Critical slowing down near a magnetic quantum phase transition with fermionic breakdown.

When a system close to a continuous phase transition is subjected to perturbations, it takes an exceptionally long time to return to equilibrium. This critical slowing down is observed universally in the dynamics of bosonic excitations, such as order-parameter collective modes, but it is not generally expected to occur for fermionic excitations. Here using terahertz time-domain spectroscopy, we find evidence for fermionic critical slowing down in YbRh2Si2 close to a quantum phase transition between an antiferromagnetic phase and a heavy Fermi liquid. In the latter phase, the relevant quasiparticles are a quantum superposition of itinerant and localized electronic states with a strongly enhanced effective mass. As the temperature is lowered on the heavy-Fermi-liquid side of the transition, the heavy-fermion spectral weight builds up until the Kondo temperature TK ≈ 25 K, then decays towards the quantum phase transition and is, thereafter, followed by a logarithmic rise of the quasiparticle excitation rate below 10 K. A two-band heavy-Fermi-liquid theory shows that this is indicative of the fermionic critical slowing down associated with heavy-fermion breakdown near the quantum phase transition. The critical exponent of this breakdown could be used to classify this system among a wider family of fermionic quantum phase transitions that is yet to be fully explored.

Estimating the Orientation of 4f Magnetic Moments by Classical Photoemission.

To use efficiently the magnetic functionalities emerging at the surfaces or interfaces of novel lanthanides-based materials, there is a need for complementary methods to probe the atomic-layer resolved magnetic properties. Here, we show that 4f photoelectron spectroscopy is highly sensitive to the collective orientation of 4f magnetic moments and, thus, a powerful tool for characterizing the related properties. To demonstrate this, we present the results of systematic study of a family of layered crystalline 4f-materials, which are crystallized in the body-centered tetragonal ThCr2Si2 structure. Analysis of 4f spectra indicates that the 4f moments at the surface experience a strong reorientation with respect to the bulk, caused by changes of the crystal-electric field. The presented database of the computed 4f spectra for all trivalent rare-earth ions in their different MJ states will facilitate the estimation of the orientation of the 4f magnetic moments in the layered 4f-systems for efficient control of their magnetic properties.

Interlayer Coupling of a Two-Dimensional Kondo Lattice with a Ferromagnetic Surface in the Antiferromagnet CeCo2P2.

The f-driven temperature scales at the surfaces of strongly correlated materials have increasingly come into the focus of research efforts. Here, we unveil the emergence of a two-dimensional Ce Kondo lattice, which couples ferromagnetically to the ordered Co lattice below the P-terminated surface of the antiferromagnet CeCo2P2. In its bulk, Ce is passive and behaves tetravalently. However, because of symmetry breaking and an effective magnetic field caused by an uncompensated ferromagnetic Co layer, the Ce 4f states become partially occupied and spin-polarized near the surface. The momentum-resolved photoemission measurements indicate a strong admixture of the Ce 4f states to the itinerant bands near the Fermi level including surface states that are split by exchange interaction with Co. The temperature-dependent measurements reveal strong changes of the 4f intensity at the Fermi level in accordance with the Kondo scenario. Our findings show how rich and diverse the f-driven properties can be at the surface of materials without f-physics in the bulk.

Spin Orientation of Two-Dimensional Electrons Driven by Temperature-Tunable Competition of Spin-Orbit and Exchange-Magnetic Interactions.

Finding ways to create and control the spin-dependent properties of two-dimensional electron states (2DESs) is a major challenge for the elaboration of novel spin-based devices. Spin-orbit and exchange-magnetic interactions (SOI and EMI) are two fundamental mechanisms that enable access to the tunability of spin-dependent properties of carriers. The silicon surface of HoRh2Si2 appears to be a unique model system, where concurrent SOI and EMI can be visualized and controlled by varying the temperature. The beauty and simplicity of this system lie in the 4f moments, which act as a multiple tuning instrument on the 2DESs, as the 4f projections parallel and perpendicular to the surface order at essentially different temperatures. Here we show that the SOI locks the spins of the 2DESs exclusively in the surface plane when the 4f moments are disordered: the Rashba-Bychkov effect. When the temperature is gradually lowered and the system experiences magnetic order, the rising EMI progressively competes with the SOI leading to a fundamental change in the spin-dependent properties of the 2DESs. The spins rotate and reorient toward the out-of-plane Ho 4f moments. Our findings show that the direction of the spins and the spin-splitting of the two-dimensional electrons at the surface can be manipulated in a controlled way by using only one parameter: the temperature.

