YbRh(2)Si(2): pronounced non-fermi-liquid effects above a low-lyingmagnetic phase transition

On the Ytterbium Valence and the Physical Properties in Selected Intermetallic Phases

The present review summarizes important aspects of the crystal chemistry of ytterbium-based intermetallic compounds along with a selection of their outstanding physical properties. These originate in many cases from the ytterbium valence. Different valence states are possible here, divalent (4f14), intermediate-valent, or trivalent (4f13) ytterbium, resulting in simple diamagnetic, Pauli or Curie-Weiss paramagnetic, or valence fluctuating behavior. Especially, some of the Yb3+ intermetallics have gained deep interest due to their Kondo or heavy Fermion ground states. We have summarized their property investigations using magnetic and transport measurements, specific heat data, NMR, ESR, and Mössbauer spectroscopy, elastic and inelastic neutron scattering, and XAS data as well as detailed thermoelectric measurements.

Magnetotransport and Fermi surface segmentation in Pauli limited superconductors

We report the first theoretical investigation of the spectroscopic, electrical and optical transport signatures ofd-wave Pauli limited superconductors, based on a non perturbative numerical approach. We demonstrate that the high magnetic field low temperature regime of these materials host a finite momentum paired superconducting phase. Multi-branched dispersion spectra with finite energy superconducting gaps, anisotropic segmentation of the Fermi surface and spatial modulations of the superconducting order characterizes this finite momentum paired phase and should be readily accessible through angle resolved photo emission spectroscopy, quasiparticle interference and differential conductance measurements. Based on the electrical and optical transport properties we capture the non Fermi liquid behavior of these systems at high temperatures, dominated by local superconducting correlations and characterized by resilient quasiparticles which survive the breakdown of the Fermi liquid description. We map out the generic thermal phase diagram of thed-wave Pauli limited superconductors and provide for the first time the accurate estimates of the thermal scales corresponding to the: (a) loss of (quasi) long range superconducting phase coherence (Tc), (b) loss of local pair correlations (Tpg), (c) breakdown of the Fermi liquid theory (Tmax) and cross-over from the non Fermi liquid to the bad metallic phase (TBR). Our thermal phase diagram mapped out on the basis of the spectroscopic and transport properties are found to be in qualitative agreement with the experimental observations on CeCoIn5andκ-BEDT, in terms of the thermodynamic phases and the phase transitions. The results presented in this paper are expected to initiate important transport and spectroscopic experiments on the Pauli limitedd-wave superconductors, providing sharp signatures of the finite momentum Cooper paired state in these materials.

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.

Superconductivity beyond the Conventional Pauli Limit in High-Pressure CeSb_{2}

We report the discovery of superconductivity at a pressure-induced magnetic quantum phase transition in the Kondo lattice system CeSb_{2}, sustained up to magnetic fields that exceed the conventional Pauli limit eightfold. Like CeRh_{2}As_{2}, CeSb_{2} is locally noncentrosymmetric around the Ce site, but the evolution of critical fields and normal state properties as CeSb_{2} is tuned through the quantum phase transition motivates a fundamentally different explanation for its resilience to applied field.

Controlled Bond Expansion for Density Matrix Renormalization Group Ground State Search at Single-Site Costs

DMRG ground state search algorithms employing symmetries must be able to expand virtual bond spaces by adding or changing symmetry sectors if these lower the energy. Traditional single-site DMRG does not allow bond expansion; two-site DMRG does, but at much higher computational costs. We present a controlled bond expansion (CBE) algorithm that yields two-site accuracy and convergence per sweep, at single-site costs. Given a matrix product state Ψ defining a variational space, CBE identifies parts of the orthogonal space carrying significant weight in HΨ and expands bonds to include only these. CBE-DMRG uses no mixing parameters and is fully variational. Using CBE-DMRG, we show that the Kondo-Heisenberg model on a width 4 cylinder features two distinct phases differing in their Fermi surface volumes.

Strong magnetic anisotropy in PrRu2Ga8and PrCo2Al8single crystals

Single crystals ofLnRu₂Ga₈andLnCo₂Al₈(Ln= La and Pr) were grown using a Ga/Al self-flux method. An orthorhombic CaCo₂Al₈-type structure with space groupPbam(No.55) of them was identified by x-ray diffraction. LaRu₂Ga₈and LaCo₂Al₈are Pauli paramagnetic down to 2 K, while PrRu₂Ga₈and PrCo₂Al₈show antiferromagnetic (AFM) order at 2.5 and 5 K, respectively. Strong magnetic anisotropy in PrRu₂Ga₈and PrCo₂Al₈single crystals was found by an anisotropic magnetic measurement. The field-induced FM state was observed in both PrRu₂Ga₈and PrCo₂Al₈forH||c. However, in the case of H⊥c, the AFM state is robust. The strong magnetic anisotropy in PrRu₂Ga₈FM and PrCo₂Al₈is due to their anisotropic magnetic interactions that FM interactions are dominant in the case ofH||cwhile AFM interactions forH⊥c.

