ESR study of the undoped heavy-fermion compound YbRh2Si2

The electron spin resonance (ESR) of the heavy-fermion metal YbRh₂Si₂ has been studied. The angular variation and the temperature dependence of the ESR line width have been measured in YbRh₂Si₂ single crystals in the temperature range of 4–25 K. The characteristic spin-fluctuation temperatureT ^* ～ 17 K estimated from these studies coincides very well with other experimental data. A well-behaved ESR signal due to local Yb³⁺ moments strongly supports the localized moment scenario for heavy-fermion quantum critical points.     

Nature of the quantum critical point as disclosed by extraordinary behavior of magnetotransport and the lorentz number in the heavy-fermion metal YbRh2Si2

Physicists are engaged in vigorous debate on the nature of the quantum critical points (QCP) governing the low-temperature properties of heavy-fermion metals. Recent experimental observations of the much-studied compound YbRh₂Si₂ in the regime of vanishing temperature incisively probe the nature of its magnetic-field-tuned QCP. The jumps revealed both in the residual resistivity ??₀ and the Hall resistivity R _H, along with violation of the Wiedemann-Franz law, provide vital clues to the origin of such non-Fermi-liquid behavior. The empirical facts point unambiguously to association of the observed QCP with a fermion-condensation phase transition. Based on this insight, the resistivities ??₀ and R _H are predicted to show jumps at the crossing of the QCP produced by application of a magnetic field, with attendant violation of the Wiedemann-Franz law. It is further demonstrated that experimentally identifiable multiple energy scales are related to the scaling behavior of the effective mass of the quasiparticles responsible for the low-temperature properties of such heavy-fermion metals.     

Unconventional superconductivity

‘Conventional’ superconductivity, as used in this review, refers to electron–phonon-coupled superconducting electron pairs described by BCS theory. Unconventional superconductivity refers to superconductors where the Cooper pairs are not bound together by phonon exchange but instead by exchange of some other kind, e.g. spin fluctuations in a superconductor with magnetic order either coexistent or nearby in the phase diagram. Such unconventional superconductivity has been known experimentally since heavy fermion CeCu₂Si₂, with its strongly correlated 4f electrons, was discovered to superconduct below 0.6?K in 1979. Since the discovery of unconventional superconductivity in the layered cuprates in 1986, the study of these materials saw T_c jump to 164?K by 1994. Further progress in high-temperature superconductivity would be aided by understanding the cause of such unconventional pairing. This review compares the fundamental properties of 9 unconventional superconducting classes of materials – from 4f-electron heavy fermions to organic superconductors to classes where only three known members exist to the cuprates with over 200 examples – with the hope that common features will emerge to help theory explain (and predict!) these phenomena. In addition, three new emerging classes of superconductors (topological, interfacial – e.g. FeSe on SrTiO₃, and H₂S under high pressure) are briefly covered, even though their ‘conventionality’ is not yet fully determined.     

Muon spin relaxation in CeCu2Si2 and muon knight shift in various heavy-fermion systems

Positive muon spin precession has been observed in various heavy-fermion systems in the transverse external magnetic field. In the superconductor CeCu_2.1Si₂, the relaxation rate of muon spins increases rapidly with decreasing temperature below T_C. This is interpreted as the results of the inhomogeneous fields due to the imperfect penetration of the external field into the type-II superconducting state. The magnetic-field penetration depth λ is derived from the observed muon spin relaxation rate. λ is about 1200 ∢ at T∼0.5T_C, and the temperature dependence of λ is consistent with the relation expected for a BCS superconductor. We have also measured the muon Knight shift K_μ in the normal (or paramagnetic) state of various heavy-fermion systems. K_μ is large and negative (about −1000∼−3000 ppm at T=10 K) for CeCu₂Si₂, UPt₃ and CeAl₃, while more complicated signals are measured in CePb₃ and CeB₆. The negative muon Knight shift in the non-magnetic heavy-fermion systems is discussed in terms of the Kondo-coupling between the conduction- and f-electrons.     

Fermi-liquid instability at magnetic–nonmagnetic quantum phase transitions

In metals with strong electronic correlations such as heavy-fermion systems or itinerant-electron magnets it is possible to change from a magnetically ordered to a nonmagnetic groundstate by variation of an external parameter such as composition or pressure. In principle a transition between these groundstates can occur at zero temperature. In case of a continuous transition quantum fluctuations take the role of thermal fluctuations in finite-temperature transitions. The abundance of low-lying magnetic excitations leads in the vicinity of the quantum critical point to unusual behavior of thermodynamic and transport properties at low temperatures T not envisioned by the classical Fermi-liquid behavior that is observed even in strongly correlated electron systems away from the quantum phase transition. We discuss in detail a few examples of this ‘non-Fermi-liquid behavior', viz., CeCu_6−xAu_x, Ce_1−xLa_xRu₂Si₂, Ce₇Ni₃, CeCu₂Si₂ and CeCu₂Ge₂, CePd₂Si₂, and UCu_1−xPd_x. In CeCu_6−xAu_x the very unusual low-T behavior of the linear specific-heat coefficient C/T−ln(T/T₀) and of the resistivity ΔρT can be attributed to quasi-two-dimensional fluctuations as determined from inelastic neutron scattering. The systems CeCu₂Ge₂ and CePd₂Si₂ are particuarly interesting since here the magnetic order which is suppressed under hydrostatic pressure gives way to superconductivity, suggesting that spin fluctuations mediate the formation of Cooper pairs at least in the latter system.     

