Impurity Magnetic Susceptibility Research Articles

Magnetic impurity in a triple-component semimetal

We investigate the effects of a magnetic impurity in a multiband touching fermion system, specifically, a triple-component semimetal with a flat band, which can be realized in a family of transition metal silicides (CoSi family). When the chemical potential coincides with the flat band, it is expected that the impurity response of this system will be very different from that of an ordinary Dirac or Weyl semimetal of which the density of states at the Fermi level vanishes. We first determine the phase diagram within the mean-field approximation. Then, we study the local moment regime by employing two different methods. In the low temperature regime, the Kondo screening is analyzed by the variational wavefunction approach and the impurity contributions to the magnetic susceptibility and heat capacity are obtained, while at higher temperature, we use the equation of motion approach to calculate the occupation number of the impurity site and the impurity magnetic susceptibility. The results are compared and contrasted with those in the usual Fermi liquid and the Dirac/Weyl semimetals.

The Impurity Magnetic Susceptibility of Semiconductors in the Case of Direct Exchange Interaction in the Ising Model

The numerical simulation was applied to study the temperature dependence of the impurity magnetic susceptibility. The direct exchange interaction of the impurity magnetic moments randomly distributed in space was considered within the Ising model. When the temperature in a system decreases, the magnetic susceptibility behavior in this system ceases to comply with the Curie law, which is associated with the formation of a spin glass phase. It is shown that the expression of the preexponential factor in the formula for the direct exchange interaction considerably influences the temperature dependence of the magnetic susceptibility only in the case of ferromagnetic exchange.

Примесная магнитная восприимчивость полупроводников в случае прямого обменного взаимодействия в модели Изинга

The dependence of the impurity magnetic susceptibility on temperature was studied by numerical simulation. The direct exchange interaction of magnetic moments of randomly distributed impurities was considered within the Ising model. The dependence of the magnetic susceptibility in such a system deviates from the Curie law at low temperature, which is associated with the formation of a spin glass phase. It is shown that the pre-exponential factor of the direct exchange interaction significantly influences on the temperature dependence of the magnetic susceptibility only in the case of ferromagnetic exchange.

One- and two-channel Kondo model with logarithmic Van Hove singularity: A numerical renormalization group solution

Simple scaling consideration and NRG solution of the one- and two-channel Kondo model in the presence of a logarithmic Van Hove singularity at the Fermi level is given. The temperature dependences of local and impurity magnetic susceptibility and impurity entropy are calculated. The low-temperature behavior of the impurity susceptibility and impurity entropy turns out to be non-universal in the Kondo sense and independent of the s–d coupling J. The resonant level model solution in the strong coupling regime confirms the NRG results. In the two-channel case the local susceptibility demonstrates a non-Fermi-liquid power-law behavior.

Determination of the Diamagnetic and Paramagnetic Impurity Magnetic Susceptibility in Ge:As near the Metal Insulator phase Transition

Low-temperature magnetic susceptibility of heavily doped Ge: As samples has been investigated by methods SQUID magnetometry and ESR spectroscopy near the metal-insulator phase transition. Paramagnetic component of the impurity magnetic susceptibility was investigated by ESR previously. Using both techniques make possible to determined the diamagnetic component of impurity susceptibility. The value of the impurity diamagnetic susceptibility equals to 5×10-8 cm3/g and corresponds to the localization radius of the As donor- electron near the metal-insulator phase transition.

Detection of impurity diamagnetic susceptibility and its behavior in n-Ge:As in the region of the insulator–metal phase transition

The method of superconducting quantum interference device (SQUID) magnetometry is used to measure and study low-temperature (T ≤ 100K) susceptibility in a series of samples of heavily doped Ge:As samples on the insulator side of the insulator–metal phase transition. Subtracting the known values of the magnetic susceptibility of the lattice from the measurement results, the values of the impurity magnetic susceptibility of the system are obtained. Using the method of electron spin resonance, the paramagnetic component of the impurity susceptibility is determined. Subtraction of the paramagnetic component from the total impurity susceptibility is used to obtain, for the first time, the values of the impurity diamagnetic susceptibility (~5 × 10–8 cm3/g). The obtained result is consistent with estimates obtained for the localization radius of an electron at an As donor. Lowering the temperature to T ≤ 4 K leads to an increase in the diamagnetic susceptibility, which is consistent with the observed increase in the paramagnetic susceptibility. The observed effect is accounted for by the transition of impurity electrons from the singlet state to the triplet one.