Stranger than metals

In traditional metals, the temperature ( T ) dependence of electrical resistivity vanishes at low or high T , albeit for different reasons. Here, we review a class of materials, known as “strange” metals, that can violate both of these principles. In strange metals, the change in slope of the resistivity as the mean free path drops below the lattice constant, or as T → 0, can be imperceptible, suggesting continuity between the charge carriers at low and high T . We focus on transport and spectroscopic data on candidate strange metals in an effort to isolate and identify a unifying physical principle. Special attention is paid to quantum criticality, Planckian dissipation, Mottness, and whether a new gauge principle is needed to account for the nonlocal transport seen in these materials.

A mechanism for the strange metal phase in rare-earth intermetallic compounds

The elusive strange metal phase (ground state) was observed in a variety of quantum materials, notably in f-electron–based rare-earth intermetallic compounds. Its emergence has remained unclear. Here, we propose a generic mechanism for this phenomenon driven by the interplay of the gapless fermionic short-ranged antiferromagnetic spin correlation and critical bosonic charge fluctuations near a Kondo breakdown quantum phase transition. It is manifested as a fluctuating Kondo-scattering–stabilized critical (gapless) fermionic spin liquid. It shows ω/T scaling in dynamical electron scattering rate, a signature of quantum criticality. Our results on quasilinear-in-temperature scattering rate and logarithmic-in-temperature divergence in specific heat coefficient as temperature vanishes were recently seen in CePd1−xNi_xAl.

A major mystery in strongly interacting quantum systems is the microscopic origin of the “strange metal” phenomenology, with unconventional metallic behavior that defies Landau’s Fermi liquid framework for ordinary metals. This state is found across a wide range of quantum materials, notably in rare-earth intermetallic compounds at finite temperatures (T) near a magnetic quantum phase transition, and shows a quasilinear-in-temperature resistivity and a logarithmic-in-temperature specific heat coefficient. Recently, an even more enigmatic behavior pointing toward a stable strange metal ground state was observed in CePd1−xNi_xAl, a geometrically frustrated Kondo lattice compound. Here, we propose a mechanism for such phenomena driven by the interplay of the gapless fermionic short-ranged antiferromagnetic spin correlations (spinons) and critical bosonic charge (holons) fluctuations near a Kondo breakdown quantum phase transition. Within a dynamical large-N approach to the Kondo–Heisenberg lattice model, the strange metal phase is realized in transport and thermodynamical quantities. It is manifested as a fluctuating Kondo-scattering–stabilized critical (gapless) fermionic spin-liquid metal. It shows ω/T scaling in dynamical electron scattering rate, a signature of quantum criticality. Our results offer a qualitative understanding of the CePd1−xNi_xAl compound and suggest a possibility of realizing the quantum critical strange metal phase in correlated electron systems in general.

Single-crystal growth and magnetic anisotropy in PrFe2Ga8

Single crystals of PrFe₂Ga₈were successfully grown by using Ga self-flux. PrFe₂Ga₈crystallizes in the CaCo₂Al₈-type orthorhombic structure with the space groupPbam(no. 55). By combining the results from the magnetic-susceptibility, specific-heat, and resistivity measurements, we show that PrFe₂Ga₈exhibits a magnetic order at 14 K. ForH//c, the antiferromagnetic order can be suppressed by magnetic fields. However, the magnetic order is robust against magnetic fields forH⊥c. Our results provide basic physical properties of PrFe₂Ga₈and will help to further understand the magnetism in this system.

Are Heavy Fermion Strange Metals Planckian?

Strange metal behavior refers to a linear temperature dependence of the electrical resistivity that is not due to electron–phonon scattering. It is seen in numerous strongly correlated electron systems, from the heavy fermion compounds, via transition metal oxides and iron pnictides, to magic angle twisted bi-layer graphene, frequently in connection with unconventional or “high temperature” superconductivity. To achieve a unified understanding of these phenomena across the different materials classes is a central open problem in condensed matter physics. Tests whether the linear-in-temperature law might be dictated by Planckian dissipation—scattering with the rate ∼kBT/ℏ—are receiving considerable attention. Here we assess the situation for strange metal heavy fermion compounds. They allow to probe the regime of extreme correlation strength, with effective mass or Fermi velocity renormalizations in excess of three orders of magnitude. Adopting the same procedure as done in previous studies, i.e., assuming a simple Drude conductivity with the above scattering rate, we find that for these strongly renormalized quasiparticles, scattering is much weaker than Planckian, implying that the linear temperature dependence should be due to other effects. We discuss implications of this finding and point to directions for further work.

