On the theory of superconductivity in Kondo lattice systems

An attempt is made to explain the occurrence of superconductivity in Kondo lattice systems with special reference to CeCu₂Si₂. Starting point is the Fermi liquid approach. It is generalized from a Kondo impurity to the Kondo lattice by means of the Korringa-Kohn-Rostocker method. From it a hybridization model is derived and discussed in detail. Two electron-phonon mechanisms are investigated which appear in Kondo lattices. One results from the additional phase shifts caused by the Kondo ions while the other is responsible for the so-called Kondo volume collapse. It is shown that the latter is sufficiently strong in order to explain why CeCu₂Si₂ is a superconductor while LaCu₂Si₂ is not. An estimate for the superconducting transition temperatureT _c produces the right order of magnitude.     

Interpretation of neutron magnetic scattering in the Kondo lattices YbPd2Si2 and YbAgCu4

We present an interpretation of published neutron inelastic scattering spectra in the Kondo lattices YbPd₂Si₂ and YbAgCu₄ obtained in terms of the Anderson impurity model, describing the hybridisation of the 4f Yb electrons with the band electrons, and also including the crystal electric field interaction. In YbPd₂Si₂, the tetragonal crystal field parameters were determined. In YbAgCu₄ the crystal field interaction was taken to exist by analogy with the isoelectronic compound YbAuCu₄ where it has been identified. Both compounds can be described by a Kondo temperature,T ₀=60 K and a Yb valency very close to 3.     

ESR of Gd-impurities in the heavy fermion compounds CeCu2Si2 and CeAl3

The heavy fermion systems CeCu₂Si₂ and CeAl₃ are characterized by a huge quasiparticle density of states responsible for the large electronic specific heat. The observation of a Gd³⁺ electron spin resonance (ESR) in single crystals CeCu₂Si₂ and in polycrystalline CeAl₃ clearly demonstrates the local character of these quasiparticles. Nevertheless, the Gd-spin relaxation shows remarkable anomalies with respect to the isostructural compounds LaCu₂Si₂ and LaAl₃: Probably via RKKY coupling, Ce 4f-spin fluctuations give rise to an enhanced Gd-spin relaxation resulting in an unusual non-linear thermal broadening around the Kondo temperature. From this we obtain information about the temperature dependence of the Ce 4f-spin correlation time.     

Structural properties and band structure of heavy fermion systems: CeCu2Si2 and LaCu2Si2

The structure of CeCu₂Si₂, isotypic with ThCr₂Si₂, has been refined in a single-crystal study. The atomic parameters were used in self-consistent LMTO band structure calculations for CeCu₂Si₂ and isostructural LaCu₂Si₂. The results are analysed in terms of energy levels, charge distribution and in particular Fermi surface properties. The Ce-4f levels are situated mainly aboveE _F , except near the Γ-point. The density-of-states atE _F is large and heavily concentrated around the Ce-4f band. This makes local Ce 4f fluctuations possible, while interaction with the rest of the band structure is small. The comparison with LaCu₂Si₂ shows that the additional Cef electron is partly promoted into the non-f bands. Large enhancement factors are required to bring band results into agreement with observed specific heat and magnetic critical field. Strong Fermi surface anisotropies are pointed out for both compounds suggesting new experiments on single crystals.     

Calorimetric investigation under high pressure of the heavy fermion superconductor CeCu2Si2

The heavy fermion compound CeCu₂Si₂ is commonly regarded as a Kondo lattice system. Though it has been shown that the heavy mass quasiparticles participate in its superconductivity below ～ 0.7 K, a detailed understanding of the interdependence of the superconducting and the Kondo lattice parameters is still to be developed. The application of pressure is one useful approach to study this problem. In this paper we present results of specific heat measurements between 0.3 K and 2 K under pressures up to 5.9 kbar. While in our sample T_c hardly changes, the normal state specific heat, which is exclusively of electronic origin in the present temperature range, is rapidly decreased in a monotonous way, qualitatively corresponding to the expected rise of the Kondo temperature with pressure. In contrast to this behaviour, a strong nonlinear change of the jump Δc(T_c) passing through a maximum near 3 kbar is observed. We suggest that this reflects changes of the Kondo lattice coherence structure in the quasiparticle density of states near E_F.     

