F. Steglich

Quantum criticality in heavy-fermion metals

Quantum criticality describes the collective fluctuations of matter undergoing a second-order phase transition at zero temperature. Heavy-fermion metals have in recent years emerged as prototypical systems to study quantum critical points. There have been considerable efforts, both experimental and theoretical, that use these magnetic systems to address problems that are central to the broad understanding of strongly correlated quantum matter. Here, we summarize some of the basic issues, including the extent to which the quantum criticality in heavy-fermion metals goes beyond the standard theory of order-parameter fluctuations, the nature of the Kondo effect in the quantum-critical regime, the non-Fermi-liquid phenomena that accompany quantum criticality and the interplay between quantum criticality and unconventional superconductivity. At a zero-temperature phase transition from one ordered state to another, fluctuations between the two states lead to quantum critical behaviour that can lead to unexpected physics. Metals with ‘heavy’ electrons often harbour such weird states.

The break-up of heavy electrons at a quantum critical point

The point at absolute zero where matter becomes unstable to new forms of order is called a quantum critical point (QCP). The quantum fluctuations between order and disorder that develop at this point induce profound transformations in the finite temperature electronic properties of the material. Magnetic fields are ideal for tuning a material as close as possible to a QCP, where the most intense effects of criticality can be studied. A previous study on the heavy-electron material YbRh2Si2 found that near a field-induced QCP electrons move ever more slowly and scatter off one another with ever increasing probability, as indicated by a divergence to infinity of the electron effective mass and scattering cross-section. But these studies could not shed light on whether these properties were an artefact of the applied field, or a more general feature of field-free QCPs. Here we report that, when germanium-doped YbRh2Si2 is tuned away from a chemically induced QCP by magnetic fields, there is a universal behaviour in the temperature dependence of the specific heat and resistivity: the characteristic kinetic energy of electrons is directly proportional to the strength of the applied field. We infer that all ballistic motion of electrons vanishes at a QCP, forming a new class of conductor in which individual electrons decay into collective current-carrying motions of the electron fluid.

Hall-effect evolution across a heavy-fermion quantum critical point

A quantum critical point (QCP) develops in a material at absolute zero when a new form of order smoothly emerges in its ground state. QCPs are of great current interest because of their singular ability to influence the finite temperature properties of materials. Recently, heavy-fermion metals have played a key role in the study of antiferromagnetic QCPs. To accommodate the heavy electrons, the Fermi surface of the heavy-fermion paramagnet is larger than that of an antiferromagnet. An important unsolved question is whether the Fermi surface transformation at the QCP develops gradually, as expected if the magnetism is of spin-density-wave (SDW) type, or suddenly, as expected if the heavy electrons are abruptly localized by magnetism. Here we report measurements of the low-temperature Hall coefficient (RH)—a measure of the Fermi surface volume—in the heavy-fermion metal YbRh2Si2 upon field-tuning it from an antiferromagnetic to a paramagnetic state. RH undergoes an increasingly rapid change near the QCP as the temperature is lowered, extrapolating to a sudden jump in the zero temperature limit. We interpret these results in terms of a collapse of the large Fermi surface and of the heavy-fermion state itself precisely at the QCP.

Magnetic-field induced quantum critical point in YbRh2Si2

We report low-temperature calorimetric, magnetic, and resistivity measurements on the antiferromagnetic (AF) heavy-fermion metal YbRh(2)Si(2) ( T(N)=70 mK) as a function of magnetic field B. While for fields exceeding the critical value B(c0) at which T(N)-->0 the low-temperature resistivity shows an AT2 dependence, a 1/(B-B(c0)) divergence of A(B) upon reducing B to B(c0) suggests singular scattering at the whole Fermi surface and a divergence of the heavy quasiparticle mass. The observations are interpreted in terms of a new type of quantum critical point separating a weakly AF ordered from a weakly polarized heavy Landau-Fermi liquid state.

Colossal Seebeck coefficient in strongly correlated semiconductor FeSb2

For more than a decade strongly correlated semiconductors and Kondo insulators have been considered as potential thermoelectric materials. Such materials have large d- or f-character of the electronic band structure close to the Fermi level that theoretically leads to Seebeck coefficients (S) with large magnitudes. In this work it is shown for the first time that the strongly correlated semiconductor FeSb2 exhibits a colossal Seebeck coefficient of ~−45000 μVK−1 at 10 K. The thermoelectric power factor PF=S2·ρ−1, where ρ is the electrical resistivity, reaches a record high value of ~2300 μWK−2 cm−1 at 12 K and is 65 times larger than that of the state-of-the-art Bi2Te3-based thermoelectric materials. However, due to a large lattice thermal conductivity the dimensionless thermoelectric figure of merit is only 0.005 at 12 K. Nonetheless, the potential of FeSb2 as a future solid-state thermoelectric cooling device at cryogenic temperatures is underlined.