Superconductivity in an extreme strange metal

Some of the highest-transition-temperature superconductors across various materials classes exhibit linear-in-temperature 'strange metal' or 'Planckian' electrical resistivities in their normal state. It is thus believed by many that this behavior holds the key to unlock the secrets of high-temperature superconductivity. However, these materials typically display complex phase diagrams governed by various competing energy scales, making an unambiguous identification of the physics at play difficult. Here we use electrical resistivity measurements into the micro-Kelvin regime to discover superconductivity condensing out of an extreme strange metal state-with linear resistivity over 3.5 orders of magnitude in temperature. We propose that the Cooper pairing is mediated by the modes associated with a recently evidenced dynamical charge localization-delocalization transition, a mechanism that may well be pertinent also in other strange metal superconductors.

Temperature-dependent change of the electronic structure in the Kondo lattice system YbRh2Si2

The heavy-fermion behavior in intermetallic compounds manifests itself in a quenching of local magnetic moments by developing Kondo spin-singlet many-body states combined with a drastic increase of the effective mass of conduction electrons, which occurs below the lattice Kondo temperatureT_K. This behavior is caused by interactions between the strongly localized 4felectrons and itinerant electrons. A controversially discussed question in this context is how the localized electronic states contribute to the Fermi surface upon changing the temperature. One expects that hybridization between the local moments and the itinerant electrons leads to a transition from a small Fermi surface in a non-coherent regime at high temperatures to a large Fermi surface once the coherent Kondo lattice regime is realized belowT_K. We demonstrate, using hard x-ray angle-resolved photoemission spectroscopy that the electronic structure of the prototypical heavy fermion compound YbRh₂Si₂changes with temperature between 100 and 200 K, i.e. far above the Kondo temperature,T_K= 25 K, of this system. Our results suggest a transition from a small to a large Fermi surface with decreasing temperature. This result is inconsistent with the prediction of the dynamical mean-field periodic Anderson model and supports the idea of an independent energy scale governing the change of band dispersion.

Uniaxial and fourfold basal anisotropy in GdRh2Si2

The magnetocrystalline anisotropy of GdRh₂Si₂ is examined in detail via the electron spin resonance (ESR) of its well-localised Gd³⁺ moments. Below T _N = 107 K, long range magnetic order sets in with ferromagnetic layers in the (aa)-plane stacked antiferromagnetically along the c-axis of the tetragonal structure. Interestingly, the easy-plane anisotropy allows for the observation of antiferromagnetic resonance at X- and Q-band microwave frequencies. In addition to the easy-plane anisotropy we have also quantified the weaker fourfold anisotropy within the easy plane. The obtained resonance fields are modelled in terms of eigenoscillations of the two antiferromagnetically coupled sublattices. Conversely, this model provides plots of the eigenfrequencies as a function of field and the specific anisotropy constants. Such calculations have rarely been done. Therefore our analysis is prototypical for other systems with fourfold in-plane anisotropy. It is demonstrated that the experimental in-plane ESR data may be crucial for a precise knowledge of the out-of-plane anisotropy.

Concomitant singularities of Yb-valence and magnetism at a critical lattice parameter of icosahedral quasicrystals and approximants

Non-Fermi-liquid (NFL), a significant deviation from Fermi-liquid theory, usually emerges near an order-disorder phase transition at absolute zero. Recently, a diverging susceptibility toward zero temperature was observed in a quasicrystal (QC). Since an electronic long-range ordering is normally absent in QCs, this anomalous behaviour should be a new type of NFL. Here we study high-resolution partial-fluorescence-yield x-ray absorption spectroscopy on Yb-based intermediate-valence icosahedral QCs and cubic approximant crystals (ACs), some of which are new materials, to unveil the mechanism of the NFL. We find that for both forms of QCs and ACs, there is a critical lattice parameter where Yb-valence and magnetism concomitantly exhibit singularities, suggesting a critical-valence-fluctuation-induced NFL. The present result provides an intriguing structure–property relationship of matter; size of a Tsai-type cluster (that is a common local structure to both forms) tunes the NFL whereas translational symmetry (that is present in ACs but absent in QCs) determines the nature of the NFL against the external/chemical pressure.

Scaling theory of magnetism in frustrated Kondo lattices

A scaling theory of the Kondo lattices with frustrated exchange interactions is developed, criterium of antiferromagnetic ordering and quantum-disordered state being investigated. The calculations taking into account magnon and incoherent spin dynamics are performed. Depending on the bare model parameters, one or two quantum phase transitions into non-magnetic spin-liquid and Kondo Fermi-liquid ground states can occur with increasing the bare coupling constant. Whereas the renormalization of the magnetic moment in the ordered phase can reach orders of magnitude, spin fluctuation frequency and coupling constant are moderately renormalized in the spin-liquid phase. This justifies application of the scaling approach. Possibility of a non-Fermi-liquid behavior is treated.

