Fermi Volume Evolution and Crystal-Field Excitations in Heavy-Fermion Compounds Probed by Time-Domain Terahertz Spectroscopy.

We measure the quasiparticle weight in the heavy-fermion compound CeCu_{6-x}Au_{x} (x=0, 0.1) by time-resolved terahertz spectroscopy for temperatures from 2 up to 300 K. This method distinguishes contributions from the heavy Kondo band and from the crystal-electric-field satellite bands by different terahertz response delay times. We find that the formation of heavy bands is controlled by an exponentially enhanced, high-energy Kondo scale once the crystal-electric-field states become thermally occupied. We corroborate these observations by temperature-dependent dynamical mean-field calculations for the multiorbital Anderson lattice model and discuss consequences for quantum-critical scenarios.

Magnetic and Structural Quantum Phase Transitions in CeCu_{6-x}Au_{x} are Independent.

The heavy-fermion compound CeCu_{6-x}Au_{x} has become a model system for unconventional magnetic quantum criticality. For small Au concentrations 0≤x<0.16, the compound undergoes a structural transition from orthorhombic to monoclinic crystal symmetry at a temperature T_{s} with T_{s}→0 for x≈0.15. Antiferromagnetic order sets in close to x≈0.1. To shed light on the interplay between quantum-critical magnetic and structural fluctuations we performed neutron-scattering and thermodynamic measurements on samples with 0≤x≤0.3. The resulting phase diagram shows that the antiferromagnetic and monoclinic phase coexist in a tiny Au concentration range between x≈0.1 and 0.15. The application of hydrostatic and chemical pressure allows us to clearly separate the transitions from each other and to explore a possible effect of the structural transition on the magnetic quantum-critical behavior. Our measurements demonstrate that at low temperatures the unconventional quantum criticality exclusively arises from magnetic fluctuations and is not affected by the monoclinic distortion.

Entropy Evolution in the Magnetic Phases of Partially Frustrated CePdAl.

In the heavy-fermion metal CePdAl, long-range antiferromagnetic order coexists with geometric frustration of one-third of the Ce moments. At low temperatures, the Kondo effect tends to screen the frustrated moments. We use magnetic fields B to suppress the Kondo screening and study the magnetic phase diagram and the evolution of the entropy with B employing thermodynamic probes. We estimate the frustration by introducing a definition of the frustration parameter based on the enhanced entropy, a fundamental feature of frustrated systems. In the field range where the Kondo screening is suppressed, the liberated moments tend to maximize the magnetic entropy and strongly enhance the frustration. Based on our experiments, this field range may be a promising candidate to search for a quantum spin liquid.

Evolution of the magnetic structure in CeCu(5.5)Au(0.5) under pressure towards quantum criticality.

In the prototypical heavy-fermion system CeCu(6-x)Au(x), a magnetic quantum critical point can be tuned by Au concentration x, hydrostatic pressure p, or magnetic field B. A striking equivalence of the tuning behavior with x or p had been found with respect to thermodynamic and transport properties. By means of elastic neutron scattering on single crystalline CeCu(5.5)Au(0.5), we demonstrate this x-p equivalence on a microscopic level by showing that the magnetic ordering wave vector q(m) can be tuned accordingly. At ambient pressure,CeCu(5.5)Au(0.5) orders at q(m)≈(0.59 0 0). Upon applying p=4.1 kbar, q(m)≈(0.61 0 0.21) is found corresponding to CeCu(5.6)Au(0.4) at ambient pressure. The transition seems to occur in a first-order fashion and to be governed by slight changes in the nesting properties of the Fermi surface.

Magnetism and superconductivity driven by identical 4f states in a heavy-fermion metal.

The apparently inimical relationship between magnetism and superconductivity has come under increasing scrutiny in a wide range of material classes, where the free energy landscape conspires to bring them in close proximity to each other. Particularly enigmatic is the case when these phases microscopically interpenetrate, though the manner in which this can be accomplished remains to be fully comprehended. Here, we present combined measurements of elastic neutron scattering, magnetotransport, and heat capacity on a prototypical heavy fermion system, in which antiferromagnetism and superconductivity are observed. Monitoring the response of these states to the presence of the other, as well as to external thermal and magnetic perturbations, points to the possibility that they emerge from different parts of the Fermi surface. Therefore, a single 4f state could be both localized and itinerant, thus accounting for the coexistence of magnetism and superconductivity.

Onset of antiferromagnetism in heavy-fermion metals

There are two main theoretical descriptions of antiferromagnets. The first arises from atomic physics, which predicts that atoms with unpaired electrons develop magnetic moments. In a solid, the coupling between moments on nearby ions then yields antiferromagnetic order at low temperatures. The second description, based on the physics of electron fluids or 'Fermi liquids' states that Coulomb interactions can drive the fluid to adopt a more stable configuration by developing a spin density wave. It is at present unknown which view is appropriate at a 'quantum critical point' where the antiferromagnetic transition temperature vanishes. Here we report neutron scattering and bulk magnetometry measurements of the metal CeCu(6-x)Au(x), which allow us to discriminate between the two models. We find evidence for an atomically local contribution to the magnetic correlations which develops at the critical gold concentration (x(c) = 0.1), corresponding to a magnetic ordering temperature of zero. This contribution implies that a Fermi-liquid-destroying spin-localizing transition, unanticipated from the spin density wave description, coincides with the antiferromagnetic quantum critical point.

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.

Interplay between crystal field splitting and Kondo effect in CeNi9Ge(4-x)Si(x).