Many-particle effects in adsorbed magnetic atoms with easy-axis anisotropy: the case of Fe on the CuN/Cu(100) surface

We study the effects of the exchange interaction between an adsorbed magnetic atom with easy-axis magnetic anisotropy and the conduction-band electrons from the substrate. We model the system using an anisotropic Kondo model and we compute the impurity spectral function, which is related to the differential conductance (dI/dV) spectra measured using a scanning tunneling microscope. To make contact with the known experimental results for iron atoms on the CuN/Cu(100) surface (Hirjibehedin et al 2007 Science 317 1199), we calculated the spectral functions in the presence of an external magnetic field of varying strength applied along all three spatial directions. It is possible to establish an upper bound on the coupling constant J: in the range of the magnetic fields for which the experimental results are currently known (up to 7 T), the low-energy features in the calculated spectra agree well with the measured dI/dV spectra if the exchange coupling constant J is at most half as large as that for cobalt atoms on the same surface. We show that for an even higher magnetic field (between 8 and 9 T) applied along the ‘hollow direction’, the impurity energy states cross, giving rise to a Kondo effect which takes the form of a zero-bias resonance. The coupling strength J could be determined experimentally by performing tunneling spectroscopy in this range of magnetic fields. On the technical side, the paper introduces an approach for calculating the expectation values of global spin operators and all the components of the impurity magnetic susceptibility tensor (including the out-of-diagonal ones) in numerical renormalization group (NRG) calculations with no spin symmetry. An appendix contains a density functional theory (DFT) study of the Co and Fe adsorbates on the CuN/Cu(100) surface: we compare magnetic moments, as well as orbital energies, occupancies, centers and spreads, by calculating the maximally localized Wannier orbitals of the adsorbates.

Negative impurity magnetic susceptibility and heat capacity in a Kondo model with narrow peaks in the local density of electron states

Temperature dependences of the impurity magnetic susceptibility, entropy, and heat capacity have been obtained by the method of numerical renormalization group and exact diagonalization for the Kondo model with peaks in the electron density of states near the Fermi energy (in particular, with logarithmic Van Hove singularities). It is shown that these quantities can be negative. A new effect has been predicted (which, in principle, can be observed experimentally), namely, the decrease in the magnetic susceptibility and heat capacity of a nonmagnetic sample upon the addition of magnetic impurities into it.

Experimental study of manifestations of resonance scattering of conduction electrons on transition-element impurities in mercury selenide

An interpretation of the experimental data on the low-temperature conductivity and magnetic susceptibility of mercury selenide containing donor impurities of transition elements is developed on the basis of electron resonance scattering theory in the Friedel approach. Both existing data and results obtained in the present study, for solid solutions of chromium, cobalt, and gadolinium, are considered. The results of a fitting of the measured temperature dependence of the electron mobility in HgSe:Cr crystals and concentration dependence of the Curie constant in the impurity magnetic susceptibility of HgSe:Co crystals are analyzed to obtain quantitative confirmation of the idea that resonance donor levels of the impurities chromium and cobalt are present in the conduction band of the respective crystals. The resonance level widths are determined and are found to be an order of magnitude larger than those of iron. It is shown that the observed concentration maximum of the electron mobility in mercury selenide containing gadolinium impurities can be explained on the basis of resonance scattering theory, although the existing data are insufficient for justification of such an explanation of the origin of that maximum.