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.

Divalent EuRh2Si2 as a reference for the Luttinger theorem and antiferromagnetism in trivalent heavy-fermion YbRh2Si2

Application of the Luttinger theorem to the Kondo lattice YbRh2Si2 suggests that its large 4f-derived Fermi surface (FS) in the paramagnetic (PM) regime should be similar in shape and volume to that of the divalent local-moment antiferromagnet (AFM) EuRh2Si2 in its PM regime. Here we show by angle-resolved photoemission spectroscopy that paramagnetic EuRh2Si2 has a large FS essentially similar to the one seen in YbRh2Si2 down to 1 K. In EuRh2Si2 the onset of AFM order below 24.5 K induces an extensive fragmentation of the FS due to Brillouin zone folding, intersection and resulting hybridization of the Fermi-surface sheets. Our results on EuRh2Si2 indicate that the formation of the AFM state in YbRh2Si2 is very likely also connected with similar changes in the FS, which have to be taken into account in the controversial analysis and discussion of anomalies observed at the quantum critical point in this system.

Thermodynamic signatures of quantum criticality in cuprate superconductors

The three central phenomena of cuprate (copper oxide) superconductors are linked by a common doping level p*-at which the enigmatic pseudogap phase ends and the resistivity exhibits an anomalous linear dependence on temperature, and around which the superconducting phase forms a dome-shaped area in the phase diagram¹. However, the fundamental nature of p* remains unclear, in particular regarding whether it marks a true quantum phase transition. Here we measure the specific heat C of the cuprates Eu-LSCO and Nd-LSCO at low temperature in magnetic fields large enough to suppress superconductivity, over a wide doping range² that includes p*. As a function of doping, we find that C_el/T is strongly peaked at p* (where C_el is the electronic contribution to C) and exhibits a log(1/T) dependence as temperature T tends to zero. These are the classic thermodynamic signatures of a quantum critical point^3-5, as observed in heavy-fermion⁶ and iron-based⁷ superconductors at the point where their antiferromagnetic phase comes to an end. We conclude that the pseudogap phase of cuprates ends at a quantum critical point, the associated fluctuations of which are probably involved in d-wave pairing and the anomalous scattering of charge carriers.

Similar temperature scale for valence changes in Kondo lattices with different Kondo temperatures

The Kondo model predicts that both the valence at low temperatures and its temperature dependence scale with the characteristic energy T_K of the Kondo interaction. Here, we study the evolution of the 4f occupancy with temperature in a series of Yb Kondo lattices using resonant X-ray emission spectroscopy. In agreement with simple theoretical models, we observe a scaling between the valence at low temperature and T_K obtained from thermodynamic measurements. In contrast, the temperature scale T_v at which the valence increases with temperature is almost the same in all investigated materials while the Kondo temperatures differ by almost four orders of magnitude. This observation is in remarkable contradiction to both naive expectation and precise theoretical predictions of the Kondo model, asking for further theoretical work in order to explain our findings. Our data exclude the presence of a quantum critical valence transition in YbRh₂Si₂.

The competition between interactions promoting magnetic order and those suppressing magnetism causes unusual electronic behaviour in Kondo lattice materials. Here, the authors show the energy scale for valence fluctuations is not controlled by the Kondo scale, contrary to expectations from single-site models.

Effects of crystalline electronic field and onsite interorbital interaction in Yb-based quasicrystal and approximant crystal

To get an insight into a new type of quantum critical phenomena recently discovered in the quasicrystal Yb₁₅Al₃₄Au₅₁ and approximant crystal (AC) Yb₁₄Al₃₅Au₅₁ under pressure, we discuss the property of the crystalline electronic field (CEF) at Yb in the AC and show that uneven CEF levels at each Yb site can appear because of the Al/Au mixed sites. Then we construct the minimal model for the electronic state on the AC by introducing the onsite Coulomb repulsion between the 4f and 5d orbitals at Yb. Numerical calculations for the ground state shows that the lattice constant dependence of the Yb valence well explains the recent measurement done by systematic substitution of elements of Al and Au in the quasicrystal and AC, where the quasicrystal Yb₁₅Al₃₄Au₅₁ is just located at the point from where the Yb-valence starts to change drastically. Our calculation convincingly demonstrates that this is indeed the evidence that this material is just located at the quantum critical point of the Yb-valence transition.

