Electronuclear Transition into a Spatially Modulated Magnetic State in YbRh_{2}Si_{2}.

The nature of the antiferromagnetic order in the heavy fermion metal YbRh_{2}Si_{2}, its quantum criticality, and superconductivity, which appears at low mK temperatures, remain open questions. We report measurements of the heat capacity over the wide temperature range 180 µK-80 mK, using current sensing noise thermometry. In zero magnetic field we observe a remarkably sharp heat capacity anomaly at 1.5 mK, which we identify as an electronuclear transition into a state with spatially modulated electronic magnetic order of maximum amplitude 0.1 µ_{B}. We also report results of measurements in magnetic fields in the range 0 to 70 mT, applied perpendicular to the c axis, which show eventual suppression of this order. These results demonstrate a coexistence of a large moment antiferromagnet with putative superconductivity.

Electron Doping of the Iron-Arsenide Superconductor CeFeAsO Controlled by Hydrostatic Pressure.

In the iron-pnictide material CeFeAsO not only the Fe moments, but also the local 4f moments of the Ce order antiferromagnetically at low temperatures. We elucidate on the peculiar role of the Ce on the emergence of superconductivity. While application of pressure suppresses the iron SDW ordering temperature monotonously up to 4 GPa, the Ce-4f magnetism is stabilized until both types of magnetic orders disappear abruptly and a narrow SC dome develops. With further increasing pressure characteristics of a Kondo-lattice system become more and more apparent in the electrical resistivity. This suggests a connection of the emergence of superconductivity with the extinction of the magnetic order and the onset of Kondo screening of the Ce-4f moments.

Evolution from Ferromagnetism to Antiferromagnetism in Yb(Rh_{1-x}Co_{x})_{2}Si_{2}.

Yb(Rh_{1-x}Co_{x})_{2}Si_{2} is a model system to address two challenging problems in the field of strongly correlated electron systems. The first is the intriguing competition between ferromagnetic (FM) and antiferromagnetic (AFM) order when approaching a magnetic quantum critical point (QCP). The second is the occurrence of magnetic order along a very hard crystalline electric field (CEF) direction, i.e., along the one with the smallest available magnetic moment. Here, we present a detailed study of the evolution of the magnetic order in this system from a FM state with moments along the very hard c direction at x=0.27 towards the yet unknown magnetic state at x=0. We first observe a transition towards an AFM canted state with decreasing x and then to a pure AFM state. This confirms that the QCP in YbRh_{2}Si_{2} is AFM, but the phase diagram is very similar to those observed in some inherently FM systems like NbFe_{2} and CeRuPO, which suggests that the basic underlying instability might be FM. Despite the huge CEF anisotropy the ordered moment retains a component along the c axis also in the AFM state. The huge CEF anisotropy in Yb(Rh_{1-x}Co_{x})_{2}Si_{2} excludes that this hard-axis ordering originates from a competing exchange anisotropy as often proposed for other heavy-fermion systems. Instead, it points to an order-by-disorder based mechanism.

Evidence for the Presence of the Fulde-Ferrell-Larkin-Ovchinnikov State in CeCu_{2}Si_{2} Revealed Using

Nuclear magnetic resonance measurements were performed on CeCu_{2}Si_{2} in the presence of a magnetic field close to the upper critical field µ_{0}H_{c2} in order to investigate its superconducting (SC) properties near pair-breaking fields. In lower fields, the Knight shift and nuclear spin-lattice relaxation rate divided by temperature 1/T_{1}T abruptly decreased below the SC transition temperature T_{c}(H), a phenomenon understood within the framework of conventional spin-singlet superconductivity. In contrast, 1/T_{1}T was enhanced just below T_{c}(H) and exhibited a broad maximum when magnetic fields close to µ_{0}H_{c2}(0) were applied parallel or perpendicular to the c axis; although the Knight shift decreased just below T_{c}(H). This enhancement of 1/T_{1}T, which was recently observed in the organic superconductor κ-(BEDT-TTF)_{2}Cu(NCS)_{2}, suggests the presence of high-density Andreev bound states in the inhomogeneous SC region, a hallmark of the Fulde-Ferrell-Larkin-Ovchinnikov phase.

Full-Gap Superconductivity Robust against Disorder in Heavy-Fermion CeCu_{2}Si_{2}.

