Quantum Criticality Without Tuning in the Mixed Valence Compound β-YbAlB 4

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.

Strong enhancement of magnetic ordering temperature and structural/valence transitions in EuPd3S4 under high pressure

We present a comprehensive study of the inhomogeneous mixed-valence compound, EuPd3S4, by electrical transport, X-ray diffraction, time-domain 151Eu synchrotron Mössbauer spectroscopy, and X-ray absorption spectroscopy measurements under high pressure. Electrical transport measurements show that the antiferromagnetic ordering temperature, TN, increases rapidly from 2.8 K at ambient pressure to 23.5 K at ~19 GPa and plateaus between ~19 and ~29 GPa after which no anomaly associated with TN is detected. A pressure-induced first-order structural transition from cubic to tetragonal is observed, with a rather broad coexistence region (~20 GPa to ~30 GPa) that corresponds to the TN plateau. Mössbauer spectroscopy measurements show a clear valence transition from approximately 50:50 Eu2+:Eu3+ to fully Eu3+ at ~28 GPa, consistent with the vanishing of the magnetic order at the same pressure. X-ray absorption data show a transition to a fully trivalent state at a similar pressure. Our results show that pressure first greatly enhances TN, most likely via enhanced hybridization between the Eu 4f states and the conduction band, and then, second, causes a structural phase transition that coincides with the conversion of the europium to a fully trivalent state.

Observation of a critical charge mode in a strange metal

Understanding the strange metallic behavior that develops at the brink of localization in quantum materials requires probing the underlying electronic charge dynamics. Using synchrotron radiation-based Mössbauer spectroscopy, we studied the charge fluctuations of the strange metal phase of β-YbAlB₄ as a function of temperature and pressure. We found that the usual single absorption peak in the Fermi-liquid regime splits into two peaks upon entering the critical regime. We interpret this spectrum as a single nuclear transition, modulated by nearby electronic valence fluctuations whose long time scales are further enhanced by the formation of charged polarons. These critical charge fluctuations may prove to be a distinct signature of strange metals.

Novel Valence Transition in Elemental Metal Europium around 80 GPa

Valence transition could induce structural, insulator-metal, nonmagnetic-magnetic and superconducting transitions in rare-earth metals and compounds, while the underlying physics remains unclear due to the complex interaction of localized 4f electrons as well as their coupling with itinerant electrons. The valence transition in the elemental metal europium (Eu) still has remained as a matter of debate. Using resonant x-ray emission scattering and x-ray diffraction, we pressurize the states of 4f electrons in Eu and study its valence and structure transitions up to 160 GPa. We provide compelling evidence for a valence transition around 80 GPa, which coincides with a structural transition from a monoclinic (C2/c) to an orthorhombic phase (Pnma). We show that the valence transition occurs when the pressure-dependent energy gap between 4f and 5d electrons approaches the Coulomb interaction. Our discovery is critical for understanding the electrodynamics of Eu, including magnetism and high-pressure superconductivity.

Gappability Index for Quantum Many-Body Systems

We propose an index I_{G} which characterizes the degree of gappability, namely the difficulty to induce a unique ground state with a nonvanishing excitation gap, in the presence of a symmetry G. I_{G} represents the dimension of the subspace of ambient uniquely gapped theories in the entire G-invariant "theory space." The celebrated Lieb-Schultz-Mattis theorem corresponds, in our formulation, to the case I_{G}=0 (completely ingappable) for the symmetry G including the lattice translation symmetry. We illustrate the usefulness of the index by discussing the phase diagram of spin-1/2 antiferromagnets in various dimensions, which do not necessarily have the translation symmetry.

Strongly Correlated Quantum Spin Liquids versus Heavy Fermion Metals: A Review

This review considers the topological fermion condensation quantum phase transition (FCQPT) that explains the complex behavior of strongly correlated Fermi systems, such as frustrated insulators with quantum spin liquid and heavy fermion metals. The review contrasts theoretical consideration with recent experimental data collected on both heavy fermion metals (HF) and frustrated insulators. Such a method allows to understand experimental data. We also consider experimental data collected on quantum spin liquid in Lu3Cu2Sb3O14 and quasi-one dimensional (1D) quantum spin liquid in both YbAlO3 and Cu(C4H4N2)(NO3)2 with the aim to establish a sound theoretical explanation for the observed scaling laws, Landau Fermi liquid (LFL) and non-Fermi-liquid (NFL) behavior exhibited by these frustrated insulators. The recent experimental data on the heavy-fermion metal α−YbAl1−xFexB4, with x=0.014, and on its sister compounds β−YbAlB4 and YbCo2Ge4, carried out under the application of magnetic field as a control parameter are analyzed. We show that the thermodynamic and transport properties as well as the empirical scaling laws follow from the fermion condensation theory. We explain how both the similarity and the difference in the thermodynamic and transport properties of α−YbAl1−xFexB4 and in its sister compounds β−YbAlB4 and YbCo2Ge4 emerge, as well as establish connection of these (HF) metals with insulators Lu3Cu2Sb3O14, Cu(C4H4N2)(NO3)2 and YbAlO3. We demonstrate that the universal LFL and NFL behavior emerge because the HF compounds and the frustrated insulators are located near the topological FCQPT or are driven by the application of magnetic fields.