Quasiparticles in condensed matter systems

Quasiparticles are a powerful concept of condensed matter quantum theory. In this review, the appearence and the properties of quasiparticles are presented in a unifying perspective. The principles behind the existence of quasiparticle excitations in both quantum disordered and ordered phases of fermionic and bosonic systems are discussed. The lifetime of quasiparticles is considered in particular near a continuous classical or quantum phase transition, when the nature of quasiparticles on both sides of a transition into an ordered state changes. A new concept of critical quasiparticles near a quantum critical point is introduced, and applied to quantum phase transitions in heavy fermion metals. Fractional quasiparticles in systems of restricted dimensionality are reviewed. Dirac quasiparticles emerging in so-called Dirac materials are discussed. The more recent discoveries of topologically protected chiral quasiparticles in topological matter and Majorana quasiparticles in topological superconductors are briefly reviewed.

Non-Fermi Liquid Behavior and Continuously Tunable Resistivity Exponents in the Anderson-Hubbard Model at Finite Temperature

We employ a recently developed computational many-body technique to study for the first time the half-filled Anderson-Hubbard model at finite temperature and arbitrary correlation U and disorder V strengths. Interestingly, the narrow zero temperature metallic range induced by disorder from the Mott insulator expands with increasing temperature in a manner resembling a quantum critical point. Our study of the resistivity temperature scaling T^{α} for this metal reveals non-Fermi liquid characteristics. Moreover, a continuous dependence of α on U and V from linear to nearly quadratic is observed. We argue that these exotic results arise from a systematic change with U and V of the "effective" disorder, a combination of quenched disorder and intrinsic localized spins.

Theory of scanning tunneling spectroscopy: from Kondo impurities to heavy fermion materials

Kondo systems ranging from the single Kondo impurity to heavy fermion materials present us with a plethora of unconventional properties whose theoretical understanding is still one of the major open problems in condensed matter physics. Over the last few years, groundbreaking scanning tunneling spectroscopy (STS) experiments have provided unprecedented new insight into the electronic structure of Kondo systems. Interpreting the results of these experiments-the differential conductance and the quasi-particle interference spectrum-however, has been complicated by the fact that electrons tunneling from the STS tip into the system can tunnel either into the heavy magnetic moment or the light conduction band states. In this article, we briefly review the theoretical progress made in understanding how quantum interference between these two tunneling paths affects the experimental STS results. We show how this theoretical insight has allowed us to interpret the results of STS experiments on a series of heavy fermion materials providing detailed knowledge of their complex electronic structure. It is this knowledge that is a conditio sine qua non for developing a deeper understanding of the fascinating properties exhibited by heavy fermion materials, ranging from unconventional superconductivity to non-Fermi-liquid behavior in the vicinity of quantum critical points.

Grüneisen parameter studies on heavy fermion quantum criticality

The Grüneisen parameter, experimentally determined from the ratio of thermal expansion to specific heat, quantifies the pressure dependence of characteristic energy scales of matter. It is highly enhanced for Kondo lattice systems, whose properties are strongly dependent on the pressure sensitive antiferromagnetic exchange interaction between f- and conduction electrons. In this review, we focus on the divergence of the Grüneisen parameter and its magnetic analogue, the adiabatic magnetocaloric effect, for heavy-fermion metals near quantum critical points. We compare experimental results with current theoretical models, including the effect of strong geometrical frustration. We also discuss the possibility of using materials with the divergent magnetic Grüneisen parameter for adiabatic demagnetization cooling to very low temperatures.

Electron-phonon interaction and superconductivity in BaIr2P2

Detailed calculations of the electronic structure, phonons and electron-phonon coupling of the superconducting compound BaIr2P2 were performed from first-principles. The electronic structure showed excellent agreement with the available experimental data. The total electron-phonon coupling constant was [Formula: see text] and the logarithmically averaged phonon frequency was [Formula: see text] K. From the Allen-Dynes formula, with [Formula: see text], the superconducting critical temperature was estimated to be [Formula: see text] K, which is in excellent agreement with the experiment. These results indicate that the electron-phonon coupling is of moderate strength and is easily capable of supporting the observed superconductivity.

Super-heavy electron material as metallic refrigerant for adiabatic demagnetization cooling

Low-temperature refrigeration is of crucial importance in fundamental research of condensed matter physics, because the investigations of fascinating quantum phenomena, such as superconductivity, superfluidity, and quantum criticality, often require refrigeration down to very low temperatures. Currently, cryogenic refrigerators with (3)He gas are widely used for cooling below 1 K. However, usage of the gas has been increasingly difficult because of the current worldwide shortage. Therefore, it is important to consider alternative methods of refrigeration. We show that a new type of refrigerant, the super-heavy electron metal YbCo2Zn20, can be used for adiabatic demagnetization refrigeration, which does not require (3)He gas. This method has a number of advantages, including much better metallic thermal conductivity compared to the conventional insulating refrigerants. We also demonstrate that the cooling performance is optimized in Yb1-x Sc x Co2Zn20 by partial Sc substitution, with x ~ 0.19. The substitution induces chemical pressure that drives the materials to a zero-field quantum critical point. This leads to an additional enhancement of the magnetocaloric effect in low fields and low temperatures, enabling final temperatures well below 100 mK. This performance has, up to now, been restricted to insulators. For nearly a century, the same principle of using local magnetic moments has been applied for adiabatic demagnetization cooling. This study opens new possibilities of using itinerant magnetic moments for cryogen-free refrigeration.