Long-range dynamics related to magnetic impurities in the two-dimensional Heisenberg antiferromagnet

We consider a magnetic impurity in the two-dimensional Heisenberg antifferomagnet with long range antiferromagnetic order. At low temperature the impurity magnetic susceptibility has a Curie term ($\propto 1/T$) and a logarithmic correction ($\propto \ln(T)$). We calculate the correction and derive related Ward identity for the impurity-spin-wave vertex.

Quantum magnetic impurities in magnetically ordered systems.

We discuss the problem of a spin 1/2 impurity immersed in a spin S magnetically ordered background. We show that the problem maps onto a generalization of the dissipative two level system with two independent heat baths, associated with the Goldstone modes of the magnet, that couple to different components of the impurity spin operator. Using analytical perturbative renormalization group methods and accurate numerical renormalization group we show that contrary to other dissipative models there is quantum frustration of decoherence and quasiscaling even in the strong coupling regime. We make predictions for the behavior of the impurity magnetic susceptibility. Our results may also have relevance to quantum computation.

Kondo effect in a metal with correlated conduction electrons: Diagrammatic approach

We study the low-temperature behavior of a magnetic impurity which is weakly coupled to correlated conduction electrons. To account for conduction electron interactions a diagrammatic approach in the frame of the 1/N expansion is developed. The method allows us to study various consequences of the conduction electron correlations for the ground state and the low-energy excitations. We analyse the characteristic energy scale in the limit of weak conduction electron interactions. Results are reported for static properties (impurity valence, charge susceptibility, magnetic susceptibility, and specific heat) in the low-temperature limit.

Scaling and criticality of the Kondo effect in a Luttinger liquid

A quantum Monte Carlo simulation method has been developed and applied to study the critical behavior of a single Kondo impurity in a Luttinger liquid. This numerically exact method has no finite-size limitations and allows to simulate the whole temperature range. Focusing on the impurity magnetic susceptibility, we determine the scaling functions, in particular for temperatures well below the Kondo temperature. In the absence of elastic potential scattering, we find Fermi-liquid behavior for strong electron-electron interactions, g_c < 1/2, and anomalous power laws for 1/2<g_c < 1, where g_c is the correlation parameter of the Luttinger liquid. These findings resolve a recent controversy. If elastic potential scattering is present, we find a logarithmically divergent impurity susceptibility at g_c<1/2 which can be rationalized in terms of the two-channel Kondo model.

Orbital localization and delocalization effects in the U5f2configuration: Impurity problem

Anderson models, based on quantum chemical studies of the molecule of U(C_8H_8)_2, are applied to investigate the problem of an U impurity in a metal. The special point here is that the U 5f-orbitals are divided into two subsets: an almost completely localized set and a considerably delocalized one. Due to the crystal field, both localized and delocalized U 5f-orbitals affect the low-energy physics. A numerical renormalization group study shows that every fixed point is characterized by a residual local spin and a phase shift. The latter changes between 0 and \pi/2, which indicates the competition between two different fixed points. Such a competition between the different local spins at the fixed points reflects itself in the impurity magnetic susceptibility at high temperatures. These different features cannot be obtained if the special characters of U 5f-orbitals are neglected.

Multichannel Kondo effect in an interacting electron system: Exact results for the low-temperature thermodynamics

We study the low-temperature thermodynamics of a spin-S magnetic impurity coupled to m degenerate bands of interacting electrons in one dimension. By exploiting boundary conformal field theory techniques, we derive exact results for the possible impurity thermal and magnetic response. The leading behavior of the impurity magnetic susceptibility is shown to be insensitive to the electron-electron interaction. In contrast, there are two types of scaling behavior of the impurity specific heat consistent with the symmetries of the problem: Either it remains the same as for the ordinary multichannel Kondo problem for noninteracting electrons, or it acquires a new leading term governed by an interaction-dependent critical exponent. We conjecture that the latter behavior is indeed realized when the impurity is exactly screened (m=2S).