Magnetism, f-electron localization and superconductivity in 122-type heavy-fermion metals

Both CeCu2Si2 and YbRh2Si2 crystallize in the tetragonal ThCr2Si2 crystal structure. Recent neutron-scattering results on normal-state CeCu2Si2 reveal a slowing down of the quasielastic response which complies with the scaling expected for a quantum critical point (QCP) of itinerant, i.e., three-dimensional spin-density-wave (SDW), type. This interpretation is in full agreement with the non-Fermi-liquid behavior observed in transport and thermodynamic measurements. The momentum dependence of the magnetic excitation spectrum reveals two branches of an overdamped dispersive mode whose coupling to the heavy charge carriers is strongly retarded. These overdamped spin fluctuations are considered to be the driving force for superconductivity in CeCu2Si2 (Tc = 600 mK). The weak antiferromagnet YbRh2Si2 (TN = 70 mK) exhibits a magnetic-field-induced QCP at BN = 0.06 T (B⊥c). There is no indication of superconductivity down to T = 10 mK. The magnetic QCP appears to concur with a breakdown of the Kondo effect. Doping-induced variations of the average unit-cell volume result in a detachment of the magnetic and electronic instabilities. A comparison of the properties of these isostructural compounds suggests that 3D SDW QCPs are favorable for unconventional superconductivity. The question whether a Kondo-breakdown QCP may also give rise to superconductivity, however, remains to be clarified.     

Unusual behavior of nuclear relaxation in CeCu2Si2 “possible evidence for triplet superconductivity”

Nuclear relaxation of ⁶³Cu in the superconducting state of the Kondo-lattice system CeCu₂Si₂ has been studied with the use of the ⁶³Cu nuclear quadrupole resonance technique under zero field and down to 65mK. The nuclear spin-lattice relaxation rate (1/T₁) decreases drastically just below T_c=0.67 K down to 0.5T_c without the apparent enchanced behavior and then is found to be almost temperature independent below 0.3T_c. These results suggest that the superconductivity in CeCu₂Si₂ is not in the usual BCS regime. The analysis based upon the existing triplet pairing model with an anisotropic energy gap describes well the behavior from T_c down to 0.5T_c, while the temperature independence below 0.3T_c remains unexplained.     

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.     

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     

Coexistence model of anisotropic electron hole pairing and unconventional superconductivity in Heavy Fermion compounds

Various Heavy Fermion compounds exhibit unconventional superconductivity together with another electronic instability like a spin density wave or possibly a more general type of anisotropic electron-hole pairing, e.g. a spin nematic state. The coexistence behaviour of these order parameters is studied within a simple weak coupling model. It is found that depeding on the symmetry of the order parameters coexistence or phase expulsion may occur. Whereas the former case is possibly realized for theU-based superconductors, CeCu₂Si₂ may be an example of the second case as observed and discussed in the context of elastic constant anomalies.     

Behavior of the antiferromagnetic phase transition near the fermion condensation quantum phase transition in YbRh2Si2

Low-temperature specific-heat measurements on YbRh₂Si₂ at the second order antiferromagnetic (AF) phase transition reveal a sharp peak at TN=72 mK. The corresponding critical exponent α turns out to be α=0.38, which differs significantly from that obtained within the framework of the fluctuation theory of second order phase transitions based on the scale invariance, where α?0.1. We show that under the application of magnetic field the curve of the second order AF phase transitions passes into a curve of the first order ones at the tricritical point leading to a violation of the critical universality of the fluctuation theory. This change of the phase transition is generated by the fermion condensation quantum phase transition. Near the tricritical point the Landau theory of second order phase transitions is applicable and gives α?1/2. We demonstrate that this value of α is in good agreement with the specific-heat measurements.     

Are heavy-fermion metals Fermi liquids?

We present the results of specific-heat and resistivity measurements as a function of temperature, magnetic field and hydrostatic pressure on the Kondo lattice CeNi₂Ge₂, the heavy-fermion superconductors CeCu₂Si₂ and UBe₁₃ as well as the low-carrier-density system Yb₄As₃. “Non-Fermi-liquid” effects in the low-temperature normalstate properties of the three former systems are consistent with the existence of a “nearby” quantum critical point, presumably of antiferromagnetic type. Yb₄As₃, though showing the outward appearance of a Landau-type heavy-fermion metal, behaves very differently, i.e. as an extreme two-fluid system.     

