Kondo effect,spin dynamics and magnetism in anomalous rare earth and actinide compounds

The influence of spin dynamics on the Kondo effect manifestations in the Kondo lattices is investigated within perturbation theory with respect to thes-f interaction. It may give rise to Kondo-like divergencies in the electron self-energy already in the second order, resulting in an appreciable effective mass enhancement. As for usual Kondo contributions to thermodynamic and transport properties, the effect of spin dynamics reduces roughly to the replacement ln , with the characteristic spin-fluctuation energy. The thermoelectric power of dense Kondo systems is discussed. Singular contributions to the electron self-energies in the ferro-and antiferromagnetic state are considered. Kondo-like corrections to the intersite exchange interactions, saturation magnetic moment and total energy in a magnetically ordered state are calculated. The strong-coupling regionT<T _K is investigated within the Anderson lattice model. A decrease ofT _K due to spin fluctuations is demonstrated.     

Concentrated Kondo systems

This review considers the experimental and theoretical studies of concentrated Kondo systems (CKS), Kondo lattices, substitutional solid solutions and their transition from Kondo impurity to Kondo lattice, and ‘intermediate valence compounds’ which are, in fact, high T _K CKS (T _K is the Kondo temperature). The anomalous low temperature properties of CKS are related to the formation of the narrow (～k _B T _K) high-amplitude Abrikosov-Suhl resonance E _R in the vicinity of the Fermi level E _F. This resonance is situated exactly at E _F in low T _K CKS with T _K < Δ_CF and near E _F in high T _K CKS with T _K > Δ_CF (Δ_CF is the crystal field splitting). In low T _K ‘j=1/2’ CKS the condition E _R=E _F leads to an increase of the density of states at E _F, which is large enough to induce heavy fermion superconductivity in CeCu₂Si₂, UBe₁₃. We demonstrate that the transition from low T _K (E _R=E _F) to high T _K CKS (E _R≠E _F) might be what was formerly considered as a ‘Kondo-lattice-intermediate valence state’ transition. It appears that in many cases the essentially non-integer valence state of the rare-earth elements in metallic compounds is thermodynamically unstable with respect to a transition to an almost integer valence state, because it realizes the maximum gain in free energy from the Kondo condensation.     

Pseudogap and symmetry of superconducting order parameter in cuprates

The phase diagram, nature of the normal state pseudogap, type of the Fermi surface, and behavior of the superconducting gap in various cuprates are discussed in terms of a correlated state with valence bonds. The variational correlated state, which is a band analogue of the Anderson (RVB) states, is constructed using local unitary transformations. Formation of valence bonds causes attraction between holes in the d-channel and corresponding superconductivity compatible with antiferromagnetic spin order. Our calculations indicate that there is a fairly wide range of doping with antiferromagnetic order in isolated CuO₂ planes. The shape of the Fermi surface and phase transition curve are sensitive to the value and sign of the hopping interaction t′ between diagonal neighboring sites. In underdoped samples, the dielectrization of various sections of the Fermi boundary, depending on the sign of t′, gives rise to a pseudogap detected in photoemission spectra for various quasimomentum directions. In particular, in bismuth-and yttrium-based ceramics (t′>0), the transition from the normal state of overdoped samples to the pseudogap state of underdoped samples corresponds to the onset of dielectrization on the Brillouin zone boundary near k=(0,π) and transition from “large” to “small” Fermi surfaces. The hypothesis about s-wave superconductivity of La-and Nd-based ceramics has been revised: a situation is predicted when, notwithstanding the d-wave symmetry of the superconducting order parameter, the excitation energy on the Fermi surface does not vanish at all points of the phase space owing to the dielectrization of the Fermi boundary at k _x=± k _y. The model with orthorhombic distortions and two peaks on the curve of T _c versus doping is discussed in connection with experimental data for the yttrium-based ceramic. Zh. éksp. Teor. Fiz. 115, 649–674 (February 1999)     

Quantum temperature fluctuations in the magnetization of antiferromagnetic semimetals

It is shown that in semimetallic, low-temperature antiferromagnetic materials located in a quantizing magnetic field, the part of the band magnetization M _∼ which oscillates in H can have a nonmonotonic temperature dependence. This non-Fermi liquid behavior will show up experimentally in the form of quantum temperature fluctuations of the magnetization when the decrease with rising temperature is oscillatory, rather than the usual monotonic decrease. It is shown that the magnetization from an individual spin electron (or hole) subband has the form of weakly damped periodic oscillations as a function of T ². This result makes it possible to develop an efficient method for studying the electronic structure of antiferromagnetic semimetals based on an examination of the quantum temperature fluctuations. Calculations show that quantum temperature fluctuations can be observed, for example, in the cerium monopnictides CeP and CeAs, which are strongly correlated, antiferromagnetic, compensated semimetals with low Neel temperatures. Fiz. Tverd. Tela (St. Petersburg) 40, 1674–1680 (September 1998)     

