Using numerical renormalization group techniques, we study static and dynamic properties of a family of single-channel Kondo impurity models with axial magnetic anisotropy $DS_z^2$ terms; such models are appropriate to describe magnetic impurity atoms adsorbed on non-magnetic surfaces, which may exhibit surface Kondo effect. We show that for positive anisotropy $D$ and for any spin $S$, the systems behave at low temperatures as regular Fermi liquids with fully compensated impurity spin. The approach to the stable fixed point depends on the value of the spin $S$ and on the ratio $D/T_K^{(0)}$, where $T_K^{(0)}$ is the Kondo temperature in the absence of the anisotropy. For S=1, the screening occurs in two stages if $D<T_K^{(0)}$; the second Kondo temperature is exponentially reduced in this case. More generally, there is an effective spin-1/2 Kondo effect for any integer $S$ if $D<T_K^{(0)}$ and for any half-integer $S$ if $D>T_K^{(0)}$. For negative anisotropy $D$, the system is a non-Fermi liquid with residual anisotropic exchange interaction. However, the presence of transverse magnetic anisotropy $E(S_x^2-S_y^2)$ restores Fermi-liquid behavior in real systems.
Physical properties of anisotropic superconductors like the critical temperature and others depend sensitively on the electron mean free path. The sensitivity to impurity scattering and the resulting anomalies are considered a characteristic feature of strongly anisotropic pairing. These anomalies are usually analyzed in terms of s-wave impurity scattering which leads to universal pair breaking effects depending on only two scattering parameters, the mean free path and the impurity cross section. We investigate here corrections coming from anisotropies in the scattering cross section, and find…
Using the numerical renormalization group method, we study the splitting of the Kondo resonance by a magnetic field applied in different directions in the Kondo model for anisotropic magnetic impurities. Several types of magnetic anisotropy are considered: the XXZ exchange coupling anisotropy J_perp J_z, the longitudinal magnetic anisotropy DS_z^2, and the transverse magnetic anisotropy E(S_x^2-S_y^2). In the spin-1/2 model with the XXZ exchange coupling anisotropy we find very small direction dependence in the magnitude of the splitting. In the spin-3/2 model with the easy-plane (D>0) anisotr…
The thermodynamics of finite open antiferromagnetic XXZ chains is studied using field theory, Bethe Ansatz and quantum Monte Carlo methods. For the susceptibility a parameter-free result as a function of the number of sites L and temperature T beyond the scaling limit is derived. The limiting cases T/J >> 1/L (J being the exchange constant), where the boundary correction shows a logarithmically suppressed Curie behaviour, and T/J << 1/L, where a crossover to the ground state behaviour takes place, are discussed in detail. Based on this analysis we present a simple formula for the averaged susc…
Magnetic impurities adsorbed on graphene are coupled magnetically via the itinerant electrons. This interaction opens a gap in the band structure of graphene. The result strongly depends on how the magnetic impurities are distributed. While random doping produces a semiconductor, if all or most impurities are located in the same sublattice, the spin degeneracy is removed and a spin-polarized semiconductor arises.
The intrinsic spin Hall conductivity in a two dimensional electron gas with Rashba spin-orbit coupling is evaluated by taking account of anisotropic coupling between magnetic impurities and itinerant electrons. In our calculation Kubo's linear response formalism is employed and the vertex correction is considered. In the semiclassical limit $μ\gg 1/τ$, a non-vanishing spin Hall conductivity $σ^{}_{sH}$ is found to depend on the momentum relaxation time $τ$, spin-orbit splitting $Δ$ and the anisotropic coefficient of interaction between itinerant electrons and magnetic impurities. The clean lim…
In this letter, we construct a Hamiltonian of the impurity model within the framework of the open boundary Heisenberg XYZ spin chain. This impurity model is an exactly solved one and it degenerates to the integrable XXZ impurity model under the triangular limit. This approach is the first time to add the integrable impurities to the completely anisotropic Heisenberg spin model with the open boundary conditions.