Exotic superconducting state embedded in the hidden order state of URu2Si2

The heavy-fermion compound URu₂Si₂ has mystified researchers since the superconducting state (T_c = 1.45 K) is embedded within the enigmatic ‘‘hidden order” phase (T_h = 17.5 K). Here, we report charge and thermal transport measurements on ultraclean single crystals of URu₂Si₂ with very large residual-resistivity-ratio down to 30 m K (∼T_c/50), which reveal a number of unprecedented superconducting properties. The results provide strong evidence for a new type of unconventional superconductivity with two distinct gaps having different nodal topology. We propose a gap function with chiral d-wave form Δ(k) = Δ₀k_z(k_x + ik_y). We also demonstrate that a distinct flux line lattice melting transition with outstanding characters occurs well below the upper critical fields even at sub-Kelvin temperature. The intriguing superconducting state of URu₂Si₂ adds a unique and exciting example to the list of unconventional superconductors.     

Magnetism and Superconductivity inCeCu2(Si1−xGex)2 Probed by Cu NQR

We report Cu-NQR results on Ge-doped heavy-fermion superconductor CeCu₂(Si_1–x Ge _x )₂ (0<x0.2) and undoped Ce_0.99Cu_2.02Si₂. The main effect of the Ge doping is considered to be a negative pressure, since the strength of hybridization decreases by the Ge doping. With increasing x, the dynamical characteristics of the magnetic order at x=0 change to more static ones which suggests a localized regime above x0.25. From the derived T–x phase diagram, it is suggested that the magnetic and the superconducting phases are almost degenerate in undoped CeCu₂Si₂. An exotic interplay between the magnetism characterized by the slow fluctuations and the superconductivity is implied in the region of small x.     

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)     

Quantum critical behaviour in the CePd2Si2/CeNi2Ge2 system

We have explored the vicinity of the antiferromagnetic quantum critical point in the related heavy fermion metals CePd₂Si₂ and CeNi₂Ge₂ as a function of hydrostatic pressure. The normal state resistivity of the antiferromagnet CePd2Si2 near the critical pressure, at which magnetic order disappears, varies as ρ ～ T^χ(1:1 < χ < 1:4) over nearly two orders of magnitude in temperature up to about 30 K. This anomalous form for the resistivity appears to defy not only Fermi-liquid theory, but also simple phenomenological models for the effect of spin fluctuations close to a quantum critical point. An analogous unconventional behaviour is observed in the ambient pressure resistivity of the electronically and structurally equivalent, non-magnetic metal CeNi₂Ge₂. At pressures above 15 kbar, a new and unexpected superconducting transition appears in CeNi₂Ge₂ below 220 mK, which rises to higher temperatures with increasing pressure, reaching 400 mK at 26 kbar.     

Crystallographic investigations and comparison of superconducting and nonsuperconducting CeCu2Si2

Two samples of CeCu _x Si₂ withx=1.8 (non superconducting) andx=2.2 (superconducting) have been investigated by neutron powder diffraction. Both samples were characterized crystallographically and then their impurity content and lattice site occupation were determined. Anisotropic thermal vibrations of the Cu and Si atoms is detected at low temperatures. A relationship between the structural parameterz (defining the distance Ce to Si) and the occurance of superconductivity is suggested.     

Nuclear and muon hyperfine techniques in the study of heavy-fermion superconductors

Nuclear magnetic resonance and relaxation, and the related techniques of muon spin rotation and relaxation, have been used to study local spin polarization and quasiparticle excitations in the heavy-fermion superconductors CeCu₂Si₂, pure and thoriated UBe₁₃, and UPt₃. Measurements of nuclear and positive muon Knight shifts, linewidths, and spinlattice relaxation rates give some hints as to the nature of Cooper pairing in these exotic materials.     

Thin-film preparation,superconductivity and transport properties of the heavy-fermion system CeCu2Si2

The preparation and superconducting and transport properties of thin films of the heavy fermion superconductor CeCu₂Si₂ are reported. Superconductivity with onset temperatures above 600 mK was observed. The resistively measured temperature dependence of the upper critical field could be self-consistently fitted by Werthamer-Helfand-Hohenberg-theory with a Maki parameter α ≈ 20 and a spin-orbit scattering parameter λ_SO ≈ 6. The electrical resistivity was measured up to 300 K revealing characteristic structures slightly more pronounced than is known from bulk material and a clear T² behavior below 2 K. The formation of heavy quasiparticles at low temperature appears to be also the origin of the measured unusual temperature dependences of the Hall-effect and magnetoresistance.