Volume collapse in the Kondo lattice

The α-γ transition of Ce and its compounds are explained within a compressible Kondo lattice model where the variation of |J|/D with volume is taken into account. We show that, contrary to the valence change model, the Kondo contribution is sufficient to induce a first order transition at low temperature from a magnetic to a Kondo phase. The disappearance of magnetism is then related to an extremely high Kondo temperature. Applications to Ce and CeAl₂ cases are given.     

Gauge invariance and spinon-dopon confinement in the t-J model: implications for Fermi surface reconstruction in the cuprates

We discuss the application of the two-band spin-dopon representation of the t-J model to address the issue of the Fermi surface reconstruction observed in the cuprates. We show that the electron no double occupancy (NDO) constraint plays a key role in this formulation. In particular, the auxiliary lattice spin and itinerant dopon degrees of freedom of the spin-dopon formulation of the t-J model are shown to be confined in the emergent U(1) gauge theory generated by the NDO constraint. This constraint is enforced by the requirement of an infinitely large spin-dopon coupling. As a result, the t-J model is equivalent to a Kondo-Heisenberg lattice model of itinerant dopons and localized lattice spins at infinite Kondo coupling at all dopings. We show that mean-field treatment of the large vs. small Fermi surface crossing in the cuprates which leaves out the NDO constraint, leads to inconsistencies and it is automatically excluded form the t-J model framework.     

On the competition between magnetic order and local Kondo effect in Kondo lattice

We investigate the competition between magnetic order and local Kondo effect in a Kondo lattice model (i.e. the Coqblin-Schrieffer Hamiltonian extended to a lattice) in a mean-field approximation, taking account of the spin-orbit degeneracy of each localized f level. This leads to the definition of a dependent Kondo temperature. We study the Kondo phase and compare its energy with the energies of magnetic phases, when the number of the conduction band electron per site is near one. We present a phase diagram which shows the occurrence of three phases: Kondo, antiferromagnetic and paramagnetic phases. Our model in the mean-field approximation also shows a somewhat flat Kondo temperature, for large values of , as a function of the exchange coupling J between conduction and localized f electrons. Finally we show some scaling effects between and J and we define a corresponding Kondo temperature. Received 21 September 1998 and Received in final form 8 February 1999     

Finite cell calculations on the periodic Anderson Hamiltonian

We report finite cell calculations on the one-dimensional periodic Anderson Hamiltonian. The ground state for two electrons per site is found to be an insulating non-magnetic singlet, which evolves continuously from the noninteracting U = 0 limit to the large U mixed valence and Kondo lattice regimes. The calculations for four sites given energy gaps which agree well with results for the infinite lattice in the few cases where they are known.     

Magnetic and non-magnetic ground states of the Kondo lattice

We use the variational method to investigate the ground state phase diagram of the Kondo lattice Hamiltonian for arbitraryJ/W, and conduction electron concentrationn _c (J is the Kondo coupling andW the bandwidth). We are particularly interested in the question under which circumstances the globally singlet (collective Kondo) Fermi liquid type ground state becomes unstable against magnetic ordering. For the collective Kondo singlet we use the lattice generalization of Yosida's wavefunction which implies the existence of a large Fermi volume, in accordance with Luttinger's theorem. Using the Gutzwiller approximation, we derive closed-form results for the ground state energy at arbitraryJ/W andn _c, and for the Kondo gap atn _c=1. We introduce simple trial states to describe ferromagnetic, antiferromagnetic, and spiral ordering in the small-J (RKKY) regime, and Nagaoka type ferromagnetism at largeJ/W. We study three particular cases: a band with a constant density of states, and the (tight binding) linear chain, and square lattice periodic Kondo models. We find that the lattice enhancement of the Kondo effect, which is described in our theory of the Fermi liquid state, pushes the RKKY-to-nonmagnetic phase boundary to much smaller values ofJ/W than it was previously thought. In our study of the square lattice case, we also find a region of itinerant, Nagaoka-type ferromagnetism at largeJ/W forn _c 1/3.     

