Magnetic Impurities In Metals Research Articles

Inhomogeneous Kondo destruction by RKKY correlations

The competition between the indirect exchange interaction (IEC) of magnetic impurities in metals and the Kondo effect gives rise to a rich quantum phase diagram, the Doniach Diagram (Doniach, 1977). A Kondo screened phase is separated from a spin ordered phase when the local exchange coupling J and the concentration of magnetic moments nM are varied. In disordered metals, both the Kondo temperature and the IEC are widely distributed due to the scattering of the conduction electrons from the impurity potential. Therefore, it is a question of fundamental importance, how this Doniach diagram is modified by the disorder, and if one can still identify separate phases. Recently, Nejati et al. (2017) investigated the effect of Ruderman–Kittel–Kasuya–Yosida (RKKY) correlations on the Kondo effect of two magnetic impurities, renormalizing the Kondo interaction based on the Bethe–Salpeter equation and performing the poor men’s renormalization group (RG) analysis with the RKKY-renormalized Kondo coupling. In the present study, we extend this theoretical framework, allowing for different Kondo temperatures of two RKKY-coupled magnetic impurities due to different local exchange couplings and density of states. As a result, we find that the smaller one of the two Kondo temperatures is suppressed more strongly by the RKKY interaction, thereby enhancing their initial inequality. In order to find out if this relevance of inequalities between Kondo temperatures modifies the distribution of the Kondo temperature in a system of a finite density of randomly distributed magnetic impurities, we present an extension of the RKKY coupled Kondo RG equations. We discuss the implication of these results for the interplay between Kondo coupling and RKKY interaction in disordered electron systems and the Doniach diagram in disordered electron systems.

Thermodynamic perturbation theory for noninteracting quantum particles with application to spin-spin interactions in solids

The determination of the Landau free energy (the grand thermodynamic potential) by a perturbation theory is advanced to arbitrary order for the specific case of non-interacting fermionic systems perturbed by a one-particle potential. Peculiar features of the formalism are highlighted, and its applicability for bosons is indicated. The results are employed to develop a more explicit approach describing exchange interactions between spins of Anderson's magnetic impurities in metals, semiconductors, and insulators. Within the fourth order our theory provides on the equal footing formulae for the Ruderman-Kittel-Kasuya-Yosida, Bloembergen-Rowland, superexchange, and two-electron exchange integrals at non-zero temperature.

Observation of ferromagnetism in black phosphorus nanosheets with high magnetization by liquid exfoliation

The Black Phosphorus (BP) nanosheets were prepared by liquid ultrasonic exfoliating the grinded layered BP bulk in organic solutions under protecting atmosphere. The samples were characterized by X-ray diffraction (XRD), Raman spectroscopy, X-ray photoelectron spectroscopy (XPS), scanning electron microscopy (SEM), transmission electron microscopy (TEM), as well as selective electron diffraction (SED). The possible magnetic (Fe, Co, Ni) impurities in the BP material were analyzed by an inductively coupled plasma-atomic emission spectrometry (ICP-AES). Magnetization measurements were performed using a vibrating sample magnetometer (VSM, Quantum Design PPMS-9T). The results indicate that the BP nanosheets sample has a weak ferromagnetic ordering with high magnetization 1.83 emu/g at room temperature. Analysis states the ferromagnetism is intrinsic to the BP samples, ruling out extrinsic ferromagnetism arising from magnetic metal impurities. The combination effects of magnetic moments resulting from defects or vacancies, the formation of edge states and the p orbital spin polarization of the oxygen and phosphorus atoms of the surface PO bonds contribute to the observed ferromagnetism in BP nanosheets sample. The conversion of ferromagnetism of 2D material BP at room temperature will be of great implication for spintronics application in the future.