One particle excitation spectrum of the Kondo-lattice

The renormalized time ordered perturbation approach for the (impurity -) Anderson model with respect to hybridization is combined with a random walk treatment of coherent scattering in order to calculate the one particle excitation spectrum of an Anderson lattice in the Kondo regime. It is found that the Kondo resonance at the Fermi-level splits into two narrow peaks. With decreasing temperature a gap develops in between these peaks due to coherence effects. These results furnish a more rigorous basis for phenomenological theories explaining experimental data in Kondo lattice systems like CeCu₂Si₂.     

Crystal-field effects in the intermediate-valence compound YbCu2Si2

Inelastic thermal-neutron scattering is used to study the intermediate-valence system YbCu₂Si₂. The magnetic scattering in two nonoverlapping ranges of transfer energies, 2<ε<5 meV and 5<ε<100 meV, is analyzed under the assumption that the regions influence each other only weakly. As a result, two sets of phenomenological crystal-field parameters are established, and their difference constitutes the experimental error in determining these parameters. A comparison of the fourth-order crystal field with other compounds belonging to the RCu₂Si₂ series (R stands for a rare-earth element) suggests that in YbCu₂Si₂ hybridization occurs between f electrons and copper electrons, in contrast to the heavy-fermion system CeCu₂Si₂, for which it was established earlier that hybridization occurs between f electrons and Si p electrons. Zh. éksp. Teor. Fiz. 114, 291–314 (July 1998)     

Upper critical field of a superconductor with arbitrary spin-orbit scattering: CeCu2Si2 and UBe13

The upper critical field is determined for an even-parity singlet pairing state in the presence of arbitrary spin-orbit scattering. Comparison with critical field experiments suggests that superconductivity in CeCu₂Si₂ is a singlet pairing state, and in UBe₁₃ is either a triplet pairing state or is a singlet state with restrictive conditions that the pair orbital be nearly isotropic and that strong spin-orbit scattering increase strongly as the field increases.     

Synchrotron X-ray diffraction and absorption studies of CeM2X2 (M=Cu, Ni and X=Si, Ge) at high pressure

The equations of state of CeCu₂Si₂ and CeCu₂Ge₂ to about 60 GPa, as well as that of CeNi₂Ge₂ to 22 GPa and the valence state of Ce in CeCu₂Ge₂ to 20 GPa have been studied at room temperature in a diamond-anvil cell using synchrotron radiation sources. In each compound, the ambient-pressure phase (tetragonal ThCr₂Si₂-type structure) persisted to the highest pressure studied. The unit cell volumes of CeNi₂Ge₂ at ∼5 GPa and CeCu₂Ge₂ at ∼7 GPa, respectively, approached that of CeCu₂Si₂ taken at ambient pressure. From the equation-of-state data, the bulk modulus was derived to be 112.0±5.1 GPa for CeCu₂Si₂, 125.6±4.3 GPa for CeCu₂Ge₂, and 178.4±14.3 GPa for CeNi₂Ge₂. The valence state of Ce in CeCu₂Ge₂ remained trivalent throughout the pressure range investigated.     

Electron spin resonance investigation of the Heavy-Fermion compound CeCu2(Si1−x Ge x )2

The Kondo-lattice system CeCu₂(Si_1?x Ge _x )₂ exhibits an alloying induced transition from a coherent Fermi-liquid (x=0) with strongly enhanced effective masses to an antiferromagnetically ordered heavy-fermion system (x=1). This transition is studied by Gd³⁺ ESR in oriented powder samples. The temperature dependence of the ESR line width follows a characteristic pattern which allows one to distinguish between the different ground states. The results obtained in polycrystalline CeCu₂Si₂ are in good agreement with the measurements performed in single crystals. Finally we compare our results with⁶³Cu-NMR data obtained from CeCu₂Si₂ and CeCu₂Ge₂.     

