Heavy-fermion Metals Research Articles

Field-induced long-range magnetic order in the spin-singlet ground-state system YbAl3C3: Neutron diffraction study

The $4f$-electron system YbAl$_3$C$_3$ with a non-magnetic spin-dimer ground state has been studied by neutron diffraction in an applied magnetic field. A long-range magnetic order involving both ferromagnetic and antiferromagnetic components has been revealed above the critical field H$_C\sim $ 6T at temperature T=0.05K. The magnetic structure indicates that the geometrical frustration of the prototype hexagonal lattice is not fully relieved in the low-temperature orthorhombic phase. The suppression of magnetic ordering by the remanent frustration is the key factor stabilizing the non-magnetic singlet ground state in zero field. Temperature dependent measurements in the applied field H=12T revealed that the long-range ordering persists up to temperatures significantly higher than the spin gap indicating that this phase is not directly related to the singlet-triplet excitation. Combining our neutron diffraction results with the previously published phase diagram, we support the existence of an intermediate disordered phase as the first excitation from the non-magnetic singlet ground state. Based on our results, we propose YbAl$_3$C$_3$ as a new material for studying the quantum phase transitions of heavy-fermion metals under the influence of geometrical frustration.

Interplay between Kondo Suppression and Lifshitz Transitions inYbRh2Si2at High Magnetic Fields

We investigate the magnetic field dependent thermopower, thermal conductivity, resistivity, and Hall effect in the heavy fermion metal YbRh2Si2. In contrast to reports on thermodynamic measurements, we find in total three transitions at high fields, rather than a single one at 10 T. Using the Mott formula together with renormalized band calculations, we identify Lifshitz transitions as their origin. The predictions of the calculations show that all experimental results rely on an interplay of a smooth suppression of the Kondo effect and the spin splitting of the flat hybridized bands.

Strongly correlated quantum spin liquid in herbertsmithite

Strongly correlated Fermi systems are among the most intriguing and fundamental systems in physics. We show that the herbertsmithite ZnCu3(OH)6Cl2 can be viewed as a new type of strongly correlated electrical insulator that possesses properties of heavy-fermion metals with one exception: it resists the flow of electric charge. We demonstrate that herbertsmithite's low temperature properties are defined by a strongly correlated quantum spin liquid made with such hypothetic particles as fermionic spinons which carry spin 1/2 and no charge. Our calculations of its thermodynamic and relaxation properties are in good agreement with recent experimental facts and allow us to reveal their scaling behavior which strongly resembles that observed in heavy-fermion metals. Analysis of the dynamic magnetic susceptibility of strongly correlated Fermi systems suggests that there exist at least two types of its scaling.

Spin excitons from hybridized heavy quasiparticles in YbB12 and CeB6

In f-electron compounds the small indirect hybridization gap which is on the scale of the Kondo temperature leads to an enhanced bare spin response around the zone boundary wave vector, Q′ = (π, π, π). Due to the interaction of hybridized quasiparticles a collective spin exciton resonance mode may appear within or at the gap threshold around Q′. It was found in the small hybridization gap semiconductor YbB12 as well as in the heavy fermion metal CeB6. There are similarities to the spin excitons observed within the excitation gap of unconventional superconductors. We use an Anderson lattice type model supplemented by the molecular fields of hidden and magnetic order in the case of CeB6 to calculate the RPA spin response in these compounds. It exhibits the salient feature in frequency and momentum dependence around Q′ found by inelastic neutron scattering.

Doping-induced band shifts and Lifshitz transitions in heavy-fermion metals

For some heavy-fermion compounds, it has been suggested that a Fermi-surface-changing Lifshitz transition, which can be driven, e.g., by varying an applied magnetic field, occurs inside the heavy- fermion regime. Here we discuss, based on microscopic calculations, how the location of such a transition can be influenced by carrier doping. Due to strong correlations, a heavy band does not shift rigidly with the chemical potential. Intriguingly, we find that the actual shift is determined by the interplay of heavy and additional light bands crossing the Fermi level: doped carriers tend to populate heavy and light bands equally, despite the fact that the latter contribute a small density of states of excitations only. This invalidates naive estimates of the transition shift based on the low-temperature specific heat of the heavy Fermi liquid. We discuss applications of our results.