Preserved entropy and fragile magnetism

A large swath of quantum critical and strongly correlated electron systems can be associated with the phenomena of preserved entropy and fragile magnetism. In this overview we present our thoughts and plans for the discovery and development of lanthanide and transition metal based, strongly correlated systems that are revealed by suppressed, fragile magnetism, quantum criticality, or grow out of preserved entropy. We will present and discuss current examples such as YbBiPt, YbAgGe, YbFe2Zn20, PrAg2In, BaFe2As2, CaFe2As2, LaCrSb3 and LaCrGe3 as part of our motivation and to provide illustrative examples.

Foundations of heavy-fermion superconductivity: lattice Kondo effect and Mott physics

This article overviews the development of heavy-fermion superconductivity, notably in such rare-earth-based intermetallic compounds which behave as Kondo-lattice systems. Heavy-fermion superconductivity is of unconventional nature in the sense that it is not mediated by electron-phonon coupling. Rather, in most cases the attractive interaction between charge carriers is apparently magnetic in origin. Fluctuations associated with an antiferromagnetic (AF) quantum critical point (QCP) play a major role. The first heavy-fermion superconductor CeCu2Si2 turned out to be the prototype of a larger group of materials for which the underlying, often pressure-induced, AF QCP is likely to be of a three-dimensional (3D) spin-density-wave (SDW) variety. For UBe13, the second heavy-fermion superconductor, a magnetic-field-induced 3D SDW QCP inside the superconducting phase can be conjectured. Such a 'conventional', itinerant QCP can be well understood within Landau's paradigm of order-parameter fluctuations. In contrast, the low-temperature normal-state properties of a few heavy-fermion superconductors are at odds with the Landau framework. They are characterized by an 'unconventional', local QCP which may be considered a zero-temperature 4 f-orbital selective Mott transition. Here, as concluded for YbRh2Si2, the breakdown of the Kondo effect concurring with the AF instability gives rise to an abrupt change of the Fermi surface. Very recently, superconductivity was discovered for this compound at ultra-low temperatures. Therefore, YbRh2Si2 along with CeRhIn5 under pressure provide a natural link between the large group of about fifty low-temperature heavy-fermion superconductors and other families of unconventional superconductors with substantially higher T c, e.g. the doped Mott insulators of the perovskite-type cuprates and the organic charge-transfer salts.

SOLID-STATE PHYSICS. Scalable T² resistivity in a small single-component Fermi surface

Scattering among electrons generates a distinct contribution to electrical resistivity that follows a quadratic temperature (T) dependence. In strongly correlated electron systems, the prefactor A of this T(2) resistivity scales with the magnitude of the electronic specific heat, γ. Here we show that one can change the magnitude of A by four orders of magnitude in metallic strontium titanate (SrTiO3) by tuning the concentration of the carriers and, consequently, the Fermi energy. The T(2) behavior persists in the single-band dilute limit despite the absence of two known mechanisms for T(2) behavior: distinct electron reservoirs and Umklapp processes. The results highlight the absence of a microscopic theory for momentum decay through electron-electron scattering in various Fermi liquids.

Quantum Criticality in Quasi-Two-Dimensional Itinerant Antiferromagnets

Quasi-two-dimensional itinerant fermions in the antiferromagnetic (AFM) quantum-critical region of their phase diagram, such as in the Fe-based superconductors or in some of the heavy-fermion compounds, exhibit a resistivity varying linearly with temperature and a contribution to specific heat or thermopower proportional to TlnT. It is shown, here, that a generic model of itinerant anti-ferromagnet can be canonically transformed so that its critical fluctuations around the AFM-vector Q can be obtained from the fluctuations in the long wavelength limit of a dissipative quantum XY model. The fluctuations of the dissipative quantum XY model in 2D have been evaluated recently, and in a large regime of parameters, they are determined, not by renormalized spin fluctuations, but by topological excitations. In this regime, the fluctuations are separable in their spatial and temporal dependence and have a spatial correlation length which is proportional to the logarithm of the temporal correlation length, i.e., for some purposes, the effective dynamic exponent z=∞. The time dependence gives ω/T scaling at criticality. The observed resistivity and entropy then follow. Several predictions to test the theory are also given.