Magnetic order in a Kondo lattice: A neutron scattering study of CeCu2Ge2

Elastic and inelastic neutron scattering studies of the Kondo lattice CeCu₂Ge₂ were performed. AtT _N=4.1 K an incommensurate magnetic order develops with an ordering wave vectorq ₀=(0.28, 0.28, 0.54) and an ordered moment µ _s =0.74 µB. The crystalline electric field splits the 4f ¹-J-multiplet of the Ce ion into a ground state doublet and a quartet at 191 K. The wave function of the ground state yields an ordered moment of 1.54µB. Thus, due to the onset of the formation of a Kondo singlet the magnetic moment is considerably reduced. The magnetic relaxation rate was investigated via quasielastic neutron scattering. The temperature dependence of (T) is characteristic of heavy-fermion systems with a high temperature square root dependence and a limiting low temperature value, yielding a Kondo temperatureT _K10K. The quasielastic component of the scattered neutron intensities persists down to the lowest temperatures, well belowT _N. This quasielastic line is regarded as a characteristic feature of heavy-fermion systems and corresponds to the enhanced value of the linear term of the specific heat.     

Superconductivity in heavy fermion systems

The heavy fermion state in the f-electron systems is due to competition between the RKKY interaction and the Kondo effect. The typical compound is CeCu₆. To understand the electronic state, we studied the Fermi surface properties via the de Haas–van Alphen (dHvA) experiment and energy band calculation for CeSn₃,CeRu₂Si₂,UPt₃, and nowadays, transuranium compounds. Pressure is also an important technique to control the electronic state. The Néel temperature T_N decreases with increasing pressure P and becomes zero at the critical pressure for . The typical compound is an antiferromagnet CeRhIn₅, which we studied from the dHvA experiment under pressure. A change of the 4f-electronic state from localized to itinerant is realized at , revealing the first-order phase transition, together with a divergent tendency of the cyclotron mass at P_c. It is stressed that appearance of superconductivity in CeRhIn₅ is closely related to the heavy fermion state. It is also noted that the parity-mixed novel superconducting state might be realized in a pressure-induced superconductor CeIrSi₃ without inversion symmetry in the crystal structure.     

EPR study of exchange interactions in the nonmagnetic Kondo system La1−x CexCu6

The EPR of paramagnetic impurities Gd³⁺ and Mn²⁺ was studied in nonmagnetic Kondo system La_1−x Ce_xCu₆ containing in the 1.6–200 K range. The exchange interaction parameters of gadolinium and manganese ions with conduction electrons, of cerium ions with conduction electrons and with one another, the Kondo temperature of cerium ions, and the temperature behavior of cerium-ion spin-fluctuation rate have been determined. A pseudogap in the density of states at the Fermi level has been detected in the CeCu₆ regular system, which is apparently due to s-f hybridization. This pseudogap can be destroyed by introducing an aluminum impurity, which induces strong conduction-electron scattering. It was also found that RKKY interaction among manganese ions in CeCu_6−y Mn_y is considerably stronger than it is in LaCu_6−y Mn_y, which implies enhancement of nonlocal spin susceptibility due to an f band contribution to conduction-electron states. Fiz. Tverd. Tela (St. Petersburg) 40, 593–599 (April 1998)     

First-principles calculations on TiO2 doped by N, Nd, and vacancy

First-principles density functional theory calculations have been carried out to investigate electronic structures of anatase TiO₂ with substitutional dopants of N, Nd, and vacancy, which replace O, Ti, and O, respectively. The calculation on N-doped TiO₂ with the local density approximation (LDA) demonstrates that N doping introduces some states located at the valence band maximum and thus makes the original band gap of TiO₂ smaller. Examining the effect of the strong correlation of Nd 4f electrons on the electronic structure of Nd-doped TiO₂, we have obtained the half-metallic ground state with the LDA and the insulating ground state with the LDA+U (Hubbard coefficient), respectively. In addition, the calculation on vacancy-doped TiO₂ with the LDA shows that a vacancy can induce some states in the band-gap region, which act as shallow donors.     