Fourier transform scanning tunneling spectroscopy (FT-STS) measures the scattering of conduction electrons from impurities and defects, giving information about the electronic structure of both the host material and adsorbed impurities. We interpret such FT-STS measurements in terms of the quasiparticle interference (QPI), investigating the QPI due to magnetic impurities adsorbed on a range of representative non-magnetic host surfaces, and contrasting with the case of a simple scalar impurity or point defect. We demonstrate how the electronic correlations present for magnetic impurities marked…
We study a Kondo impurity model with additional uniaxial anisotropy D in a non-zero magnetic field B using the Numerical Renormalization Group (NRG). The ratio g_e/g_S of electron and impurity g-factor is regarded as a free parameter and, in particular, the special cases of a "local" (g_e=0) and "bulk" (g_e=g_S) field are considered. For a bulk field, the relationship between the impurity magnetization M and the impurity contribution to the magnetization M_imp is investigated. Furthermore, we study how the value of g_e affects the impurity magnetization curves. In case of an isotropic impurity…
We have investigated the dilute magnetic impurity effect on the magnetic properties of a quantum spin liquid candidate Ba3ZnRu2O9 and a spin gapped compound Ba3CaRu2O9. The magnetic ground state of each compound stands against 2% substitution of magnetic impurities for Zn or Ca. We have found that the magnetic response of these impurities, which behave as paramagnetic spins, depends on the host materials and the difference of the two manifests itself in the Weiss temperature, which can hardly be explained by the dilute magnetic impurities alone in the case of Ba3ZnRu2O9. We consider a contribu…
In this letter, the Kondo magnetic effect is studied for the $XXZ$ spin chain where the impurities are coupled to the edges of the system. The Hamiltonian of our model can be constructed from the transfer matrix. It is exactly solvable and the exchange constants between the bulk and the boundary impurities are arbitrary. The finite size corrections to the ground state energy are obtained for the magnetic impurities and the boundary condition. The specific heat and the susceptibility contributed by the impurities are derived and the Kondo temperature is given explicitly by the use of the Luttin…
The magnitude of the staggered field is calculated from the EPR data for CuGeO3 doped with Co and Fe magnetic impurities. It is found that this parameter demonstrate an anomalous temperature and magnetic field dependence probably due to (i) the specific mechanism of the staggered field generation in doped CuGeO3 and (ii) a competition between antiferromagnetic interchain exchange and staggered Zeeman energy.
We consider the contribution of magnetic impurities to the nuclear magnetic susceptibility $χ$ and to the specific heat $C$ of a metal. The impurity contribution to the magnetic susceptibility has a $1/T^2$ behaviour, and the impurity contribution to the specific heat has a $1/T$ behaviour, both in an extended region of temperatures $T$. In the case of a dirty metal the RKKY interaction of nuclear spins and impurity spins is suppressed for low temperatures and the main contribution to $C$ and $χ$ is given by their dipole-dipole interaction.
In this paper we use the semiclassical Boltzmann equation to investigate the transport properties of Dirac fermion on the surface of topological insulator with magnetic impurities. The results obtained show that there is also a minimal conductivity in this system as in graphene. We also argue the low temperature transport property, and find that there is no low temperature anomaly known as Kondo effect when the temperature is T>10^{-6}K.
We study S=1/2 dimers which are weakly coupled by three-dimensional antiferromagnetic interactions J'. It is commonly known that doping with non-magnetic impurities immediately induces a long-range Neel order. We show that application of an external magnetic field H may drive the system back to a disordered phase. We discuss the zero temperature phase diagram in the (H,J') plane and we propose suggestions for experiments.