Overscreening of magnetic impurities indx2−y2-wave superconductors

We consider the screening of a magnetic impurity in a $d_{x^2-y^2}$ wave superconductor. The properties of the $d_{x^2-y^2}$ state lead to an unusual behavior in the impurity magnetic susceptibility, the impurity specific heat and in the quasiparticle phase shift which can be used to diagnose the nature of the condensed state. We construct an effective theory for this problem and show that it is equivalent to a multichannel (one per node) non-marginal Kondo problem with linear density of states and coupling constant J. There is a quantum phase transition from an unscreened impurity state to an overscreened Kondo state at a critical value J_c which varies with $\Delta_0$, the superconducting gap away from the nodes. In the overscreened phase, the impurity Fermi level $\epsilon_f$ and the amplitude $\Delta$ of the ground state singlet vanish at J_c like $\Delta_0 \exp(- const. / \Delta)$ and J-J_c respectively. We derive the scaling laws for the susceptibility and specific heat in the overscreened phase at low fields and temperatures.

Electronic structure and magnetic properties of aluminium clusters containing 3d impurity atoms

The electronic structure, local magnetic moments and magnetic susceptibility of Fe, Co and Ni substitutional impurities in Al clusters are calculated within the framework of the local spin-density approximation and the model of an 'atom embedded in a jellium sphere'. Clusters containing up to 100 atoms are considered. It is obtained that the 3d impurities may be magnetic or non-magnetic depending on the Al cluster size. The impurity magnetic susceptibility is an oscillating function of cluster size that results from the size dependence of the position of the virtual bound states relative to the host Fermi energy. The magnetic susceptibility for Fe impurity atoms in Al clusters is positive, the magnetic susceptibility for Co atoms oscillates around zero, and the Ni impurity is diamagnetic. The results are in agreement with experimental data for dilute Al-based alloys.

Quantum Monte Carlo and Numerical Renormalization Group Studies of Magnetic Impurities in Nonmetallic Systems

We study magnetic properties of a single-impurity Anderson model in the symmetric case, in which the density of states for conduction electrons vanishes in a finite energy gap containing the Fermi energy. A quantum Monte Carlo simulation at finite temperatures and low-energy excitations calculated by a numerical renormalization group method reveal that at low temperatures the impurity magnetic susceptibility follows Curie's law. This behavior is consistent that the ground state is a doublet. The low-temperature Curie constant decreases monotonically with decreasing energy gap and the critical point is the zero gap. In the narrow gap limit, the impurity g-value of the doublet state is proportional to the gap width. This situation is due to the special feature of the symmetric case.

Exact solution of the single-impurity model with two-particle s-d interaction

An integrable model describing the two-particle interaction between the localized level and band electrons is presented. The impurity magnetic susceptibility, the localized electron number, and the energy of the ground state are calculated.

Self-consistent large-N expansion for normal-state properties of dilute magnetic alloys.

Finite-temperature properties of the infinite-$U$ Anderson model for rare-earth alloys are calculated within a unified approach. The impurity-electron density of states and magnetic moment spectrum provide a natural framework for describing both static and dynamic properties. The density of states and moment spectrum exhibit low-energy "Kondo resonances" with approximate single-parameter scaling, which persists for impurity valences in the range 1.0-0.7. The position of the resonance in the zero-temperature density of states, ${T}_{0}$, sets the scale for all low-temperature properties. Results are reported for the impurity valence, resistivity, thermopower, thermal conductivity, magnetic susceptibility, specific heat, photoemission and inverse-photoemission spectra, and neutron scattering linewidth. The effect of spin-orbit interactions is incorporated in the theory. The calculation is a diagrammatic approximation motivated by the simplifying concept of large angular momentum degeneracy ($N$). The approximate solution is thermodynamically consistent and satisfies all pertinent sum rules. Static properties (magnetic susceptibility and specific heat) are in good agreement with exact results of the Bethe ansatz. Experimental results on both dilute and concentrated Ce alloys are described quantitatively with use of a one-parameter (${T}_{0}$) theory.