Crystal field in valence-fluctuating CeNi-based compounds

The effects of the crystal field (CF) on the paramagnetic Pr ion in a number of compounds of the type R_1−x Pr_xNi (R = Ce, La, Y), in which a transition of the cerium ions from an intermediate-valence into a Kondo state occurs as La is substituted for Ce, are investigated. The level schemes of the Pr ion in the CF are reconstructed from inelastic neutron scattering spectra and the temperature dependence of the heat capacity in different magnetic fields (B=0–8 T). The parameters of the low-symmetry CF in the compounds RNi are determined from the experimental data. It is established that in the Kondo regime the hybridization of the f electrons with conduction electrons only gives a proportional increase in all the parameters of the CF potential. At the same time, partial delocalization of the f electrons in the intermediate-valence state results in charge redistribution, which is manifested in different scales for the changes in the different CF parameters. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 12, 947–952 (25 June 1996)     

Peculiarities of crystal field effects in CeInCu2 based heavy-fermion compounds

We have studied the evolution of the inelastic neutron magnetic scattering spectra of a compound with cubic symmetry, CeInCu₂, in the temperature range 10–130 K, and also their transformation with variation of the Kondo temperature T _K due to substitution of cerium ions in the system Ce_1−x (La,Y)_xInCu₂ at T=10 K. It turns out that the energy of the transition between the ground state and excited state of the 4 f electrons (Δ_CF) in the crystal electric field in CeInCu₂ increases with growth of the population of the ground state as the temperature is reduced, with a slight change in its intensity. Such behavior is inconsistent with the notion of classical one-ion effects of the crystal electric field. We have found that the scale of the observed variations in the excitation spectra of the 4f electrons depends on the Kondo temperature T _K and is insensitive to disorder in the rare-earth sublattice. Thus, despite the fact that T _K ≪Δ_CF, hybridization with states in the conduction band has a substantial effect on all parameters of the excitation spectrum of the ground multiplet of the 4f electrons at low temperatures. Zh. éksp. Teor. Fiz. 115, 2197–2206 (June 1999) A. A. Baikov Institute of Metallurgy     

Superconductivity in CeCu2Si2

Resistivity measurements of CeCu₂Si₂ are carried out under pressures p up to 12 kbars. Unlike polycrystalline samples, no traces of superconductivity have been observed in CeCu₂Si₂ at ambient pressure. When pressure is applied, CeCu₂Si₂ monocrystals become superconducting with anomalously large ratio H_c2(0)/T_c (0) = 34 K0e/K and with the derivative dH_c2/dT(T=T_c) = 140 K0e/K     

Low temperature properties of a new compound based on (Yb,Zr)B<Subscript>12</Subscript> substitution

The thermodynamic, kinetic, and magnetic characteristics of (Yb, Zr)B₁₂ have been investigated in detail in the temperature range from 4 to 300 K to reveal the effect of the band structure on the properties of the YbB₁₂ Kondo insulator ground state. It is found that electron doping due to 20% substitution in the Yb sublattice significantly changes the properties of the low-temperature ground state of YbB₁₂ Kondo insulator and only slightly affects the high-temperature spin-fluctuating state forming at T > 50 K.     

Magnetic properties of CePd2Ga3

Field dependent specific heat measurements and a study of elastic neutron scattering experiments characterize CePd₂Ga₃ as a ferromagnetic Kondo compound with ordering in the basal plane belowT _C 6 K. The crystal field ground state of cerium in this hexagonal compound is the |±1/2> eigenstate. In the scope of a phenomenological model, the coupling constant and the Kondo temperature have been deduced.     

X-ray photoemission spectra measurements of CeNi2Sb2 and CeCu2Sb2

X-ray photoemission spectra, resistivity and susceptibility of CeNi₂Sb₂ and CeCu₂Sb₂ were measured and are discussed. The results indicate that these alloys are Kondo systems. For comparison of the valence band properties, the spectra of the isostructural alloys of RT₂X₂-type with R = La, Gd, T = Cu, Ni and X = Sn, Sb were investigated, too.