Strong coupling between local moments and superconducting ’heavy‘ electrons in UPd2Al3.

The electronic structure of heavy-fermion compounds arises from the interaction of nearly localized 4f- or 5f-shell electrons (with atomic magnetic moments) with the free-electron-like itinerant conduction-band electrons. In actinide or rare-earth heavy-fermion materials, this interaction yields itinerant electrons having an effective mass about 100 times (or more) the bare electron mass. Moreover, the itinerant electrons in UPd2Al3 are found to be superconducting well below the magnetic ordering temperature of this compound, whereas magnetism generally suppresses superconductivity in conventional metals. Here we report the detection of a dispersive excitation of the ordered f-electron moments, which shows a strong interaction with the heavy superconducting electrons. This ‘magnetic exciton’ is a localized excitation which moves through the lattice as a result of exchange forces between the magnetic moments. By combining this observation with previous tunnelling measurements on this material, we argue that these magnetic excitons may produce effective interactions between the itinerant electrons, and so be responsible for superconductivity in a manner analogous to the role played by phonons in conventional superconductors.

Heavy Fermions and Quantum Phase Transitions

From Simplicity to Complexity The relatively simple properties of isolated electrons become rich and complex when the particle-particle interactions are strong enough to form a correlated system. Emergence of complex behavior from relatively simple subunits is an intensely studied topic in condensed-matter physics and applies to many systems in superconductivity and magnetism. Si and Steglich (p. 1161) review the physics of heavy fermion intermetallic compounds. These make ideal materials for study because they can exhibit metallic, magnetic, and superconducting behavior showing novel quantum phases and unconventional quantum criticality. Quantum phase transitions arise in many-body systems because of competing interactions that promote rivaling ground states. Recent years have seen the identification of continuous quantum phase transitions, or quantum critical points, in a host of antiferromagnetic heavy-fermion compounds. Studies of the interplay between the various effects have revealed new classes of quantum critical points and are uncovering a plethora of new quantum phases. At the same time, quantum criticality has provided fresh insights into the electronic, magnetic, and superconducting properties of the heavy-fermion metals. We review these developments, discuss the open issues, and outline some directions for future research.

First-Order Superconducting Phase Transition in CeCoIn5

The superconducting phase transition in heavy fermion CeCoIn5 (T(c)=2.3 K in zero field) becomes first order when the magnetic field H parallel [001] is greater than 4.7 T, and the transition temperature is below T0 approximately 0.31T(c). The change from second order at lower fields is reflected in strong sharpening of both specific heat and thermal expansion anomalies associated with the phase transition, a strong magnetocaloric effect, and a steplike change in the sample volume. This effect is due to Pauli limiting in a type-II superconductor, and was predicted theoretically in the mid-1960s.

Divergence of the Grüneisen Ratio at Quantum Critical Points in Heavy Fermion Metals

We present low-temperature volume thermal expansion, beta, and specific heat, C, measurements on high-quality single crystals of CeNi2Ge2 and YbRh2(Si0.95Ge0.05)(2) which are located very near to quantum critical points. For both systems, beta shows a more singular temperature dependence than C, and thus the Grüneisen ratio Gamma proportional to beta/C diverges as T-->0. For CeNi2Ge2, our results are in accordance with the spin-density wave (SDW) scenario for three-dimensional critical spin fluctuations. By contrast, the observed singularity in YbRh2(Si0.95Ge0.05)(2) cannot be explained by the itinerant SDW theory but is qualitatively consistent with a locally quantum critical picture.

High-field phase diagram of the heavy-fermion metal YbRh2Si2

The tetragonal heavy-fermion (HF) metal YbRh2Si2 (Kondo temperature TK≈ 25 K) exhibits a magnetic field-induced quantum critical point related to the suppression of very weak antiferromagnetic (AF) ordering (TN = 70 mK) at a critical field of Bc = 0.06 T (B⊥ c). To understand the influence of magnetic fields on quantum criticality and the Kondo effect, we study the evolution of various thermodynamic and magnetic properties upon tuning the system by magnetic field. At B > Bc, the AF component of the quantum critical fluctuations becomes suppressed, and FM fluctuations dominate. Their polarization with magnetic field gives rise to a large increase of the magnetization. At B* = 10 T, the Zeeman energy becomes comparable to kB TK, and a steplike decrease of the quasi-particle mass deduced from the specific-heat coefficient indicates the suppression of HF behaviour. The magnetization M(B) shows a pronounced decrease in slope at B* without any signature of metamagnetism. The field dependence of the linear magnetostriction coefficient suggests an increase of the Yb-valency with field, reaching 3+ at high fields. A negative hydrostatic pressure dependence of B* is found, similar to that of the Kondo temperature. We also compare the magnetization behaviour in pulsed fields up to 50 T with that of the isoelectronic HF system YbIr2Si2, which, due to a larger unit-cell volume, has an enhanced TK of about 40 K.