Field and pressure studies of Ce2Pd2In

Various measurements performed on the new ternary compound Ce₂Pd₂In indicate Kondo type interaction (T _K ≈1K) in the presence of strong crystal field splitting. Both an antiferromagnetic and a ferromagnetic transition were observed (T _N =4.4 K,T _C =3.8 K). Work supported by the Austrian FWF, P10269.     

Experimental study of electrical conduction in RuO2-based thick resistive films

We have found direct evidence for the dynamical instability of Pr, which could be observed in Pr_0.015 Pd by inelastic neutron scattering, and as such is first ever to be found for Pr ions. Crystalfield analysis of the measured dynamic susceptibility reveals that the spin instability is similar to that of Ce Kondo systems. We show that the previously observed resistivity increase belowT=25 K is a true Kondo effect and is not related to crystal field effects. We conclude that Pr diluted in Pd is a Kondo system withT _K =2.5 K.     

Thermoelectric power of heavy-fermion compounds

We calculate the diffusion thermopower of the Anderson lattice as a model for heavyfermion compounds in a semi-phenomenological theory. In this theory, the thermopower is expressed by the dynamical susceptibility which describes spin fluctuations and can be measured by neutron scattering. The Kondo effect is taken into account for a singlef-electron spin which is coupled to all other spins and to the conduction electrons. This approach neglects multiple intesite-scattering of the conduction electrons. We obtain a Kondo termS ₍₁₎ ^d (T) (in which the thermopower of non-interacting spins is multiplied by a factor which describes the spin dynamics) and a resonance termS ₍₂₎ ^d (T) of opposite sign which vanishes for vanishing interactions. The superposition of both terms leads to a broad maximum of the thermopower roughly at the Kondo temperatureT _K and to an additional minimum belowT _K . ForT0 the termS ₍₁₎ ^d vanishes asT ² and the termS ₍₂₎ ^d becomes proportional toT. We also show that the Sommerfeld expansion leads to an incorrect result for the low temperature resistivity of the Anderson lattice and that the Gorter-Nordheim relation does not hold at low temperatures.     

Local magnetism of Ce in the Kondo lattice compound CeFeGe3

Local magnetism of Ce in the Kondo lattice compound CeFeGe₃ studied by measuring local susceptibility χ_loc at ¹⁴⁰Ce probe site using TDPAC method is presented. The magnitude and temperature dependence of χ_loc reflect Kondo behaviour with Kondo temperature T_K∼150 K. This revised version was published online in August 2006 with corrections to the Cover Date.     

Numerical renormalization group studies of SU(4) Kondo effect in quantum dots

We theoretically study an enhancement of the Kondo effect in quantum dots with two orbitals and spin . The Kondo temperature and conductance are evaluated as functions of energy difference Δ between the orbitals, using the numerical renormalization group method. The Kondo temperature is maximal around the degeneracy point (Δ=0) and decreases with increasing |Δ| following a power law, T_K(Δ)=T_K(0)(T_K(0)/|Δ|)^γ, which is consistent with the scaling analysis. The conductance at T=0 is almost constant 2e²/h. Both the orbitals contribute to the conductance around Δ=0, whereas the current through the upper orbital is negligibly small when |Δ|T_K(0). These are characteristics of SU(4) Kondo effect.     

Singlet-triplet Hamiltonian for spin excitations in a Kondo insulator

In the nonsymmetric version of the periodic Anderson model for a Kondo insulator, an effective singlet-triplet Hamiltonian Ĥ _s−t with indirect antiferromagnetic f-f exchange is constructed, which makes it possible to analyze the dynamic magnetic susceptibility χ _f (k, ω) of f electrons. Hamiltonian Ĥ _s−t is used to describe the experimentally observed dispersion of the three-level spin excitation spectrum in YbB₁₂. A distinguishing feature of this analysis is the introduction of small-radius singlet and triplet collective f-d excitations that form low- and high-lying spin bands during motion over the lattice.     