Emergence of superconductivity in the canonical heavy-electron metal YbRh2Si2.

The smooth disappearance of antiferromagnetic order in strongly correlated metals commonly furnishes the development of unconventional superconductivity. The canonical heavy-electron compound YbRh2Si2 seems to represent an apparent exception from this quantum critical paradigm in that it is not a superconductor at temperature T ≥ 10 millikelvin (mK). Here we report magnetic and calorimetric measurements on YbRh2Si2, down to temperatures as low as T ≈ 1 mK. The data reveal the development of nuclear antiferromagnetic order slightly above 2 mK and of heavy-electron superconductivity almost concomitantly with this order. Our results demonstrate that superconductivity in the vicinity of quantum criticality is a general phenomenon.

Two crown-ether-coordinated caesium halogen salts.

The crystal structures of two crown-ether-coordinated caesium halogen salt hydrates, namely di-µ-bromido-bis[aqua(1,4,7,10,13,16-hexaoxacyclooctadecane)caesium(I)] dihydrate, [Cs2Br2(C12H24O6)2(H2O)2]·2H2O, (I), and poly[[diaquadi-µ-chlorido-µ-(1,4,7,10,13,16-hexaoxacyclooctadecane)dicaesium(I)] dihydrate], {[Cs2Cl2(C12H24O6)(H2O)2]·2H2O}n, (II), are reported. In (I), all atoms are located on general positions. In (II), the Cs(+) cation is located on a mirror plane perpendicular to the a axis, the chloride anion is located on a mirror plane perpendicular to the c axis and the crown-ether ring is located around a special position with site symmetry 2/m, with two opposite O atoms exactly on the mirror plane perpendicular to the a axis; of one water molecule, only the O atom is located on a mirror plane perpendicular on the a axis, while the other water molecule is completely located on a mirror plane perpendicular to the c axis. Whereas in (I), hydrogen bonds between bromide ligands and water molecules lead to one-dimensional chains running along the b axis, in (II) two-dimensional sheets of water molecules and chloride ligands are formed which combine with the polymeric caesium-crown polymer to give a three-dimensional network. Although both compounds have a similar composition, i.e. a Cs(+) cation with a halogen, an 18-crown-6 ether and a water ligand, the crystal structures are rather different. On the other hand, it is remarkable that (I) is isomorphous with the already published iodide compound.

Ferromagnetic quantum critical point in the heavy-fermion metal YbNi4(P(1-x)As(x))2.

Unconventional superconductivity and other previously unknown phases of matter exist in the vicinity of a quantum critical point (QCP): a continuous phase change of matter at absolute zero. Intensive theoretical and experimental investigations on itinerant systems have shown that metallic ferromagnets tend to develop via either a first-order phase transition or through the formation of intermediate superconducting or inhomogeneous magnetic phases. Here, through precision low-temperature measurements, we show that the Grüneisen ratio of the heavy fermion metallic ferromagnet YbNi(4)(P(0.92)As(0.08))(2) diverges upon cooling to T = 0, indicating a ferromagnetic QCP. Our observation that this kind of instability, which is forbidden in d-electron metals, occurs in a heavy fermion system will have a large impact on the studies of quantum critical materials.

Thermal and electrical transport across a magnetic quantum critical point.