Spin glass and ferromagnetism in Kondo lattice compounds

The Kondo lattice model has been analyzed in the presence of a random inter-site interaction among localized spins with non zero mean J₀ and standard deviation J. Following the same framework previously introduced by us, the problem is formulated in the path integral formalism where the spin operators are expressed as bilinear combinations of Grassmann fields. The static approximation and the replica symmetry ansatz have allowed us to solve the problem at a mean field level. The resulting phase diagram displays several phase transitions among a ferromagnetically ordered region,a spin glass one, a mixed phase and a Kondo state depending on J₀, J and its relation with the Kondo interaction coupling J_K. These results could be used to address part of the experimental data for the CeNi _{1 - x} Cu _x compound, when x ⩽ 0.8. Received 24 June 2002 Published online 31 December 2002     

Kondo lattice behaviour in CePt2(Si1−xSnx)2 alloys

Measurements of electrical resistivity are presented for polycrystalline alloys in the CePt₂(Si_1−xSn_x)₂ system. Results of X-ray diffraction indicate that the tetragonal region of the CePt₂(Si_1−xSn_x)₂ alloy system that is amenable for study only extends up to x=0.3. The resistivity maximum characteristic of a Kondo lattice is observed at a temperature T_max=63 K for the parent compound CePt₂Si₂ and shifts to lower temperatures with increase in Sn content. The compressible Kondo lattice model is applied to describe the results of T_max in terms of the on-site Kondo exchange interaction J and the electron density of states at the Fermi level N(E_F). A value of |JN(E_F)|=0.060±0.009 for the parent compound is obtained from the experimental results.     

On the chiral hubbard model and the chiral Kondo lattice model

The integrability of the one-dimensional chiral Hubbard model is discussed in the limit of strong interaction,U=. The system is shown to be integrable in the sense of the existence of an infinite number of constants of motion. The system is related to a chiral Kondo lattice model at strong interactionJ=+.     

The effect of pressure on the resistivity of a gold-chromium Kondo alloy and on the low temperature phonon resistivity of pure gold

The electrical resistivity of the Kondo alloy Au (20ppm Cr) and of pure gold has been determined in the temperature range 1.3 – 20 K at pressures up to 80 kbar. For pure gold the pressure dependence of the temperature dependent part of the lattice resistivity can be explained fairly well by the Bloch-Grüneisen theory. Expressions for the volume dependence of the ideal lattice resistivity and of the Debye-temperature for gold are derived. — The Kondo temperatureT _K of Au(Cr) is found to increase with pressure to more than twice the value atp=0 kbar.Therefrom the volume dependence of the effective exchange constantJ is calculated. The results are similar as in other Kondo alloys described previously.     

Half-filled Kondo lattice on the honeycomb lattice

The unique linear density of state around the Dirac points for the honeycomb lattice brings much novel features in strongly correlated models. Here we study the ground-state phase diagram of the Kondo lattice model on the honeycomb lattice at half-filling by using an extended mean-field theory. By treating magnetic interaction and Kondo screening on an equal footing, it is found that besides a trivial discontinuous first-order quantum phase transition between well-defined Kondo insulator and antiferromagnetic insulating state, there can exist a wide coexistence region with both Kondo screening and antiferromagnetic orders in the intermediate coupling regime. In addition, the stability of Kondo insulator requires a minimum strength of the Kondo coupling. These features are attributed to the linear density of state, which are absent in the square lattice. Furthermore, fluctuation effect beyond the mean-field decoupling is analyzed and the corresponding antiferromagnetic spin-density-wave transition falls into the O(3) universal class. Comparatively, we also discuss the Kondo necklace and the Kane-Mele-Kondo (KMK) lattice models on the same lattice. Interestingly, it is found that the topological insulating state is unstable to the usual antiferromagnetic ordered states at half-filling for the KMK model. The present work may be helpful for further study on the interplay between conduction electrons and the densely localized spins on the honeycomb lattice.     