Classical spin liquid properties of the infinite-component spin vector model on a fully frustrated two dimensional lattice

Thermodynamic quantities and correlation functions (CFs) of the classical antiferromagnet on the checkerboard lattice are studied for the exactly solvable infinite-component spin-vector model, D↦∞. In contrast to conventional two-dimensional magnets with continuous symmetry showing extended short-range order at distances smaller than the correlation length, r ξ _c∝ exp(T ^*/T), correlations in the checkerboard-lattice model decay already at the scale of the lattice spacing due to the strong degeneracy of the ground state characterized by a macroscopic number of strongly fluctuating local degrees of freedom. At low temperatures, spin CFs decay as < >∝ 1/r ² in the range a ₀≪r≪ξ _c∝T ^-1/2, where a₀ is the lattice spacing. Analytical results for the principal thermodynamic quantities in our model are very similar with MC simulations, exact and analytical results for the classical Heisenberg model (D = 3) on the pyrochlore lattice. This shows that the ground state of the infinite-component spin vector model on the checkerboard lattice is a classical spin liquid. Received 16 November 2001 and Received in final form 12 February 2002     

Incoherent Kondo ground state in CeCu1.54Si1.46

Measurements of the magnetic susceptibility, magnetization, specific heat and electrical resistivity on a new Kondo lattice compound CeCu_1.54Si_1.46 have revealed an antiferromagnetic phase transition at 6.9 K. The analysis of the specific heat demonstrates that this compound is a moderately heavy electron system with strong spin fluctuations. Based on the resistivity result, we maintain that the coherence between Kondo states at Ce sites is hindered by the disorder in the Cu and Si sublattice in this non-stoichiometric compound.     

Pseudo spin gap in high‐Tc oxides observed by NMR

From the temperature dependence of the ⁶³Cu nuclear spin‐lattice relaxation rate, 1/T₁T, in the planar Cu(2) sites, it is now well established that a highly enhanced and strongly temperature dependent relaxation process due to antiferromagnetic Cu spin fluctuations exists in all of the high‐T_c’s. The data also exhibit the opening of a gap in the low‐lying magnetic excitations with an energy comparable to the superconducting gap, particularly for the so‐called low doping regime. It is also found that, irrespective of the system, the temperature at which the spin‐gap opens, T_sg, determined as the peak of 1/T₁T vs. T, has a linear decrease with increasing of the doping concentration. A spin‐gap phase diagram is proposed. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the behaviour of the new Kondo lattice CeCuAl3

The temperature dependence of the electrical resistivity, thermopower, specific heat, susceptibility and magnetization of CeCuAl₃ are presented. CeCuAl₃ behaves as a Kondo lattice system with antiferromagnetic ground state properties (T _N 2.8 K). The valency of Ce in this tetragonal compound is close to 3 and the overall crystal field splitting found from our results is about 150 K. The Kondo temperatureT _K in the crystal field ground state, estimated from the magnetic susceptibility and the specific heat, is of the order of 8 K.     

Low-frequency spin dynamics in the CeMIn5 materials

We measure the spin lattice relaxation of the planar In(1) nuclei in the CeMIn5 materials, extract quantitative information about the low energy spin dynamics of the lattice of Ce moments in both CeRhIn5 and CeCoIn5, and identify a crossover in the normal state. Above a temperature T(*) the Ce lattice exhibits "Kondo gas" behavior characterized by local fluctuations of independently screened moments; below T(*) both systems exhibit a "Kondo liquid" regime in which interactions between the local moments contribute to the spin dynamics. Both the antiferromagnetic and superconducting ground states in these systems emerge from the Kondo liquid regime. Our analysis provides strong evidence for quantum criticality in CeCoIn5.     

Quantum spin liquid on 2D rectangular frustrated AF lattice

The state of a 2D rectangular spin lattice with first, second and third nearest-neighbour anisotropic antiferromagnetic interactions is investigated. In a special line of parameter space, it is proved that the quantum spin liquid is the exact eigenstate of the system. For general parameter values, Green's function method with cut-off approximation is used to determine the phase diagram at zero temperature, and it is found that the quantum spin liquid appears on a rectangular lattice when the third nearest-neighbour interaction in the direction with shorter lattice spacing is introduced. The relations to the possibility of mixture of the spin liquid and the Fermi liquid in high-T _c superconductors are discussed.     

Resistance maximum across the spin glass to Kondo transition

In a recent theory of the noise model of alloys like AuFe a singular point at zero temperature was found to separate a spin glass phase at high concentrations and a Kondo phase at low concentrations. Despite this there is a resistance maximum in both “phases”, although of different characters. In the present letter a relation is given between the temperature of the maximum, T_m, the noise temperature, Δ_c, and the Kondo temperature, T_K. This extends a previously given expression, that is only valid in the spin glass limit Δ_c >> T_K, across the transition at Δ_c = T_K into the Kondo phase and values of Δ_c less than T_K.     

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