Decomposing the Bragg glass and the peak effect in a Type-II superconductor

Adding impurities or defects destroys crystalline order. Occasionally, however, extraordinary behaviour emerges that cannot be explained by perturbing the ordered state. One example is the Kondo effect, where magnetic impurities in metals drastically alter the temperature dependence of resistivity. In Type-II superconductors, disorder generally works to pin vortices, giving zero resistivity below a critical current jc. However, peaks have been observed in the temperature and field dependences of jc. This peak effect is difficult to explain in terms of an ordered Abrikosov vortex lattice. Here we test the widespread paradigm that an order-disorder transition of the vortex ensemble drives the peak effect. Using neutron scattering to probe the vortex order in superconducting vanadium, we uncover an order-disorder transition from a quasi-long-range-ordered phase to a vortex glass. The peak effect, however, is found to lie at higher fields and temperatures, in a region where thermal fluctuations of individual vortices become significant.

Kondo-like behavior and GMR effect in granular Cu90Co10 microwires

We observed a significant increase of the giant magnetoresistance (GMR) effect (up to 32% after the adequate annealing) and Kondo-like behavior in Cu90Co10 glass-coated microwires. Observed enhancement of the GMR effect can be interpreted considering the formation of the fine Co grains inside the Cu matrix as well as appearance of lamellar nanostructures allowing enhancement of the MR effect after annealing. Observed experimental data are discussed considering the regions with higher Co-ions content responsible for the presence of Co inhomogeneities or clusters and the regions with lower Co-ions content behaving as the magnetic impurities in the metallic host. Observed resistivity minimum on temperature dependence can be described considering Kondo effect mechanism involving magnetic impurities in metals. But the other mechanisms responsible for the resistivity minimum have been considered.

Role of Dzyaloshinskii-Moriya interaction for magnetism in transition-metal chains at Pt step edges

We explore the emergence of chiral magnetism in one-dimensional monatomic Mn, Fe, and Co chains deposited at the Pt(664) step-edge carrying out an ab-initio study based on density functional theory (DFT). The results are analyzed employing several models: (i) a micromagnetic model, which takes into account the Dzyaloshinskii-Moriya interaction (DMI) besides the spin stiffness and the magnetic anisotropy energy, and (ii) the Fert-Levy model of the DMI for diluted magnetic impurities in metals. Due to the step-edge geometry, the direction of the Dzyaloshinskii vector (D-vector) is not predetermined by symmetry and points in an off-symmetry direction. For the Mn chain we predict a long-period cycloidal spin-spiral ground state of unique rotational sense on top of an otherwise atomic-scale antiferromagnetic phase. The spins rotate in a plane that is tilted relative to the Pt surface by $62^\circ$ towards the upper step of the surface. The Fe and Co chains show a ferromagnetic ground state since the DMI is too weak to overcome their respective magnetic anisotropy barriers. Beyond the discussion of the monatomic chains we provide general expressions relating ab-initio results to realistic model parameters that occur in a spin-lattice or in a micromagnetic model. We prove that a planar homogeneous spiral of classical spins with a given wave vector rotating in a plane whose normal is parallel to the D-vector is an exact stationary state solution of a spin-lattice model for a periodic solid that includes Heisenberg exchange and DMI. The validity of the Fert-Levy model for the evaluation of micromagnetic DMI parameters and for the analysis of ab-initio calculations is explored for chains. The results suggest that some care has to be taken when applying the model to infinite periodic one-dimensional systems.

The beauty of impurities: Two revivals of Friedel's virtual bound-state concept

Abstract Jacques Friedel pioneered the theoretical study of impurities and magnetic impurities in metals. He discovered Friedel oscillations, introduced the concept of virtual bound-state, and demonstrated that the charge on the impurity is related to the scattering phase-shift at the Fermi level (Friedel sum-rule). After a brief review of some of these concepts, I describe how they proved useful in two new contexts. The first one concerns the Coulomb blockade in quantum dots, and its suppression by the Kondo effect. The second one is the dynamical mean-field theory of strong electronic correlations.