Effect of substitution of Ce by La in the CeNixPt1 − x dense Kondo ferromagnets

The effects of substitution of Ce by La in the orthorhombic CeNi_{1 − x}Pt_x dense Kondo ferromagnets are studied by means of magnetization and electrical resistivity measurements. A decrease of the exchange RKKY interactions leads to a decrease of the Curie temperature T_c as a function of the La content and hence to an enhancement of the Kondo character in the thermal dependence of the resisitivity. However, the Ce moment is almost independent of the La amount. The Kondo temperature being also independent, this surprising result seems in contradiction with the available Kondo lattice models.     

Effect of pressure on the Kondo temperatures of Au(Fe) and Au(Mn)

The electrical resistivity of four Kondo systems, Au-(5 p.p.m. Fe), Au-(39 p.p.m. Fe), Au-(17 p.p.m. Mn) and Au-(50 p.p.m. Mn) has been measured in the temperature range 1.3–20 K at pressures up to 80 kbar. The Kondo temperature T_K is found to increase initially with pressure at the rate of 1.1%/kbar for Au(Fe) and 6%/kbar for Au(Mn). The volume dependence of the effective exchange constant J_eff is derived.     

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.     

On some low-temperature properties of (La, Ce)B6 alloys

Some recent experimental data on the magnetic susceptibility and the low-temperature magnetization of the (La, Ce)B₆ system are discussed in the light of the theoretical results. A value of the s-f exchange constant J is estimated which is also consistent with the results obtained from both the Kondo effect and the RKKY interaction.     

Electrical resistivity and magnetoresistance of (NiAl)1−xMx,M = 3d transition metals23

Transport properties were investigated in (NiAl)_1?xM_x, M = 3d transition metals, in order to examine the extrinsic nature of NiAl. Experimental results are well described by the s?d exchange (Kondo) theory from which exchange energy J, Kondo temperature T_k, and spin value S were estimated. A comparison between our results and the results from dilute alloys is made.     

Phase separation in the strongly correlated Falicov-Kimball model in infinite dimensions

Phase separation in the strongly correlated Falicov-Kimball model in infinite dimensions is examined. We show that the phase separation can occur for any values of the interaction constant J^* when the site energy of the localized electrons is equal to zero. Electron-poor regions always have homogeneous state and electron-rich regions have chessboard state for , chessboard state or homogeneous state in dependence upon temperature for 0<J ^* <0.03 and homogeneous state for J ^* =0. For J ^* =0 and T=0, phase separation (segregation) occurs at .The obtained results are exact for the Bethe lattice with infinite number of the nearest neighbours. Received 1 December 1998 and Received in final form 12 April 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     

Yb-Based Kondo Lattices: Insight from 170Yb Mössbauer, Positive Muon and γ–γ Perturbed Angular Correlations Spectroscopies

The usefulness of local hyperfine techniques in the investigation of the physical properties of Kondo lattices is illustrated through three examples. First, we show how Mössbauer spectroscopy on ¹⁷⁰Yb down to very low temperature (0.025 K) provides evidence for the existence of an incommensurate modulated magnetic structure close to T=0 in YbPtAl; a modulated structure at T=0 is in principle forbidden for Kramers ions, but it is made possible in YbPtAl due to the presence of the Kondo coupling. Second, we present a μSR study of the Kondo insulator YbB₁₂, and we evidence the persistence of fluctuations of very small correlated Yb moments close to T=0. Third, we report on a study by Perturbed Angular Correlation spectroscopy on the isotope ¹⁷²Yb of the Kondo lattice Yb₂Co₃Ga₉, which is characterised by a high Kondo temperature (T ₀?260 K). Our aim was to compare, on a large temperature range, the thermal variations of the 4f quadrupole moment and of the magnetic susceptibility, to check whether the scaling property predicted by theory could be observed.