Magnetic impurities in gapless Fermi systems: perturbation theory

We consider a symmetric Anderson impurity model with a soft-gap hybridization vanishing at the Fermi level, with r>0. Three facets of the problem are examined. First the non-interacting limit, which despite its simplicity contains much physics relevant to the U>0case: it exhibits both strong coupling (SC) states (for r<1) and local moment states (for r>1), with characteristic signatures in both spectral properties and thermodynamic functions. Second, we establish general conditions upon the interaction self-energy for the occurence of a SC state for U>0. This leads to a pinning theorem, whereby the modified spectral function is pinned at the Fermi level for any U where a SC state obtains; it generalizes to arbitrary r the pinning condition upon familiar in the normal r=0 Anderson model. Finally, we consider explicitly spectral functions at the simplest level: second order perturbation theory in U, which we conclude is applicable for and r>1 but not for . Characteristic spectral features observed in numerical renormalization group calculations are thereby recovered, for both SC and LM phases; and for the SC state the modified spectral functions are found to contain a generalized Abrikosov-Suhl resonance exhibiting a characteristic low-energy Kondo scale with increasing interaction strength. Received 26 August 1999     

Impurity contribution to the specific heat in the Kondo model

Summary Using the Lanczos scheme (tridiagonalization) we investigate the impurity contribution to the single-impurity Kondo model. This is accomplished by obtaining the ground-state energy of aN-particle system and a (N+1)-particle system, and obtaining the functional dependence ofg(J) (whereJ is the strength of the interaction). Hereg(J) is the coefficient of a correction term which is of order 1/N. The density of states at the Fermi level is effectively changed by the factorg(J). The excess heat capacity associated with the impurity is then proportional tog(J). To speed up publication, the authors of this papers have agreed to not receive the proofs for correction.     

Some comments on Kondo lattices and the Mott transition

The so called exhaustion problem occurs when few electrons have to screen many spins in a metal with magnetic impurities. A singlet Fermi liquid ground state is possible only if all impurities are “isotropized” in such a way as to suppress their entropy. That takes a time and the corresponding energy limits the Fermi liquid range. The present note explores that issue of time and energy scales, and it concludes that is much smaller than the single impurity Kondo temperature. Similarly the relevant energy scale is proportional to the number of electrons. Recent results on the Mott metal insulator transition in infinite dimension are reconsidered in the light of these results: controversies in that respect are shown to reduce to a simple physical question, with no firm answer as to now. Received: 5 May 1998 / Received in final form and Accepted: 29 July 1998     

Kondo insulators in the periodic Anderson model: a local moment approach

The symmetric periodic Anderson model is well known to capture the essential physics of Kondo insulator materials. Within the framework of dynamical mean-field theory, we develop a local moment approach to its single-particle dynamics in the paramagnetic phase. The approach is intrinsically non-perturbative, encompasses all energy scales and interaction strengths, and satisfies the low-energy dictates of Fermi liquid theory. It captures in particular the strong coupling behaviour and exponentially small quasiparticle scales characteristic of the Kondo lattice regime, as well as simple perturbative behaviour in weak coupling. Particular emphasis is naturally given to strong coupling dynamics, where the resultant clean separation of energy scales enables the scaling behaviour of single-particle spectra to be obtained. Received 19 December 2002 Published online 14 March 2003     