Unusual weak magnetic exchange in two different structure types: YbPt2Sn and YbPt2In

We present the structural, magnetic, thermodynamic and transport properties of the two new compounds YbPt(2)Sn and YbPt(2)In. X-ray powder diffraction shows that they crystallize in different structure types, the hexagonal ZrPt(2)Al and the cubic Heusler type, respectively. Despite quite different lattice types, both compounds present very similar magnetic properties: a stable trivalent Yb(3+), no evidence for a sizeable Kondo interaction and very weak exchange interactions with a strength below 1 K as deduced from specific heat C(T). Broad anomalies in C(T) suggest short range magnetic ordering at about 250 mK and 180 mK for YbPt(2)Sn and YbPt(2)In, respectively. The weak exchange and the low ordering temperature result in a large magnetocaloric effect as deduced from the magnetic field dependence of C(T), making these compounds interesting candidates for magnetic cooling. In addition we found in YbPt(2)In evidences for a charge density wave transition at about 290 K. The occurrence of such transitions within several RET2X compound series (RE = rare earth, T = noble metal, X = In, Sn) is analyzed.

Crystal growth, structural, electrical, and magnetic properties of mixed-valent compounds YbOs2Al10 and LuOs2Al10

Single crystals of YbOs2Al10 and LuOs2Al10 were grown for the first time using an aluminum self-flux method. The compounds crystallized into a cagelike structure in space group Cmcm, similar to the prototype compound YbFe2Al10. YbOs2Al10 exhibited a mixed-valent nature, as determined by magnetic susceptibility measurements over a wide temperature range from 2 to 900 K, in which the inter-configuration-fluctuation model revealed a broad peak around 400 K. In contrast, LuOs2Al10 displayed Pauli-like paramagnetic behavior over the same temperature range. Both compounds were metallic in nature between 2 and 300 K. The electronic specific heat coefficient of 21.3(2) mJ mol(-1) K(-2) for YbOs2Al10 was determined to be larger than that for LuOs2Al10 [8.9(1) mJ mol(-1) K(-2)], reflecting the mixed-valent nature of the former. First-principles calculations predicted the presence of a mixed-valent state in YbOs2Al10, in agreement with the experimental observations. The novel compound YbOs2Al10 elucidates the evolution of the mixed-valent nature of the Yb-based ternary transition metal aluminides from the 3d to 5d elements.

Complex and strongly anisotropic magnetism in the pure spin system EuRh2Si2

In divalent Eu systems, the 4f local moment has a pure spin state J = S = 7/2. Although the absence of orbital moment precludes crystal electric field effects, we report a sizable magnetic anisotropy in single crystals of EuRh2Si2. We observed a surprisingly complex magnetic behavior with three successive phase transitions. The Eu(2+) moments order in a probably amplitude-modulated structure below 24.5 K, undergoing a further transition to a structure that is possibly of the equal-moment type, and a first order transition at lower temperatures, presumably into a spin spiral structure. The sharp metamagnetic transition observed at low fields applied perpendicular to the hard axis is consistent with a change from a spiral to a fan structure. These magnetic structures are presumably formed by ferromagnetic planes perpendicular to the c axis, stacked antiferromagnetically along c but not of type I, at least just below the ordering temperature. Since EuRh2Si2 is isoelectronic and isostructural to EuFe2As2 at room temperature, our results are also relevant for the complex Eu-magnetism observed there, especially for the transition from an antiferromagnetic to a ferromagnetic state observed in EuFe2P2 upon substituting As by P.

Hidden T-linear scattering rate in Ba0.6K0.4Fe2As2 revealed by optical spectroscopy

The optical properties of Ba0.6K0.4Fe2As2 have been determined in the normal state for a number of temperatures over a wide frequency range. Two Drude terms, representing two groups of carriers with different scattering rates (1/τ), well describe the real part of the optical conductivity σ1(ω). A "broad" Drude component results in an incoherent background with a T-independent 1/τb, while a "narrow" Drude component reveals a T-linear 1/τn resulting in a resistivity ρn≡1/σ1n(ω→0) also linear in temperature. An arctan(T) low-frequency spectral weight is also strong evidence for a T-linear 1/τ. A comparison to other materials with similar behavior suggests that the T-linear 1/τn and ρn in Ba0.6K0.4Fe2As2 originate from scattering from spin fluctuations and hence that an antiferromagnetic quantum critical point is likely to exist in the superconducting dome.

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.

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.

Verification of the Wiedemann-Franz law in YbRh2Si2 at a quantum critical point

The thermal conductivity measurements are performed on the heavy-fermion compound YbRh(2)Si(2) down to 0.04 K and under magnetic fields through a quantum critical point (QCP) at B(c)=0.66  T∥c axis. In the limit as T→0, we find that the Wiedemann-Franz law is satisfied within experimental error at the QCP despite the destruction of the standard signature of Fermi liquid. Our results place strong constraints on models that attempt to describe the nature of the unconventional quantum criticality of YbRh(2)Si(2).