From the open boundary t-J model, an impurity model is constructed in which magnetic impurities of arbitrary spins are coupled to the edges of the strongly correlated electron system. The boundary R matrices are given explicitly. The interaction parameters between magnetic impurities and electrons are related to the potentials of the impurities to preserve the integrability of the system. The Hamiltonian of the impurity model is diagonalized exactly. The integral equations of the ground state are derived and the ground state properties are discussed in details. We discuss also the string solut…
The anisotropy in the microwave conductivity of the ortho-II YBa$_2$Cu$_3$O$_{6.50}$ is studied within the kinetic energy driven superconducting mechanism. The ortho-II YBa$_2$Cu$_3$O$_{6.50}$ is characterized by a periodic alternative of filled and empty $\hat{b}$-axis CuO chains. By considering the CuO chain induced extended anisotropy impurity scattering, the main features of the anisotropy in the microwave conductivity of the ortho-II YBa$_2$Cu$_3$O$_{6.50}$ are reproduced based on the nodal approximation of the quasiparticle excitations and scattering processes, including the intensity an…
Impurity effect is systematically studied in doped Haldane material Pb(Ni$_{1-x}$$M_x$)$_2$V$_2$O$_8$ ($M$ = Mn, Co, Cu, and Mg) by use of DC and AC susceptibility, and heat capacity measurements. The occurrence of three-dimensional ordered state is universally observed for all the impurities and the complete temperature -- concentration phase diagrams are obtained, which are qualitatively similar to that in other spin-gap materials. The unique feature is found in the drastic dependence of the transition temperatures on the species of the impurities. The consideration of effective Hamiltonian …
We consider doping of non-magnetic impurities in the spin-1/2, 1/5-depleted square lattice. This structure, whose undoped phase diagram offers both magnetically ordered and spin-liquid ground states, is realized physically in CaV_4O_9. Doping into the ordered phase results in a progressive loss of order, which becomes complete at the percolation threshold. By contrast, non-magnetic impurities introduced in the spin liquids create a phase of weak but long-ranged antiferromagnetic order coexisting with the gapped state. The latter may be viewed as a true order-by-disorder phenomenon. We study th…
The magnetic polarization induced by nonmagnetic impurities such as Zn in high Tc cuprate compounds is studied by the variational Monte Carlo simulation. The variational wave function is constructed from the eigenstates obtained from Bogoliubov de Gennes mean field Hamiltonian for the two-dimensional t-J model. A Jastrow factor is introduced to account for the induced magnetic moment and the repulsion between holes and the impurity. A substantial energy gain is obtained by forming an antiferromagnetic polarization covering 4 or 5 lattice sites around the impurity. We also found the doping depe…
We report unusual effects of nonmagnetic impurities on the spin-triplet superconductor Sr2RuO4. The substitution of nonmagnetic Ti4+ for Ru4+ induces localized-moment magnetism characterized by unexpected Ising anisotropy with the easy axis along the interlayer c direction. Furthermore, for x(Ti) > 0.03 magnetic ordering occurs in the metallic state with the remnant magnetization along the c-axis. We argue that the localized moments are induced in the Ru4+ and/or oxygen ions surrounding Ti4+ and that the ordering is due to their interaction mediated by itinerant Ru-4d electrons with strong spi…
The effects of magnetic and non-magnetic impurities in spin-Peierls systems are investigated allowing for lattice relaxation and quantum fluctuations. We show that, in isolated chains, strong bonds form next to impurities, leading to the appearance of magneto-elastic solitons. Generically, these solitonic excitations do not bind to impurities. However, interchain elastic coupling produces an attractive potential at the impurity site which can lead to the formation of bound states. In addition, we predict that small enough chain segments do not carry magnetic moments at the ends.