A local moment approach to the gapped Anderson model

We develop a non-perturbative local moment approach (LMA) for the gapped Anderson impurity model (GAIM), in which a locally correlated orbital is coupled to a host with a gapped density of states. Two distinct phases arise, separated by a level-crossing quantum phase transition: a screened singlet phase, adiabatically connected to the non-interacting limit and as such a generalized Fermi liquid (GFL); and an incompletely screened, doubly degenerate local moment (LM) phase. On opening a gap (δ) in the host, the transition occurs at a critical gap δ_c, the GFL [LM] phase occurring for δ<δ_c [ δ>δ_c] . In agreement with numerical renormalization group (NRG) calculations, the critical δ_c = 0 at the particle-hole symmetric point of the model, where the LM phase arises immediately on opening the gap. In the generic case by contrast δ_c > 0, and the resultant LMA phase boundary is in good quantitative agreement with NRG results. Local single-particle dynamics are considered in some detail. The major difference between the two phases resides in bound states within the gap: the GFL phase is found to be characterised by one bound state only, while the LM phase contains two such states straddling the chemical potential. Particular emphasis is naturally given to the strongly correlated, Kondo regime of the model. Here, single-particle dynamics for both phases are found to exhibit universal scaling as a function of scaled frequency ω/ω_m ⁰ for fixed gaps δ/ω_m ⁰, where ω_m ⁰ is the characteristic Kondo scale for the gapless (metallic) AIM; at particle-hole symmetry in particular, the scaling spectra are obtained in closed form. For frequencies |ω|/ω_m ⁰ ≫δ/ω_m ⁰, the scaling spectra are found generally to reduce to those of the gapless, metallic Anderson model; such that for small gaps δ/ω_m ⁰≪ 1 in particular, the Kondo resonance that is the spectral hallmark of the usual metallic Anderson model persists more or less in its entirety in the GAIM.     

A fractional-spin phase in the power-law Kondo model

We consider a Kondo impurity coupled to a fermionic host with a power-law density of states near the Fermi level, ρ(ε) ∼ |ε|^r, with exponent r < 0. Using both perturbative renormalization group (poor man's scaling) and numerical renormalization group methods, we analyze the phase diagram of this model for ferromagnetic and antiferromagnetic Kondo coupling. Both sectors display non-trivial behavior with several stable phases separated by continuous transitions. In particular, on the ferromagnetic side there is a stable intermediate-coupling fixed point with universal properties corresponding to a fractional ground-state spin. Received 18 February 2002 Published online 31 July 2002     

Direct overlapping effect of f orbitals for valence fluctuating materials in Kondo regime

In Rare-Earth (RE) systems, direct overlapping of 4f orbitals plays a role if the distance between RE ions is sufficiently small. Especially, such a situation happens under pressure for RE metals and RE compounds. Furthermore, in Actinide systems, 5f orbitals are more extended than the previously considered 4f orbitals. Therefore, in this case, direct overlapping of 5f orbitals should be taken into account even without applying pressure. In the present work, using Standard Basis Operators, we study direct overlapping effect of f orbitals for valence fluctuating materials in Kondo regime. An important result within our present model is that direct f orbital overlapping reduces f electron effective mass.     

Generalized nonlinear sigma model approach to alternating spin chains and ladders

We generalize the nonlinear sigma model treatment of quantum spin chains to cases including ferromagnetic bonds. When these bonds are strong enough, the classical ground state is no longer the standard Néel order and we present an extension of the known formalism to deal with this situation. We study the alternating ferromagnetic-antiferromagnetic spin chain introduced by Hida. The smooth crossover between decoupled dimers and the Haldane phase is semi-quantitatively reproduced. We study also a spin ladder with diagonal exchange couplings that interpolates between the gapped phase of the two-leg spin ladder and the Haldane phase. Here again we show that there is a good agreement between DMRG data and our analytical results. Received 6 September 1999     

Exact solution for a degenerate Anderson impurity in the limit embedded into a correlated host

We consider the one-dimensional t - J model, which consists of electrons with spin S on a lattice with nearest neighbor hopping t constrained by the excluded multiple occupancy of the lattice sites and spin-exchange J between neighboring sites. The model is integrable at the supersymmetric point, J = t. Without spoiling the integrability we introduce an Anderson-like impurity of spin S (degenerate Anderson model in the limit), which interacts with the correlated conduction states of the host. The lattice model is defined by the scattering matrices via the Quantum Inverse Scattering Method. We discuss the general form of the interaction Hamiltonian between the impurity and the itinerant electrons on the lattice and explicitly construct it in the continuum limit. The discrete Bethe ansatz equations diagonalizing the host with impurity are derived, and the thermodynamic Bethe ansatz equations are obtained using the string hypothesis for arbitrary band filling as a function of temperature and external magnetic field. The properties of the impurity depend on one coupling parameter related to the Kondo exchange coupling. The impurity can localize up to one itinerant electron and has in general mixed valent properties. Groundstate properties of the impurity, such as the energy, valence, magnetic susceptibility and the specific heat coefficient, are discussed. In the integer valent limit the model reduces to a Coqblin-Schrieffer impurity. Received: 31 December 1997 / Accepted: 17 March 1998     