Generalized Wilson chain for solving multichannel quantum impurity problems

The numerical renormalization group is used to solve quantum impurity problems, which describe magnetic impurities in metals, nanodevices, and correlated materials within dynamical mean field theory. Here we present a simple generalization of the Wilson chain, which improves the scaling of computational cost with the number of conduction bands, bringing more complex problems within reach. The method is applied to calculate the $t$ matrix of the three-channel Kondo model at $T=0$, which shows universal crossovers near non-Fermi-liquid critical points. A nonintegrable three-impurity problem with three bands is also studied, revealing a rich phase diagram and novel screening and overscreening mechanisms.

Resistance minimum and heavy fermions.

The phenomenon of the resistance minimum in dilute magnetic alloys is explained in terms of the s-d interaction which takes account of scattering of the conduction electron off the magnetic impurities in metals. Some of the intermetallic compounds which involve rare earth elements or uranium show a very large electronic specific heat and remain non-magnetic even though they show a Curie-like susceptibility at higher temperatures. These phenomena are also explained based on the s-d interaction model.

Effect of Lattice Vibrations on DOS and Spectral Function in Auger and Tunneling Processes

For the theoretical investigation of the effect of electron-phonon interaction on Auger and tunneling processes, we considered the Anderson-like Hamiltonian, which was developed by P.W. Anderson (1951-1961) to address one of the most challenging problems of 20 th century physics. With suitable modifications, the powerful theoretical machinery which was invented to explain magnetic impurities in metals, could be used to predict the mixing of adsorbate electron on a metal surface. This Hamiltonian can be solved by equation of motion method of Zubarev's double time Green function of the adatoms self energy and DOS (Density of States) can be estimated. It was shown that the 4 th order of the self energy contains the Auger process and can, therefore, contribute to the tunneling process. To calculate these from 1 st principle, we investigated the effect of lattice vibrations following the Anderson model and found that both DOS and spectral function are modified with subsequent modification in the concerned surface parameters.

Aharonov-Bohm Effect as a Probe of Interaction between Magnetic Impurities

We study the effects of the RKKY interaction between magnetic impurities on the mesoscopic conductance fluctuations of a metal ring with dilute magnetic impurities. At sufficiently low temperatures and strong magnetic fields, the loss of electron coherence occurs mainly due to the scattering off rare pairs of strongly coupled magnetic impurities. We establish a relation between the dephasing rate and the distribution function of the exchange interaction within such pairs. In the case of the RKKY exchange interaction, this rate exhibits 1/B(2) behavior in strong magnetic fields. We demonstrate that the Aharonov-Bohm conductance oscillations may be used as a probe of the distribution function of the exchange interaction between magnetic impurities in metals.

Influence of superconductivity on a positronium in void

The interaction of the positronium formed in void with the conduction band electrons in normal and superconducting states are considered. In the applied model this interaction arises a result of the transformations Ps ↔ e + + e − . Mathematical treatment of such interaction is made in the present Letter on the basis of the known Anderson model for the magnetic impurity in metal. The influence of the superconducting state on the mean occupancy number n Ps of the positronium level is considered. It is shown that as the superconducting state arises with the gap 2 Δ being different from zero at T = T c , the step-like decrease of n Ps takes place. This conclusion is used to interpret the experimentally observed effect of the step-like decrease the lifetime of positrons trapped by voids at the superconducting transition of HTSC.

From Kondo Effect to Fermi Liquid

The Kondo effect has been playing an important role in strongly correlated electon systems. The important point is that the magnetic impurity in metals is a typical example of the Fermi liquid. In the system the local spin is conserved in the ground state and continuity with respect to Coulomb repulsion $U$ is satisfied. This nature is satisfied also in the periodic systems as far as the systems remain as the Fermi liquid. This property of the Fermi liquid is essential to understand the cuprate high-Tc superconductors (HTSC). On the basis of the Fermi liquid theory we develop the transport theory such as the resistivity and the Hall coefficient in strongly correlated electron systems, such as HTSC, organic metals and heavy Fermion systems. The significant role of the vertex corrections for total charge- and heat-currents on the transport phenomena is explained. By taking the effect of the current vertex corrections into account, various typical non-Fermi-liquid-like transport phenomena in systems with strong magnetic and/or superconducting flucutations are explained within the Fermi liquid theory.