A key aspect of unconventional pairing by the antiferromagnetic spin-fluctuation mechanism is that the superconducting energy gap must have the opposite sign on different parts of the Fermi surface. Recent observations of non-nodal gap structure in the heavy-fermion superconductor CeCu_{2}Si_{2} were then very surprising, given that this material has long been considered a prototypical example of a superconductor where the Cooper pairing is magnetically mediated. Here we present a study of the effect of controlled point defects, introduced by electron irradiation, on the temperature-dependent magnetic penetration depth λ(T) in CeCu_{2}Si_{2}. We find that the fully gapped state is robust against disorder, demonstrating that low-energy bound states, expected for sign-changing gap structures, are not induced by nonmagnetic impurities. This provides bulk evidence for s_{++}-wave superconductivity without sign reversal.

Emerging local Kondo screening and spatial coherence in the heavy-fermion metal YbRh2Si2.

The entanglement of quantum states is both a central concept in fundamental physics and a potential tool for realizing advanced materials and applications. The quantum superpositions underlying entanglement are at the heart of the intricate interplay of localized spin states and itinerant electronic states that gives rise to the Kondo effect in certain dilute magnetic alloys. In systems where the density of localized spin states is sufficiently high, they can no longer be treated as non-interacting; if they form a dense periodic array, a Kondo lattice may be established. Such a Kondo lattice gives rise to the emergence of charge carriers with enhanced effective masses, but the precise nature of the coherent Kondo state responsible for the generation of these heavy fermions remains highly debated. Here we use atomic-resolution tunnelling spectroscopy to investigate the low-energy excitations of a generic Kondo lattice system, YbRh(2)Si(2). We find that the hybridization of the conduction electrons with the localized 4f electrons results in a decrease in the tunnelling conductance at the Fermi energy. In addition, we observe unambiguously the crystal-field excitations of the Yb(3+) ions. A strongly temperature-dependent peak in the tunnelling conductance is attributed to the Fano resonance resulting from tunnelling into the coherent heavy-fermion states that emerge at low temperature. Taken together, these features reveal how quantum coherence develops in heavy 4f-electron Kondo lattices. Our results demonstrate the efficiency of real-space electronic structure imaging for the investigation of strong electronic correlations, specifically with respect to coherence phenomena, phase coexistence and quantum criticality.

Doped YbRh2Si2: not only ferromagnetic correlations but ferromagnetic order.

YbRh2Si2 is a prototypical system for studying unconventional antiferromagnetic quantum criticality. However, ferromagnetic correlations are present which can be enhanced via isoelectronic cobalt substitution for rhodium in Yb(Rh(1-x)Co(x))2Si2. So far, the magnetic order with increasing x was believed to remain antiferromagnetic. Here, we present the discovery of ferromagnetism for x = 0.27 below T(C) = 1.30 K in single crystalline samples. Unexpectedly, ordering occurs along the c axis, the hard crystalline electric field direction, where the g factor is an order of magnitude smaller than in the basal plane. Although the spontaneous magnetization is only 0.1 µB/Yb it corresponds to the full expected saturation moment along c taking into account partial Kondo screening.

Interplay between Kondo suppression and Lifshitz transitions in YbRh2Si2 at 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.

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.

Avoided ferromagnetic quantum critical point: unusual short-range ordered state in CeFePO.

Cerium 4f electronic spin dynamics in single crystals of the heavy-fermion system CeFePO is studied by means of ac susceptibility, specific heat, and muon-spin relaxation (µSR). Short-range static magnetism occurs below the freezing temperature T(g) ≈ 0.7 K, which prevents the system from accessing a putative ferromagnetic quantum critical point. In the µSR, the sample-averaged muon asymmetry function is dominated by strongly inhomogeneous spin fluctuations below 10 K and exhibits a characteristic time-field scaling relation expected from glassy spin dynamics, strongly evidencing cooperative and critical spin fluctuations. The overall behavior can be ascribed neither to canonical spin glasses nor other disorder-driven mechanisms.

Determining the in-plane orientation of the ground-state orbital of CeCu2Si2.

We have successfully determined the hitherto unknown sign of the B(4)(4) Stevens crystal-field parameter of the tetragonal heavy-fermion compound CeCu(2)Si(2) using vector q-dependent nonresonant inelastic x-ray scattering experiments at the cerium N(4,5) edge. The observed difference between the two different directions, q∥[100] and q∥[110], is due to the anisotropy of the crystal-field ground state in the (001) plane and is observable only because of the utilization of higher than dipole transitions possible in nonresonant inelastic x-ray scattering. This approach allows us to go beyond the specific limitations of dc magnetic susceptibility, inelastic neutron scattering, and soft x-ray spectroscopy, and provides us with a reliable information about the orbital state of the 4f electrons relevant for the quantitative modeling of the quasiparticles and their interactions in heavy-fermion systems.

Pressure tuning of the interplay of magnetism and superconductivity in CeCu2Si2.