Anomalous Reduction of the Lorenz Ratio at the Quantum Critical Point in YbAgGe

We report measurements of the electrical and thermal transport on the hexagonal heavy-fermion metal YbAgGe for temperatures T ≥ 40 mK and in magnetic fields H∥ab up to 14 T. This distorted kagome-lattice system displays a series of magnetic states and a quantum critical point at H(c) = 4.5 T. The Lorenz ratio L(T)/L0 displays a marked reduction only close to H(c). A T-linear contribution below 120 mK, present at all different fields, allows us to extrapolate the Lorenz ratio towards T = 0. At the critical field this yields L/L0 = 0.92±0.03, suggesting a violation of the Wiedemann-Franz law due to strong inelastic scattering.

Quantum phase transitions in heavy fermion metals and Kondo insulators

AbstractStrongly correlated electron systems at the border of magnetism are of active current interest, particularly because the accompanying quantum criticality provides a route towards both strange‐metal non‐Fermi liquid behavior and unconventional superconductivity. Among the many important questions is whether the magnetism acts simply as a source of fluctuations in the textbook Landau framework, or instead serves as a proxy for some unexpected new physics. We put into this general context the recent developments on quantum phase transitions in antiferromagnetic (AF) heavy fermion metals. Among these are the extensive recent theoretical and experimental studies on the physics of Kondo destruction in a class of beyond‐Landau quantum critical points (QCPs). Also discussed are the theoretical basis for a global phase diagram of AF heavy fermion metals, and the recent surge of materials suitable for studying this phase diagram. Furthermore, we address the generalization of this global phase diagram to the case of Kondo insulators, and consider the future prospect to study the interplay among Kondo coherence, magnetism, and topological states. Finally, we touch upon related issues beyond the AF settings, arising in mixed valent, ferromagnetic, quadrupolar, or spin glass f‐electron systems, as well as some general issues on emergent phases near QCPs.

Far-infrared optical conductivity of CeCu2Si2

We investigated the optical reflectivity of the heavy-fermion metal CeCu2Si2 in the energy range 3 meV–30 eV for temperatures between 4 and 300 K. The results for the charge dynamics indicate a behavior that is expected for the formation of a coherent heavy quasiparticle state: upon cooling the spectra of the optical conductivity indicate a narrowing of the coherent response. Below temperatures of 30 K a considerable suppression of conductivity evolves below a peak structure at 13 meV. We assign this gap-like feature to strong electron correlations due to the 4f-conduction electron hybridization.

Optical Study of Archetypical Valence-Fluctuating Eu Systems

We have investigated the optical conductivity of the prominent valence-fluctuating compounds EuIr(2)Si(2) and EuNi(2)P(2) in the infrared energy range to get new insights into the electronic properties of valence-fluctuating systems. For both compounds, we observe upon cooling the formation of a renormalized Drude response, a partial suppression of the optical conductivity below 100 meV, and the appearance of a midinfrared peak at 0.15 eV for EuIr(2)Si(2) and 0.13 eV for EuNi(2)P(2). Most remarkably, our results show a strong similarity with the optical spectra reported for many Ce- or Yb-based heavy-fermion metals and intermediate valence systems, although the phase diagrams and the temperature dependence of the valence differ strongly between Eu systems and Ce- or Yb-based systems. This suggests that the hybridization between 4f and conduction electrons, which is responsible for the properties of Ce and Yb systems, plays an important role in valence-fluctuating Eu systems.

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 (HF) 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 rho_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 rho_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 HF metals.