We investigate the impurity scattering induced quasiparticle interference in the ($π, 0$) spin-density wave phase of the iron pnictides. We use a five orbital tight binding model and our mean field theory in the clean limit captures key features of the Fermi surface observed in angle-resolved photoemission. We use a t-matrix formalism to incorporate the effect of doping induced impurities on this state. The impurities lead to a spatial modulation of the local density of states about the impurity site, with a periodicity of $\sim 8a_{{\rm Fe}-{\rm Fe}}$ along the antiferromagnetic direction. Th…
We present a computational study of individual and pairs of substitutional Mn impurities on the (110) surface of GaAs samples based on density functional theory. We focus on the anisotropy properties of these magnetic centers and their dependence on on-site correlations, spin-orbit interaction and surface-induced symmetry-breaking effects. For a Mn impurity on the surface, the associated acceptor-hole wavefunction tends to be more localized around the Mn than for an impurity in bulk GaAs. The magnetic anisotropy energy for isolated Mn impurities is of the order of 1 meV, and can be related to …
Recently the electron dephasing and energy relaxation due to different magnetic impurities have been extensively investigated experimentally in thin wires and in this Letter these quantities are theoretically studied. It was shown earlier that a magnetic impurity in a metallic host with strong spin-orbit interaction experiences a surface anisotropy of the form $H=K_d ({\bf n}{\bf S})^2$ which causes size effects for impurities with integer spin. Here we show that the dephasing and the energy relaxation are influenced by the surface anisotropy in very different ways for integer spin having a si…
We study the textures of generalized "charge densities" (scalar objects invariant under time reversal), in the vicinity of non-magnetic impurities in square-lattice quantum anti-ferromagnets, by order parameter field theories. Our central finding is the structure of the "vortex" in the generalized density wave order parameter centered at the non-magnetic impurity. Using exact numerical data from quantum Monte Carlo simulations on an antiferromagnetic spin model, we are able to verify the results of our field theoretic study. We extend our phenomenological approach to the period-4 bond-centered…
For the weakly coupled S=1 antiferromagnetic Heisenberg chains on a simple cubic lattice, the effects of magnetic impurities are investigated by the quantum Monte Carlo method with the continuous-time loop algorithm. The transition temperatures of the impurity-induced phase transitions for magnetic impurities with S=1/2, 3/2, and 2 are determined and compared with the transition temperature induced by the non-magnetic impurities. Implications on the experimental results are discussed.
Motivated by recent experiments on ZnCu$_3$(OH)$_6$Cl$_2$, we study the inhomogeneous Knight shifts (local susceptibilities) of spin 1/2 Kagome antiferromagnet in the presence of nonmagnetic impurities. Using high temperature series expansion, we calculate the local susceptibility and its histogram down to about T=0.4J. At low temperatures, we explore a Dirac spin liquid proposal and calculate the local susceptibility in the mean field and beyond mean field using Gutzwiller projection, finding the overall picture to be consistent with the NMR experiments.
Based on low temperature resistivity, heat capacity and magnetization investigations we show that the unusually strong suppression of superconductivity in Lu$_x$Zr$_{1-x}$B$_{12}$ BSC-type superconductors in the range $x$$<$0.08 is caused by the emergence of static spin polarization in the vicinity of non-magnetic lutetium impurities. The analysis of received results points to a formation of static magnetic moments with $μ_{eff}$$\approx$$3μ_B$ per Lu-ion. The size of these spin polarized nanodomains was estimated to be about 5 $Å$.
We investigate the dephasing rate, 1/tau_phi, of weakly disordered electrons due to scattering from diluted dynamical impurities. Our previous result for the weak-localization dephasing rate is generalized from diluted Kondo impurities to arbitrary dynamical defects with typical energy transfer larger than 1/tau_phi. For magnetic impurities, we study the influence of magnetic fields on the dephasing of Aharonov-Bohm oscillations and universal conductance fluctuations both analytically and using the numerical renormalization group. These results are compared to recent experiments.
Understanding the origin of the magnetism of high temperature superconductors is crucial for establishing their unconventional pairing mechanism. Recently, theory predicts that FeSe is close to a magnetic quantum critical point, and thus weak perturbations such as impurities could induce local magnetic moments. To elucidate such quantum instability, we have employed scanning tunneling microscopy and spectroscopy. In particular, we have grown FeSe film on superconducting Pb(111) using molecular beam epitaxy and investigated magnetic excitation caused by impurities in the proximity-induced super…
We investigate magnetic properties of lightly doped antiferromagnetic Mott insulators in the presence of non-magnetic impurities. Within the framework of the t-J model we calculate the doping dependence of the antiferromagnetic order parameter using the self-consistent diagrammatic techniques. We show that in the presence of non-magnetic impurities the antiferromagnetic order is more robust against hole doping in comparison with the impurity-free host, implying that magnetic order can re-appear upon Zn doping into lightly hole-doped cuprates. We argue that this is primarily due to the loss of …
Nonmagnetic Zn impurities are known to strongly suppress superconductivity. We review their effects on the spin excitation spectrum in $\rm YBa_2Cu_3O_{7}$, as investigated by inelastic neutron scattering measurements.