A quantum critical point (QCP) arises when a continuous transition between competing phases occurs at zero temperature. Collective excitations at magnetic QCPs give rise to metallic properties that strongly deviate from the expectations of Landau's Fermi-liquid description, which is the standard theory of electron correlations in metals. Central to this theory is the notion of quasiparticles, electronic excitations that possess the quantum numbers of the non-interacting electrons. Here we report measurements of thermal and electrical transport across the field-induced magnetic QCP in the heavy-fermion compound YbRh(2)Si(2) (refs 2, 3). We show that the ratio of the thermal to electrical conductivities at the zero-temperature limit obeys the Wiedemann-Franz law for magnetic fields above the critical field at which the QCP is attained. This is also expected for magnetic fields below the critical field, where weak antiferromagnetic order and a Fermi-liquid phase form below 0.07 K (at zero field). At the critical field, however, the low-temperature electrical conductivity exceeds the thermal conductivity by about 10 per cent, suggestive of a non-Fermi-liquid ground state. This apparent violation of the Wiedemann-Franz law provides evidence for an unconventional type of QCP at which the fundamental concept of Landau quasiparticles no longer holds. These results imply that Landau quasiparticles break up, and that the origin of this disintegration is inelastic scattering associated with electronic quantum critical fluctuations--these insights could be relevant to understanding other deviations from Fermi-liquid behaviour frequently observed in various classes of correlated materials.

Discontinuous Hall coefficient at the quantum critical point in YbRh2Si2.

YbRh2Si2 is a model system for quantum criticality. In particular, Hall effect measurements helped identify the unconventional nature of its quantum critical point. Here, we present a high-resolution study of the Hall effect and magnetoresistivity on samples of different quality. We find a robust crossover on top of a sample dependent linear background contribution. Our detailed analysis provides a complete characterization of the crossover in terms of its position, width, and height. Importantly, we find in the extrapolation to zero temperature a discontinuity of the Hall coefficient occurring at the quantum critical point for all samples. In particular, the height of the jump in the Hall coefficient remains finite in the limit of zero temperature. Hence, our data solidify the conclusion of a collapsing Fermi surface. Finally, we contrast our results to the smooth Hall effect evolution seen in chromium, the prototype system for a spin-density-wave quantum critical point.

Fermi-surface collapse and dynamical scaling near a quantum-critical point.

Quantum criticality arises when a macroscopic phase of matter undergoes a continuous transformation at zero temperature. While the collective fluctuations at quantum-critical points are being increasingly recognized as playing an important role in a wide range of quantum materials, the nature of the underlying quantum-critical excitations remains poorly understood. Here we report in-depth measurements of the Hall effect in the heavy-fermion metal YbRh(2)Si(2), a prototypical system for quantum criticality. We isolate a rapid crossover of the isothermal Hall coefficient clearly connected to the quantum-critical point from a smooth background contribution; the latter exists away from the quantum-critical point and is detectable through our studies only over a wide range of magnetic field. Importantly, the width of the critical crossover is proportional to temperature, which violates the predictions of conventional theory and is instead consistent with an energy over temperature, E/T, scaling of the quantum-critical single-electron fluctuation spectrum. Our results provide evidence that the quantum-dynamical scaling and a critical Kondo breakdown simultaneously operate in the same material. Correspondingly, we infer that macroscopic scale-invariant fluctuations emerge from the microscopic many-body excitations associated with a collapsing Fermi-surface. This insight is expected to be relevant to the unconventional finite-temperature behavior in a broad range of strongly correlated quantum systems.

Thermopower evidence for an abrupt Fermi surface change at the quantum critical point of YbRh2Si2.

We present low-temperature thermopower results, S(T), on the heavy-fermion compound YbRh2Si2 in the vicinity of its field-induced quantum critical point (QCP). At B=0, a logarithmic increase of -S(T)/T between 1 and 0.1 K reveals strong non-Fermi-liquid behavior. A pronounced downturn of -S(T)/T below T{max}=0.1 K and a sign change from negative to positive S(T) values at T{0} approximately 30 mK are observed on the low-field side of the Kondo breakdown crossover line T{*}(B). In the field-induced, heavy Landau-Fermi-liquid regime, S(T)/T assumes constant, negative values below T{LFL}. A pronounced crossover in the -S(B)/T isotherms at T{*}(B) sharpens with decreasing T and seems to evolve toward a steplike function for T-->0. This is attributed to an abrupt change of the Fermi volume upon crossing the unconventional QCP of YbRh2Si2.