Incommensurability in the magnetic excitations of the bilinear-biquadratic spin-1 chain

We study the magnetic excitation spectrum of the spin-1 chain with Hamiltonian .We focus on the range where the spin chain is in the gapped Haldane phase. The excitation spectrum and static structure factor is studied using direct Lanczos diagonalization of small systems and density-matrix renormalization group techniques combined with the single-mode approximation. The magnon dispersion has a minimum at until a critical value is reached at which the curvature (velocity) vanishes. Beyond this point, which is distinct from the VBS point and the Lifshitz point, the minimum lies at an incommensurate value that goes smoothly to when approaches , the Lai-Sutherland point. The mode remains isolated from the other states: there is no evidence of spinon deconfinement before the point .These findings explain recent observation of the behavior of the magnetization curve for . Received 16 December 1998     

A non-crossing approximation for the study of intersite correlations

We develop a Non-Crossing Approximation (NCA) for the effective cluster problem of the recently developed Dynamical Cluster Approximation (DCA). The DCA technique includes short-ranged correlations by mapping the lattice problem onto a self-consistently embedded periodic cluster of size . It is a fully causal and systematic approximation to the full lattice problem, with corrections in two dimensions. The NCA we develop is a systematic approximation with corrections . The method will be discussed in detail and results for the one-particle properties of the Hubbard model are shown. Near half filling, the spectra display pronounced features including a pseudogap and non-Fermi-liquid behavior due to short-ranged antiferromagnetic correlations. Received 16 June 1999     

Elementary excitations for the Anderson model at finite temperatures

The elementary excitation spectrums for the Anderson model at finite temperatures are calculated by using the Bethe-ansatz solution. The formulation is based on the method of Yang and Yang, which was developed for the one-dimensional boson systems with the -function type interaction. We obtain the temperature dependence of the spin and the charge excitation spectrums. When the impurity level lies deeply from the Fermi level and the Coulomb interaction is suitably large, the resonant peak structure develops in the low energy region of the spin excitation spectrum and the hump structure grows around the impurity level of the charge excitation spectrum with decreasing temperature. Received: 21 January 1998 / Accepted: 17 March 1998     

Observation of magnetic splitting in XPS MnL-spectra of Co2MnSn and Pd2MnSn Heusler alloys

The XPS MnL-spectra of Co₂MnSn, a nearly half-metallic ferromagnet (HMF) and Pd₂MnSn were investigated. The most drastical feature of the spectra observed is the well-defined magnetic splitting of the Mn 2p _3/2 , 2p _1/2 lines. This gives direct evidence of the existence of well-defined local magnetic moments in Heusler alloys in comparison with other itinerant-electron ferromagnets. The calculations of Mn2p XPS spectra of these materials were carried out using a fully relativistic generalization of the one-step model of photoemission and show excellent agreement with experiment. Received: 31 October 1997 / Received in final form: 28 November 1997 / Accepted: 18 December 1997     

Transport and thermodynamic properties of CeAuAl3

We present measurements of the specific heat, the electrical resistivity, the Hall effect, and the magnetic susceptibility of CeAuAl₃, a new heavy-electron compound that crystallizes in an ordered derivative of the tetragonal BaAl₄-type structure. For comparison we have also done some of these measurements on the isostructural non-magnetic reference compound LaAuAl₃, which appears to be a simple metal. Below K, CeAuAl₃ orders antiferromagnetically and below 1K, we encounter Fermi liquid behaviour with considerably enhanced effective masses, i.e., a quadratic temperature dependence of the resistivity with a large prefactor and a sizable linear-in-T contribution to the specific heat. This linear-in-T contribution increases by more than a factor 50 from its value at to its value at . Consequently CeAuAl₃ develops a heavy-electron ground state, coexisting with antiferromagnetic order. The small energy scales involved in the problem make CeAuAl₃ a good candidate for tuning it, by varying external parameters, towards a quantum critical point. At high temperatures we observe local moment behaviour. From the temperature dependence of the magnetic susceptibility and the specific heat we have derived the crystalline-electric-field-split level scheme of the J =5/2 multiplet. Distinct features in the electrical resistivity provide additional evidence for this level splitting. Received: 6 November 1997 / Accepted: 17 November 1997     

Density functional calculations on small bimetallic magnetic clusters

Structural and magnetic properties of small bimetallic clusters like Co_MRh_N, NiNa_N, and NiCu_N are determined in the framework of a generalized gradient-corrected approximation to density functional theory. The role of magnetism on the most stable structure and on the energy differences among the low-lying isomers is quantified by comparing magnetic and non-magnetic solutions of the Kohn-Sham equations. The correlation between structure, chemical order, and environment-dependent magnetic properties is discussed.     