We report Electronic Raman Scattering measurements on optimally doped Zn and Ni substituted YBCO in A$_{1g}$ and B$_{1g}$ channels. We show that the superconducting gap energy is independant of magnetic Ni and non-magnetic Zn substitutions. On the contrary the collective A$_{1g}$ mode follows the critical temperature $T_c$ with two distinct slopes for Ni and Zn, and tracks the magnetic resonance seen in inelastic neutron scattering. We explain the unconventionnal energy dependence of the superconducting gap and discuss the behaviour of the A$_{1g}$ mode within magnetic and non-magnetic impurit…
We study quantum interference of electronic waves that are scattered by multiple non-magnetic impurities in a d_x2-y2-wave superconductor. We show that the number of resonance states in the density-of-states (DOS), as well as their frequency and spatial dependence change significantly as the distance between the impurities or their orientation relative to the crystal lattice is varied. Since the latter effect arises from the momentum dependence of the superconducting gap, we argue that quantum interference is a novel tool to identify the symmetry of unconventional superconductors.
Dirac-like surface states on surfaces of topological insulators have a chiral spin structure that suppresses back-scattering and protects the coherence of these states in the presence of non-magnetic scatterers. In contrast, magnetic scatterers should open the back- scattering channel via the spin-flip processes and degrade the state's coherence. We present angle-resolved photoemission spectroscopy studies of the electronic structure and the scattering rates upon adsorption of various magnetic and non-magnetic impurities on the surface of Bi$_2$Se$_3$, a model topological insulator. We reveal …
We present a theory of Kondo effect caused by an induced magnetic moment near non-magnetic impurities such as Zn and Li in the cuprate superconductors. Based on the co-existence of charge order and superconductivity, a natural description of the induced moment and the resulting Kondo effect is obtained in the framework of bond-operator theory of microscopic t-J-V Hamiltonian. The local density of state near impurities is computed in a self-consistent Bogoliubov-de Gennes theory which shows a low-energy peak in the middle of superconducting gap. Our theory also suggests that the charge order ca…
We study analytically the effects of inhomogeneous pairing interactions in short coherence length superconductors, using a spatially varying Bogoliubov-deGennes model. Within the Born approximation, it reproduces all of the standard Abrikosov-Gor'kov pairbreaking and gaplessness effects, even in the absence of actual magnetic impurities. For pairing disorder on a single site, the T-matrix gives rise to bound states within the BCS gap. Our results are compared with recent scanning tunneling microscopy measurements on Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ with Zn or Ni impurities.
The effects of dilute Zn impurities on the uniform magnetic susceptibility are calculated in the normal metallic state for a model of the spin fluctuations of the layered cuprates. It is shown that scatterings from extended impurity potentials can lead to a coupling of the q~(pi,pi) and the q~0 components of the magnetic susceptibility chi(q). Within the presence of antiferromagnetic correlations, this coupling can enhance the uniform susceptibility. The implications of this result for the experimental data on Zn substituted YBa2Cu3O{7-delta} are discussed.
We study the effect of quantum magnetic impurities on d-wave spin density waves (d-SDW). The impurity spins are aligned coherently according to the spin space anisotropy of the condensate. Both the order parameter and transition temperature increases due to the coherent interplay between magnetic scatterers and d-SDW. This can explain the recent experimental data on the pseudogap enhancement of Ni substituted NdBa_2{Cu_{1-y}Ni_y}O_6.8 from Pimenov et al. (Phys. Rev. Lett. 94, 227003 (2005)).