Challenges in intermetallics: synthesis, structural characterization, and transitions

Intermetallics that contain rare-earth elements are particularly interesting because of their temperature- and pressure-dependent structural and physical transitions that make them potential candidates for magnetic applications. This article highlights synthetic routes and structural characterization advancements used to investigate intermetallic materials. Experimental and theoretical examples of three intermetallic structure types--ThCr(2)Si(2), Heusler and Laves--are discussed to present a historical review and to illustrate the grand challenges in unravelling structure-property relationships of intermetallic compounds.

Electronic Griffiths phase in the Te-doped semiconductor FeSb2

We report on the emergence of an electronic Griffiths phase in the doped semiconductor FeSb(2), predicted for disordered insulators with random localized moments in the vicinity of a metal-insulator transition. Magnetic, transport, and thermodynamic measurements of Fe(Sb(1-x)Te(x))(2) single crystals show signatures of disorder-induced non-Fermi liquid behavior and a Wilson ratio expected for strong electronic correlations. The electronic Griffiths phase states are found on the metallic boundary between the insulating state (x = 0) and a long-range albeit weak magnetic order (x ≥ 0.075).

From incommensurate correlations to mesoscopic spin resonance in YbRh2Si2

Spin fluctuations are reported near the magnetic field-driven quantum critical point in YbRh(2)Si(2). On cooling, ferromagnetic fluctuations evolve into incommensurate correlations located at q(0) = ±(δ,δ), with δ = 0.14 ± 0.04 r.l.u. At low temperatures, an in-plane magnetic field induces a sharp intradoublet resonant excitation at an energy E(0) = gμ(B)μ(0)H with g = 3.8 ± 0.2. The intensity is localized at the zone center, indicating precession of spin density extending ξ = 6 ± 2 Å beyond the 4f site.

Kondo lattice with heavy fermions: peculiarities of spin kinetics

A model of spin relaxation of Kondo lattices is proposed to explain the angular dependence of the electron spin resonance (ESR) parameters in the heavy fermion compounds Y bIr(2)Si(2) and Y bRh(2)Si(2). A perturbational scaling approach reveals a collective spin motion of Yb ions with conduction electrons in the bottleneck regime. A common energy scale due to the Kondo effect regulates the temperature dependence of different kinetic coefficients to result in a mutual cancelation of all divergent parts in a collective spin mode. The angular dependence of the ESR intensity, linewidth and resonant frequency is shown to be in good agreement with experimental data on Y bIr(2)Si(2) and Y bRh(2)Si(2). In particular, the unexpectedly weak dependence of the ESR intensity on the orientation of the microwave magnetic field agrees with the properties of the discussed model.

Structural investigations on YbRh2Si2: from the atomic to the macroscopic length scale

YbRh2Si2 has advanced to a prototype material for investigating physics related to the Kondo effect. An optimization of the synthesis resulted in single crystals of extraordinary crystalline quality. At the atomic scale, we utilize scanning tunneling microscopy to study the topography of cleaved single crystals. A structural and chemical analysis was conducted by highly accurate x-ray diffraction and wavelength dispersive x-ray spectroscopy measurements. The latter indicate a homogeneity range of the YbRh2Si2 phase between approximately 40.0–40.2 at.% Rh. For our high-quality samples the number of defects found on the atomic scale (of the order of 0.3% of the visible lattice sites) is in quantitative agreement with a very small off-stoichiometry within this homogeneity range. Comparing our results for these samples allows an assignment of the structural defects observed at the cleaved surfaces to Rh occupying Si sites and, even less numerous Si in Rh sites. Such an analysis is hampered for samples of lesser quality, but there seem to be numerous empty Si-sites. Based on these observations the results of scanning tunneling spectroscopy can be analyzed in further detail and provide insight into the Kondo physics.

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 YbRh(2)Si(2), β-YbAlB(4), YbCu(5-x)Al(x), and CeIrIn(5). 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.

Correlated disorder in a Kondo lattice

Motivated by recent experiments on Yb-doped CeCoIn5, we study the effect of correlated disorder in a Kondo lattice. Correlations between the impurities are considered at the two-particle level. We use a mean-field theory approximation for the Anderson lattice model to calculate how the emergence of coherence in the Kondo lattice is impacted by correlations between impurities. We show that the rate at which disorder suppresses coherence temperature depends on the length of the impurity correlations. As the impurity concentration increases, we generally find that the suppression of coherence temperature is significantly reduced. The results are discussed in the context of available experimental data.