Competing polarization mechanisms in the heavy-fermion paramagnet CeCu<Subscript><Emphasis Type="Bold">6</Emphasis></Subscript>

Nuclear magnetic resonance (NMR) and relaxation of ⁶³Cu and ⁶⁵Cu in a powder sample of the heavy-fermion paramagnet CeCu₆ is measured and analysed quantitatively. Five different Cu sites are accessible to a detailed analysis. We derive quadrupolar splitting frequencies, Ce to Cu transferred hyperfine field coupling constants, and transversal as well as longitudinal relaxation behaviour. Only small relaxation anomalies are observed at the orthorhombic to monoclinic structural phase transition of CeCu₆. We point to the different importance of transferred hyperfine interaction and local conduction electron density for static or dynamic part, respectively, of Cu hyperfine interaction. The different sign of the transferred hyperfine interaction from Ce³⁺ to different Cu neighbours reveals the different competing interaction mechanisms, giving rise to the heavy-fermion paramagnetic behavior of CeCu₆. Received 20 November 2001     

Single-crystal like NMR spectra of CeCu 5 Au powder samples

Single-crystal like nuclear magnetic resonance spin-echo spectra are obtained for powder samples of the antiferromagnet CeCu₅Au in the paramagnetic phase. Line shifts and quadrupolar splittings are analyzed for ⁶³Cu and ⁶⁵Cu. The influence of the extreme magnetic anisotropy of the CeCu_6-xAu_x compounds on nuclear spin relaxation is discussed. Received 19 June 2000     

Temperature dependent properties of metallic clusters containing magnetic impurities

The properties of magnetic impurities in small metallic clusters are investigated in the framework of the Anderson model by using exact diagonalization methods. Parameters representative of the Kondo limit are considered. The spin gap ΔE = E(S=1, 3/2) - E(S=0, 1/2) shows a remarkable band-filling dependence that can be interpreted in terms of the cluster-specific conduction-electron spectrum. Finite-temperature properties such as the magnetic susceptibility and specific heat are calculated exactly in the canonical and grand canonical ensembles. The structural dependence is illustrated. Received 30 November 2000     

Low-energy excitations of Yb As in a magnetic field

We discuss the effects of an applied magnetic field on the low-energy excitations in the low temperature phase of Yb₄As₃. We show also why the magnetic interaction of the Yb³⁺ ions is nearly of an isotropic Heisenberg spin-1/2 type. A small anisotropy due to an intrachain dipolar interaction leads to the opening of a gap when a magnetic field is applied. The model agrees with available experimental data. Simple experiments are suggested in order to further test the present theory. Received 3 February 1999     

Ga-NMR study of the low-energy excitations in

We report the results of ⁶⁹Ga- and ⁷¹Ga-NMR measurements on NdGa₂ at temperatures between 0.1 and and in applied magnetic fields between zero and 74 kOe. NdGa₂ orders antiferromagnetically below and undergoes several metamagnetic transitions in external magnetic fields. In zero applied magnetic field and below the temperature dependence of the spin-lattice relaxation rate T1 ^-1 ( T ) shows a large linear-in-T term, about two orders of magnitude higher than for the reference compound LaGa₂. This strong enhancement confirms the presence of low-energy excitations in the antiferromagnetic phase of NdGa₂ as was previously indicated by specific heat data. Above , T1 ^-1 ( T ) is dominated by an exponential term, which we associate with excitations between the lowest energy levels of the f-electron system. The separation of these energy levels is determined by exchange, crystal-field and Zeeman interactions. Received 3 September 1998 and Received in final form 3 November 1998