The pseudo-ternary solid solution CeNi(9)Ge(4-x)Si(x) (0 ≤ x ≤ 4) has been investigated by means of x-ray diffraction, magnetic susceptibility, specific heat, electrical resistivity, thermopower and inelastic neutron scattering studies. The isoelectronic substitution of germanium by silicon atoms causes a dramatic change of the relative strength of competing Kondo, RKKY and crystal field (CF) energy scales. The strongest effect is the continuous elevation of the Kondo temperature T(K) from approximately 3.5 K for CeNi(9)Ge(4) to about 70 K for CeNi(9)Si(4). This increase of the Kondo temperature is attended by a change of the CF level scheme of the Ce ions. The interplay of the different energy scales results in an incipient reduction of the ground state degeneracy from an effectively fourfold degenerate non-magnetic Kondo ground state with unusual non-Fermi-liquid features of CeNi(9)Ge(4) to a lower one, followed by an increase towards a sixfold, fully degenerate ground state multiplet in CeNi(9)Si(4) (T(K) ∼ Δ(CF)).

High-temperature signatures of quantum criticality in heavy-fermion systems.

We propose a new criterion for distinguishing the Hertz-Millis (HM) and the local quantum critical (LQC) mechanism in heavy-fermion systems with a magnetic quantum phase transition (QPT). The criterion is based on our finding that the complete spin screening of Kondo ions can be suppressed by the Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling to the surrounding magnetic ions even without magnetic ordering and that, consequently, the signature of this suppression can be observed in spectroscopic measurements above the magnetic ordering temperature. We apply the criterion to high-resolution photoemission measurements on CeCu(6 - x)Au(x) and conclude that the QPT in this system is dominated by the LQC scenario.

Superconductivity versus quantum criticality: what can we learn from heavy fermions?

Two quantum critical point (QCP) scenarios are being discussed for different classes of antiferromagnetic (AF) heavy-fermion (HF) systems. In the itinerant one, where AF order is of the spin-density wave (SDW) type, the heavy 'composite' charge carriers keep their integrity at the QCP. The second one implies a breakdown of the Kondo effect and a disintegration of the composite fermions at the AF QCP. We discuss two isostructural compounds as exemplary materials for these two different scenarios: CeCu(2)Si(2) exhibits a three-dimensional (3D) SDW QCP and superconductivity, presumably mediated by SDW fluctuations, as strongly suggested by recent inelastic neutron scattering experiments. In Y bRh(2)Si(2), the AF QCP is found to coincide with a Kondo-destroying one. However, in the latter compound these two QCPs can be detached by varying the average unit-cell volume, e.g. through the application of chemical pressure, as realized by partial substitution of either Ir or Co for Rh. A comparison of CeCu(2)Si(2) and Y bRh(2)Si(2) indicates that the apparent differences in quantum critical behaviour go along with disparate behaviour concerning the (non-) existence of superconductivity (SC). No sign of SC could be detected in Y bRh(2)Si(2) down to mK temperatures. A potential correlation between the specific nature of the QCP and the occurrence of SC, however, requires detailed studies on further quantum critical HF superconductors, e.g. on ß-Y bAlB(4), UBe(13), CeCoIn(5) and CeRhIn(5).

Signature of quantum criticality in photoemission spectroscopy.

A quantum phase transition in a heavy-fermion compound may destroy the Fermi-liquid ground state. However, the conditions for this breakdown have remained obscure. We report the first direct investigation of heavy quasiparticle formation and breakdown in the canonical system CeCu(6-x)Au(x) by ultraviolet photoemission spectroscopy at elevated temperatures without the complications of lattice coherence. Surprisingly, the single-ion Kondo energy scale T(K) exhibits an abrupt step near the quantum critical Au concentration of x(c) = 0.1. We show theoretically that this step is expected from a highly nonlinear renormalization of the local spin coupling at each Ce site, induced by spin fluctuations on neighboring sites. It provides a general high-temperature indicator for heavy-fermion quasiparticle breakdown at a quantum phase transition.

Direct observation of the superconducting gap in phonon spectra.

We show that the superconducting energy gap 2Delta can be directly observed in phonon spectra, as predicted by recent theories. In addition, since each phonon probes the gap on only a small part of the Fermi surface, the gap anisotropy can be studied in detail. Our neutron scattering investigation of the anisotropic conventional superconductor YNi2B2C demonstrates this new application of phonon spectroscopy.

Magnetic fluctuations at a field-induced quantum phase transition.

We report an inelastic neutron-scattering study at the field-induced magnetic quantum phase transition of CeCu5.8Au0.2. The data can be described better by the spin-density-wave scenario than by a local quantum critical point, while the latter scenario was shown to be applicable to the zero-field concentration-tuned quantum phase transition in CeCu6-xAux for x=0.1. This constitutes direct microscopic evidence for a difference in the quantum fluctuation spectra at a magnetic quantum critical point driven by different tuning parameters.

Quantum criticality in the cubic heavy-fermion system CeIn3-xSnx.

We report a comprehensive study of CeIn3-xSnx (0.55

Nature of the A phase in CeCu2Si2.

Neutron diffraction experiments have been performed on a magnetically ordered CeCu2Si2 single crystal exhibiting A-phase anomalies in specific heat and thermal expansion. Below T(N) approximately 0.8 K antiferromagnetic superstructure peaks have been detected. The propagation vector of the magnetic order appears to be determined by the topology of the Fermi surface of heavy quasiparticles as indicated by renormalized band-structure calculations. The observation of long-range incommensurate antiferromagnetic order as the nature of the A phase in CeCu2Si2 suggests that a spin-density-wave instability is the origin of the quantum critical point in CeCu2Si2.