Tunable nonlocal spin control in a coupled-quantum dot system.

The effective interaction between magnetic impurities in metals that can lead to various magnetic ground states often competes with a tendency for electrons near impurities to screen the local moment (known as the Kondo effect). The simplest system exhibiting the richness of this competition, the two-impurity Kondo system, was realized experimentally in the form of two quantum dots coupled through an open conducting region. We demonstrate nonlocal spin control by suppressing and splitting Kondo resonances in one quantum dot by changing the electron number and coupling of the other dot. The results suggest an approach to nonlocal spin control that may be relevant to quantum information processing.

Spin fluctuation theory for the insulating ground state ofYbB12

It is proposed that the insulating ground state of the compound ${\mathrm{YbB}}_{12}$ originates from a localized superposition of ${f}^{14}$ and ${f}^{13}{d}^{1}$ configurations of Yb in a singlet spin state. The theory is formally similar to the well-known spin-fluctuation mechanism for magnetic impurities in metals. It explains both the insulating ground state and the band of dispersive excited states recently observed by neutron scattering. By making a few reasonable approximations for finite temperatures and spin-orbit coupling effects, we obtain a phenomenological model for the bulk properties that explains the temperature dependence of the specific heat, the susceptibility, and the inelastic neutron scattering line shape for powder samples.

Kondo physics in carbon nanotubes.

The connection of electrical leads to wire-like molecules is a logical step in the development of molecular electronics, but also allows studies of fundamental physics. For example, metallic carbon nanotubes are quantum wires that have been found to act as one-dimensional quantum dots, Luttinger liquids, proximity-induced superconductors and ballistic and diffusive one-dimensional metals. Here we report that electrically contacted single-walled carbon nanotubes can serve as powerful probes of Kondo physics, demonstrating the universality of the Kondo effect. Arising in the prototypical case from the interaction between a localized impurity magnetic moment and delocalized electrons in a metallic host, the Kondo effect has been used to explain enhanced low-temperature scattering from magnetic impurities in metals, and also occurs in transport through semiconductor quantum dots. The far greater tunability of dots (in our case, nanotubes) compared with atomic impurities renders new classes of Kondo-like effects accessible. Our nanotube devices differ from previous systems in which Kondo effects have been observed, in that they are one-dimensional quantum dots with three-dimensional metal (gold) reservoirs. This allows us to observe Kondo resonances for very large electron numbers (N) in the dot, and approaching the unitary limit (where the transmission reaches its maximum possible value). Moreover, we detect a previously unobserved Kondo effect, occurring for even values of N in a magnetic field.

Quantum Dots as Tunable Kondo Impurities

Advances in mesoscopic physics are enabling fundamental properties of solids to be studied at an unprecedented level of detail. In his Perspective, von Delft highlights the study by van der Wiel et al., who have demonstrated almost complete screening of the local spin of a quantum dot. This behavior mirrors the well-known Kondo effect for magnetic impurities in metals. Because they are tunable, quantum dots allow detailed tests of models for the Kondo effect, but experiments are ahead of theory at this time.

Asymmetric Nonlinear Differential Resistance of Mesoscopic AuFe Spin-Glass Wires.