The charge dynamics of Ba(Fe$_{1-x}$TM$_x$)$_2$As$_2$ (TM = Mn and Cr) has been investigated by optical spectroscopy. It was found that in addition to the strong suppression of the coherent charge transport, the magnetic impurity induces a novel spectral feature related to the carrier localization in the far-infrared region above the antiferromagnetic transition temperature. We attribute it to the cooperative effect between conduction electrons and local magnetic order induced by magnetic impurities. The present results demonstrate that Mn and Cr are not conventional magnetic pair-breakers in …
To explore the origin of the observed giant magnetic moments ($\sim 7 μ_B$) of Fe impurities on the surface and in the bulk of Cs films, we have performed the relativistic LSDA + U calculations using the linearized muffin-tin orbital (LMTO) band method. We have found that Fe impurities in Cs behave differently from those in noble metals or in Pd. Whereas the induced spin polarization of Cs atoms is negligible, the Fe ion itself is found to be the source of the giant magnetic moment. The 3d electrons of Fe in Cs are localized as the 4f electrons in rare-earth ions so that the orbital magnetic m…
We consider chiral electrons moving along the 1D helical edge of a 2D topological insulator and interacting with a disordered chain of Kondo impurities. Assuming the electron-spin couplings of random anisotropies, we map this system to the problem of the pinning of the charge density wave by the disordered potential. This mapping proves that arbitrary weak anisotropic disorder in coupling of chiral electrons with spin impurities leads to the Anderson localization of the edge states.
We analyse the behavior of the density of states in a singlet s-wave superconductor with weak magnetic impurities in the clean limit by using the method of optimal fluctuation. We show that the density of states varies as $\ln N(E)\propto -|E-Δ_0|^{(7-d)/4}$ near the mean field gap edge $Δ_0$ in a d-dimensional superconductor. The optimal fluctuation in d>1 is strongly anisotropic. We compare the density of states with that obtained in other recent approaches.
The influence of La non magnetic impurities on the spin dynamics of CeCoIn$_{5}$ was studied by inelastic neutron scattering. In La-substituted systems, the spin resonance peak (observed at $Ω_{res}=0.55 meV$ in the pure system) is shifted to lower energies but the ratio $Ω_{res}/k_{B}T_{c}$ remains unchanged. The excitation broadens till it reaches 0.3 meV equal to the value of the quasi-elastic signal in the normal state. The evolution of La substitution is compared with the evolution of the magnetic resonance in Ni and Zn substituted YBa$_{2}$Cu$_{3}$O$_{7}$.
We propose that localized defects in magnetic semiconductors act as deep impurities and can be described by the Anderson model. Within this model, hybridization of d-orbitals and p-orbitals gives rise to a non-RKKY indirect exchange mechanism, when the localized d-electrons are exchanged through both conduction and valence bands. For semiconductors with indirect band gap the non-RKKY part of exchange integral is antiferromagnetic, which suppresses ferromagnetism. In case of direct band gap, this exchange mechanism can, under certain conditions, lead to enhancement of ferromagnetism. The indire…
The recently discovered kagome superconductors $A$V$_3$Sb$_5$ ($A$ = K, Rb, Cs) possess a unique band structure with van Hove singularities and Dirac dispersions, in which unusual charge-density-wave (CDW) orders with time-reversal and rotational symmetry breaking have been reported. One of the most crucial unresolved issues is identifying the symmetry of the superconductivity that develops inside the CDW phase. Theory predicts a variety of unconventional superconducting symmetries, including exotic states with chiral and topological properties accompanied by a sign-changing superconducting ga…
We present Monte Carlo simulations for a classical antiferromagnetic Heisenberg model with both nearest ($J_1$) and next-nearest ($J_2$) exchange couplings on the square lattice in the presence of non-magnetic impurities. We show that the order-by-disorder entropy selection, associated with the Ising-like phase transition that appears for $J_2/J_1>1/2$ in the pure spin model, is quenched at low temperature due to the presence of non-magnetic impurities. Evidences that a new competing order is stabilized around the impurities, and in turn induces a re-entrance phase transition are reported. Imp…
It is generally believed that superconductivity only weakly affects the indirect exchange between magnetic impurities. If the distance r between impurities is smaller than than the superconducting coherence length (r < ξ), this exchange is thought to be dominated by RKKY interactions, identical to the those in a normal metallic host. This perception is based upon a perturbative treatment of the exchange interaction. Here, we provide a non-perturbative analysis and demonstrate that the presence of Yu-Shiba-Rusinov bound states induces a strong 1/r^2 anti-ferromagnetic interaction that can domin…