We carried out specific-heat and ac-susceptibility experiments under hydrostatic pressure to investigate the interplay of spin-density-wave antiferromagnetism (A) and superconductivity (S) in single-crystalline AS-type CeCu(2)Si(2). We find evidence for a line of magnetic-field- and pressure-tuned quantum critical points in the normal state in the zero-temperature magnetic field-pressure plane. Our analysis suggests an extension of this line into the superconducting state and corroborates the close connection of the underlying mechanisms leading to the formation of the antiferromagnetic and the superconducting states in AS-type CeCu(2)Si(2).

Determination of gap symmetry from angle-dependent H(c2) measurements on CeCu2Si2.

The tetragonal heavy-fermion compound CeCu2Si2 exhibits a superconducting ground state (S type, T(c) = 0.67 K) close to a magnetic instability. Here, we present angle-resolved resistivity measurements of the upper critical field H(c2). In-plane rotation of S-type CeCu2Si2 single crystals reveals a fourfold oscillation of H(c2). An extended weak-coupling BCS model for a d-wave symmetry including strong Pauli-limiting effects confirms the aforementioned angular dependence and points towards d(xy) symmetry of the order parameter.

Insight into the f-derived Fermi surface of the heavy-fermion compound YbRh2Si2.

Angle-resolved photoelectron spectroscopy (ARPES) was used to study the Fermi surface of the heavy-fermion system YbRh(2)Si(2) at a temperature of about 10 K, i.e., a factor of 2 below the Kondo energy scale. We observed sharp structures with a well-defined topology, which were analyzed by comparing with results of band-structure calculations based on the local-density approximation (LDA). The observed bulk Fermi surface presents strong similarities with that expected for a trivalent Yb state, but is slightly larger, has a strong Yb-4f character, and deviates from the LDA results by a larger region without states around the Γ point. These properties are qualitatively explained in the framework of a simple f-d hybridization model. Our analysis highlights the importance of taking into account surface states and doing an appropriate projection along k(z) when comparing ARPES data with results from theoretical calculations.

Field-induced transition within the superconducting state of CeRh2As2.

Materials with multiple superconducting phases are rare. Here, we report the discovery of two-phase unconventional superconductivity in CeRh2As2 Using thermodynamic probes, we establish that the superconducting critical field of its high-field phase is as high as 14 tesla, even though the transition temperature is only 0.26 kelvin. Furthermore, a transition between two different superconducting phases is observed in a c axis magnetic field. Local inversion-symmetry breaking at the cerium sites enables Rashba spin-orbit coupling alternating between the cerium sublayers. The staggered Rashba coupling introduces a layer degree of freedom to which the field-induced transition and high critical field seen in experiment are likely related.

Evidence for a non-Fermi-liquid phase in Ge-substituted YbRh2Si2.

The canonical view of heavy fermion quantum criticality assumes a single quantum critical point separating the paramagnet from the antiferromagnet. However, recent experiments on Yb-based heavy fermion compounds suggest the presence of non-Fermi liquid behavior over a finite zero-temperature region. Using detailed susceptibility and transport measurements we show that the classic quantum critical system, Ge-substituted YbRh(2)Si(2), also displays such behavior. We advance arguments that this is not due to a disorder-smeared quantum critical point, but represents a new class of metallic phase.

k Dependence of the crystal-field splittings of 4f states in rare-earth systems.

The occupation, energy separation, and order of the crystal-field-split 4f states are crucial for the understanding of the magnetic properties of rare-earth systems. We provide the experimental evidence that crystal-field-split 4f states exhibit energy dispersion in momentum space leading to variations of energy spacings between them and even of their energy sequence across the Brillouin zone. These observations were made by performing angle-resolved photoemission experiments on YbRh(2)Si(2) and properly simulated within a simple model based on results obtained by inelastic neutron scattering experiments and band structure calculations. Our findings should be generally applicable to rare-earth systems and have considerable impact on the understanding of magnetism and related phenomena.

CeFePO: f-d hybridization and quenching of superconductivity.

As a homologue to the new, Fe-based type of high-temperature superconductors, the electronic structure of the heavy-fermion compound CeFePO was studied by means of angle-resolved resonant photoemission. It was experimentally found-and later on confirmed by local-density approximation (LDA) as well as dynamical mean-field theory (DMFT) calculations-that the Ce 4f states hybridize to the Fe 3d states of d{3z{2}-r{2}} symmetry near the Fermi level that discloses their participation in the occurring electron-correlation phenomena and provides insight into mechanism of superconductivity in oxopnictides.

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 (R(H))--a measure of the Fermi surface volume--in the heavy-fermion metal YbRh2Si2 upon field-tuning it from an antiferromagnetic to a paramagnetic state. R(H) 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.

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.