Optical spectroscopy shows that the normal state of URu 2 Si 2 is an anomalous Fermi liquid

Fermi showed that, as a result of their quantum nature, electrons form a gas of particles whose temperature and density follow the so-called Fermi distribution. As shown by Landau, in a metal the electrons continue to act like free quantum mechanical particles with enhanced masses, despite their strong Coulomb interaction with each other and the positive background ions. This state of matter, the Landau-Fermi liquid, is recognized experimentally by an electrical resistivity that is proportional to the square of the absolute temperature plus a term proportional to the square of the frequency of the applied field. Calculations show that, if electron-electron scattering dominates the resistivity in a Landau-Fermi liquid, the ratio of the two terms, b, has the universal value of b = 4. We find that in the normal state of the heavy Fermion metal URu(2)Si(2), instead of the Fermi liquid value of 4, the coefficient b = 1 ± 0.1. This unexpected result implies that the electrons in this material are experiencing a unique scattering process. This scattering is intrinsic and we suggest that the uranium f electrons do not hybridize to form a coherent Fermi liquid but instead act like a dense array of elastic impurities, interacting incoherently with the charge carriers. This behavior is not restricted to URu(2)Si(2). Fermi liquid-like states with b ≠ 4 have been observed in a number of disparate systems, but the significance of this result has not been recognized.

Hall effect in heavy fermion metals

The heavy fermion systems present a unique platform in which strong electronic correlations give rise to a host of novel, and often competing, electronic and magnetic ground states. Amongst a number of potential experimental tools at our disposal, measurements of the Hall effect have emerged as a particularly important one in discerning the nature and evolution of the Fermi surfaces of these enigmatic metals. In this article, we present a comprehensive review of Hall effect measurements in the heavy-fermion materials, and examine the success it has had in contributing to our current understanding of strongly correlated matter. Particular emphasis is placed on its utility in the investigation of quantum critical phenomena which are thought to drive many of the exotic electronic ground states in these systems. This is achieved by the description of measurements of the Hall effect across the putative zero-temperature instability in the archetypal heavy-fermion metal YbRh$_2$Si$_2$. Using the Ce$M$In$_5$ (with $M =$ Co, Ir) family of systems as a paradigm, the influence of (antiferro-)magnetic fluctuations on the Hall effect is also illustrated. This is compared to prior Hall effect measurements in the cuprates and other strongly correlated systems to emphasize on the generality of the unusual magnetotransport in materials with non-Fermi liquid behavior.

Magnetic field dependence of the residual resistivity of the heavy-fermion metal CeCoIn5

An explanation of paradoxical behavior of the residual resistivity rho_0 of the heavy-fermion metal CeCoIn5 in magnetic fields and under pressure is developed. The source of this behavior is identified as a flattening of the single-particle spectrum, which exerts profound effects on the specific heat, thermal expansion coefficient, and magnetic susceptibility in the normal state, the specific heat jump at the point of superconducting phase transition, and other properties of strongly correlated electron systems in solids. It is shown that application of a magnetic field or pressure to a system possessing a flat band leads to a strong suppression of rho_0. Analysis of its measured thermodynamic and transport properties yields direct evidence for the presence of a flat band in CeCoIn5.

Spin-orbit density wave induced hidden topological order in URu2Si2.

The conventional order parameters in quantum matters are often characterized by ‘spontaneous’ broken symmetries. However, sometimes the broken symmetries may blend with the invariant symmetries to lead to mysterious emergent phases. The heavy fermion metal URu2Si2 is one such example, where the order parameter responsible for a second-order phase transition at Th = 17.5 K has remained a long-standing mystery. Here we propose via ab-initio calculation and effective model that a novel spin-orbit density wave in the f-states is responsible for the hidden-order phase in URu2Si2. The staggered spin-orbit order spontaneously breaks rotational, and translational symmetries while time-reversal symmetry remains intact. Thus it is immune to pressure, but can be destroyed by magnetic field even at T = 0 K, that means at a quantum critical point. We compute topological index of the order parameter to show that the hidden order is topologically invariant. Finally, some verifiable predictions are presented.

Scaling in dynamic susceptibility of herbertsmithite and heavy-fermion metals

We present a theory of the dynamic magnetic susceptibility of quantum spin liquid. The obtained results are in good agreement with experimental facts collected on herbertsmithite ZnCu3(OH)6Cl2 and on heavy-fermion metals, and allow us to predict a new scaling in magnetic fields in the dynamic susceptibility. Under the application of strong magnetic fields quantum spin liquid becomes completely polarized. We show that this polarization can be viewed as a manifestation of gapped excitations when investigating the spin-lattice relaxation rate.

