problem for a Heisenberg ferromagnet with a single magnetic impurity atom is obtained. The spectrum of the system is determined and the exact wave functions of the continuous and discrete spectra of the system with a unit spin deviation are found. The theorem of completeness for eigenfunctions is proved. The treatment is performed with reference to the example of an infinite crystal with a simple cubic lattice.

Electromagnetic penetration depth in superconductors with magnetic impurities

The electromagnetic penetration depth lambda in the local limit is calculated for superconductors containing magnetic impurities and having local excited states within the energy gap according to Shiba's theory. The penetration depth is presented as a function of the normal-state conductivity sigma/sub n/, the temperature T, the transition temperature T/sub c/ of the alloy and that T/sub c//sub 0/ of the pure host metal, and Shiba's parameter epsilon/sub 0/ (the normalized position in the energy gap of the excited state associated with a single magnetic-impurity atom).

Finite concentrations of localized moments in metals

In earlier work, density functional methods have been used to study the magnetism of pure metals and the problem of local moment formation on a single magnetic impurity. In the present paper these methods are reviewed and applied to the case of an arbitrary concentration of impurity atoms. It is shown that the Hartree-Fock treatment of the system and a local environment effect can be reproduced very easily in the density functional framework. More importantly, the present formulation allows one some insight into the effects of correlation. Although correlation density functionals are difficult to obtain, it is shown that a class of models of the many impurity system can be solved exactly.

The renormalization group: Critical phenomena and the Kondo problem

This review covers several topics involving renormalization group ideas. The solution of the $s$-wave Kondo Hamiltonian, describing a single magnetic impurity in a nonmagnetic metal, is explained in detail. See Secs. VII-IX. "Block spin" methods, applied to the two dimensional Ising model, are explained in Sec. VI. The first three sections give a relatively short review of basic renormalization group ideas, mainly in the context of critical phenomena. The relationship of the modern renormalization group to the older problems of divergences in statistical mechanics and field theory and field theoretic renormalization is discussed in Sec. IV. In Sec. V the special case of "marginal variables" is discussed in detail, along with the relationship of the modern renormalization group to its original formulation by Gell-Mann and Low and others.

Thermalization of a Magnetic Impurity in the IsotropicXYModel

We carry out an exact study of the relaxation of a single magnetic impurity embedded in a linear quantum chain. We obtain a rigorous result for the expectation value of any spin in the chain, and find that it relaxes to its equilibrium value as ${t}^{\ensuremath{-}1}$.

Interface Effects in Normal Metal Tunneling

In this paper, two model tunneling junctions are studied. In the first model, a single magnetic impurity is assumed to be present near a sharp metal-barrier interface. In the second, phonons with a single Einstein frequency are assumed to exist throughout one electrode and into the barrier region. The effect of the electron-spin (phonon) interaction on the conductance has been calculated. It is found that the zero-bias conductance anomaly produced by the magnetic impurity in model I is a sensitive function of the magnetic-impurity position, being of one sign in the barrier and oscillating in the electrode. In model II, we find, contrary to what had been believed that, when the phonons are strictly confined to the metal electrode and a local electron-phonon coupling is assumed, the conductance decreases at the phonon emission threshold. This decrease quickly becomes an increase, however, if the phonons are allowed to penetrate significantly into the barrier.

Influence of the interaction between conduction electrons at the impurity sites on the Kondo effect

Thes−d exchange model is generalized by taking into account (besides a spin independent potential scattering term) the interaction between the conduction electrons at the magnetic impurity sites, where it is most important. Employing the equation of motion approach in an approximation which is consistent with the factorization proposed by Nagoaka, thet-matrix for the scattering by a single magnetic impurity can be calculated at all temperatures. It turns out that it depends on the total spin at the impurity site, which (together with a trivial renormalization of the spin independent interaction) is determined self-consistently and which in general depends on temperature.

New Approach to the Theory of Itinerant Electron Ferromagnets with Local-Moment Characteristics

The understanding of ferromagnets, like iron, which exhibit localized moment behavior above the Curie point yet show itinerancy has long stood as a major theoretical problem. An account will be given of recent progress on this problem which was achieved through functional integral methods. This technique transforms the interacting electron system into an average over a system of noninteracting electrons moving in a Gaussian-weighted external ``magnetic'' field which acts only on the electronic spins. For a single magnetic impurity in a free electron metal, a single approximation allows one to go from Pauli paramagnetism to localized moment behavior in a smooth manner as the atomic exchange interaction is increased. The two impurity problem leads to an effective exchange coupling as in the Heisenberg model, which is antiferromagnetic for the nondegenerate orbital case studied here. Application of the technique to homogeneous systems leads to damped spin waves in the ferromagnet in lowest approximation.

Application of the Cluster Variation Method to thes−dInteraction Hamiltonian

Ground state energy for single magnetic impurity dissolved in nonmagnetic metal, applying cluster variation method to s-d interaction Hamiltonian