The placement of a transition metal impurity in a noble metal host induces a collective response in the electron gas which attempts to screen the magnetic moment of the impurity. At low impurity concentration, enhanced scattering of electrons from the screened impurity leads to a characteristic logarithmic increase of the resistance with decreasing temperature, the well-known Kondo effect [1]. If the concentration of impurities is high, the interaction of the screening electrons around one impurity with those around other impurities leads to an effective impurity-impurity interaction, the RKKY (Ruderman-Kittel-Kasuya-Yosida) interaction [2]. At high temperatures, the thermal energy of the impurity spins is sufficient to overcome the RKKY interaction, and each individual spin is free to rotate independently. As the temperature is reduced, however, the impurity spins are increasingly fixed in random orientations by the RKKY interaction. The onset of this spin-glass order is signaled by a drop in the resistance of the host metal due to the reduced magnetic scattering of the conduction electrons. In combination with the Kondo effect at higher temperatures, this gives rise to a maximum in the resistance as a function of temperature which is characteristic of spin glasses [2]. Earlier work on magnetic impurities in metals concentrated on the properties of bulk materials; recently, with the opportunities presented by nanolithography, interest has focused on the properties of samples whose dimensions are comparable to relevant microscopic length scales. A number of such microscopic length scales have been proposed for both the Kondo effect [3] and spin glasses [4]. The hope is that measurements on mesoscopic samples would allow one to verify directly the existence of these microscopic length scales. However, the experimental evidence in both Kondo systems and spin glasses has so far been inconclusive. For example, measurements by some groups [5,6] of the Kondo effect in thin films, wires, and small point contacts defined by break junctions show a definite size dependence, but on vastly different length scales, while measurements by other groups [7] on AuFe wires found no size dependence on the Kondo effect. The situation is similar for samples in the spin-glass regime [8 ‐ 11]. Thus the issue of the existence of fundamental length scales in both the spin-glass and the Kondo regimes remains open. In this Letter, we report on measurements of the low temperature differential resistance RsId › dV ydI of AuFe wires as a function of dc current bias I .A s reported previously by other groups in measurements on CuCr wires [9] and point contact break-junction devices [10], we find that the shape of RsId reflects the behavior of the temperature dependent resistance RsT d, in that it has a maximum at a particular current Im. In addition, however, we find that RsId is asymmetric in I, even in zero magnetic field. The asymmetry is small at high temperatures, but grows by more than an order of magnitude as the temperature is lowered, indicating that it is associated with enhanced spin scattering at low temperatures. The degree of asymmetry is sample specific, being larger in some samples and smaller in other nominally identical samples. Furthermore, we find that the asymmetric component of RsId is sensitive to the particular configuration of contact leads used in a four terminal measurement. We also find that the asymmetry depends on the size of the wire, being generally larger for shorter and narrower wires and disappearing entirely for very long samples. These observations are indicative of the mesoscopic nature of this phenomenon. The samples in this experiment were patterned onto oxidized silicon substrates by conventional e-beam lithography techniques. After thermal deposition of 99.999% Au, the samples were implanted with Fe ions at energies and dosages calculated to give impurity concentrations of 0.2 and 0.4 at. % [12]. All samples of one concentration were fabricated and ion-implanted at the same time to ensure uniform film properties. The inset of Fig. 1(a) shows a schematic of one of the samples. The thickness of the films was 33 nm, and the sheet resistance Rh was ,1 V at 4.2 K after ion implantation. The samples were measured in 4 He and 3 He cryostats (for the 0.4 at. % samples),

Integrable model describing the behavior of magnetic impurities in metals.

We present an integrable impurity model describing the exchange and the correlated hybridized interactions between localized electronic states of an impurity and conduction electrons of a metal. The impurity magnetization, the Kondo limit, and the Fermi-liquid behavior at low temperatures are treated analytically on the basis of the Bethe ansatz solution.

Maximum-entropy approach to series extrapolation and analytic continuation

The authors use information theory (the principle of maximum entropy) to develop an approach to the problem of extrapolating power series. They suggest a well-defined way to map the extrapolation problem onto a moment problem, and show that the use of additional information about the function being extrapolated (such as asymptotic behaviour for large arguments) is important to obtaining accurate extrapolations. They apply the method to the virial expansion for the classical hard sphere equation of state, the quantum harmonic oscillator with octic perturbation and the symmetric Anderson model of relevance to magnetic impurities in metals. In each case the method yields excellent pointwise estimates of the function being extrapolated.