New universality class of quantum criticality in Ce- and Yb-based heavy fermions

A new universality class of quantum criticality emerging in itinerant electron systems with strong local electron correlations is discussed. The quantum criticality of a Ce- or Yb-valence transition gives us a unified explanation for unconventional criticality commonly observed in heavy fermion metals such as YbRh2Si2, β-YbAlB4, YbCu5−xAlx, and CeIrIn5. The key origin is due to the locality of the critical valence fluctuation mode emerging near the quantum critical end point of the first-order valence transition, which is caused by strong electron correlations for f electrons. The wider relevance of this new criticality and important future measurements to uncover its origin are also discussed.

Thermodynamic evidence for broken fourfold rotational symmetry in the hidden-order phase of URu2Si2

Despite more than a quarter century of research, the nature of the second-order phase transition in the heavy-fermion metal URu2Si2 remains enigmatic. The key question is which symmetry is being broken below this “hidden order” transition. We review the recent progress on this issue, particularly focusing on the thermodynamic evidence from very sensitive micro-cantilever magnetic torque measurements that the fourfold rotational symmetry of the underlying tetragonal crystal is broken. The angle dependence of the torque under in-plane field rotation exhibits the twofold oscillation term, which sets in just below the transition temperature. This observation restricts the symmetry of the hidden order parameter to the E+- or E−-type, depending on whether the time reversal symmetry is preserved or not.

Spin Exciton Formation inside the Hidden Order Phase ofCeB6

The heavy fermion metal CeB(6) exhibits a hidden order of the antiferroquadrupolar (AFQ) type below T(Q)=3.2 K and a subsequent antiferromagnetic (AFM) order at T(N)=2.3 K. It was interpreted as an ordering of the quadrupole and dipole moments of a Γ(8) quartet of localized Ce 4f(1) electrons. This established picture has been profoundly shaken by recent inelastic neutron scattering (G. Friemel et al., arXiv:1111.4151) that found the evolution of a feedback spin exciton resonance within the hidden order phase at the AFQ wave vector which is stabilized by the AFM order. We develop an alternative theory based on a fourfold degenerate Anderson lattice model, including both order parameters as particle-hole condensates of itinerant heavy quasiparticles. This explains in a natural way the appearance of the spin exciton resonance and the momentum dependence of its spectral weight, in particular, around the AFQ vector and its rapid disappearance in the disordered phase. Analogies to the feedback effect in unconventional heavy fermion superconductors are pointed out.

Critical quasiparticle theory applied to heavy fermion metals near an antiferromagnetic quantum phase transition

We use the recently developed critical quasiparticle theory to derive the scaling behavior associated with a quantum critical point in a correlated metal. This is applied to the magnetic-field induced quantum critical point observed in YbRh(2)Si(2), for which we also derive the critical behavior of the specific heat, resistivity, thermopower, magnetization and susceptibility, the Grüneisen coefficient, and the thermal expansion coefficient. The theory accounts very well for the available experimental results.

Resonant magnetic exciton mode in the heavy-fermion antiferromagnet CeB6

Resonant magnetic excitations are recognised as hallmarks of unconventional superconductivity in copper oxides, iron pnictides and heavy-fermion compounds. Model calculations have related these modes to the microscopic properties of the pair wave function, but the mechanisms of their formation are still debated. Here we report the discovery of a similar resonant mode in the non-superconducting antiferromagnetic heavy-fermion metal CeB(6). Unlike conventional magnons, the mode is non-dispersive and is sharply peaked around a wave vector separate from those characterising the antiferromagnetic order. It is likely associated with a co-existing order parameter of the unusual antiferro-quadrupolar phase of CeB(6), which has long remained hidden to neutron-scattering probes. The mode energy increases continuously below the onset temperature for antiferromagnetism, in parallel to the opening of a nearly isotropic spin gap throughout the Brillouin zone. These attributes are similar to those of the resonant modes in unconventional superconductors. This unexpected commonality between the two disparate ground states indicates the dominance of itinerant spin dynamics in the ordered low-temperature phases of CeB(6) and throws new light on the interplay between antiferromagnetism, superconductivity and 'hidden' order parameters in correlated-electron materials.