Anisotropy-driven quantum criticality in an intermediate valence system

Intermetallic compounds containing f-electron elements have been prototypical materials for investigating strong electron correlations and quantum criticality (QC). Their heavy fermion ground state evoked by the magnetic f-electrons is susceptible to the onset of quantum phases, such as magnetism or superconductivity, due to the enhanced effective mass (m^*) and a corresponding decrease of the Fermi temperature. However, the presence of f-electron valence fluctuations to a non-magnetic state is regarded an anathema to QC, as it usually generates a paramagnetic Fermi-liquid state with quasiparticles of moderate m^*. Such systems are typically isotropic, with a characteristic energy scale T₀ of the order of hundreds of kelvins that require large magnetic fields or pressures to promote a valence or magnetic instability. Here we show the discovery of a quantum critical behaviour and a Lifshitz transition under low magnetic field in an intermediate valence compound α-YbAlB₄. The QC origin is attributed to the anisotropic hybridization between the conduction and localized f-electrons. These findings suggest a new route to bypass the large valence energy scale in developing the QC.

The nature of quantum criticality in intermetallic f-electron compounds exhibiting valence fluctuations is not well understood. Here, using a combination of experimental techniques, the authors attribute quantum criticality in YbAlB₄ to the anisotropic hybridization between the conduction and f-electrons.

Non-Fermi liquid behavior below the Néel temperature in the frustrated heavy fermion magnet UAu2

The term Fermi liquid is almost synonymous with the metallic state. The association is known to break down at quantum critical points (QCPs), but these require precise values of tuning parameters, such as pressure and applied magnetic field, to exactly suppress a continuous phase transition temperature to the absolute zero. Three-dimensional non-Fermi liquid states, apart from superconductivity, that are unshackled from a QCP are much rarer and are not currently well understood. Here, we report that the triangular lattice system uranium diauride (UAu₂) forms such a state with a non-Fermi liquid low-temperature heat capacity [Formula: see text] and electrical resistivity [Formula: see text] far below its Néel temperature. The magnetic order itself has a novel structure and is accompanied by weak charge modulation that is not simply due to magnetostriction. The charge modulation continues to grow in amplitude with decreasing temperature, suggesting that charge degrees of freedom play an important role in the non-Fermi liquid behavior. In contrast with QCPs, the heat capacity and resistivity we find are unusually resilient in magnetic field. Our results suggest that a combination of magnetic frustration and Kondo physics may result in the emergence of this novel state.

Mechanisms for Pressure-Induced Isostructural Phase Transitions in EuO

We study pressure-induced isostructural electronic phase transitions in the prototypical mixed valence and strongly correlated material EuO using the global-hybrid density functional theory. The simultaneous presence in the valence of highly localized d- and f-type bands and itinerant s- and p-type states, as well as the half-filled f-type orbital shell with seven unpaired electrons on each Eu atom, have made the description of the electronic features of this system a challenge. The electronic band structure, density of states, and atomic oxidation states of EuO are analyzed in the 0-50 GPa pressure range. An insulator-to-metal transition at about 12 GPa of pressure was identified. The second isostructural transition at approximately 30-35 GPa, previously believed to be driven by an oxidation from Eu(II) to Eu(III), is shown instead to be associated with a change in the occupation of the Eu d orbitals, as can be determined from the analysis of the corresponding atomic orbital populations. The Eu d band is confined by the surrounding oxygens and split by the crystal field, which results in orbitals of e_{g} symmetry (i.e., d_{x^{2}-y^{2}} and d_{2z^{2}-x^{2}-y^{2}}, pointing along the Eu-O direction) being abruptly depopulated at the transition as a means to alleviate electron-electron repulsion in the highly compressed structures.

Pristine quantum criticality in a Kondo semimetal

The observation of quantum criticality in diverse classes of strongly correlated electron systems has been instrumental in establishing ordering principles, discovering new phases, and identifying the relevant degrees of freedom and interactions. At focus so far have been insulators and metals. Semimetals, which are of great current interest as candidate phases with nontrivial topology, are much less explored in experiments. Here, we study the Kondo semimetal CeRu4Sn6 by magnetic susceptibility, specific heat, and inelastic neutron scattering experiments. The power-law divergence of the magnetic Grünesien ratio reveals that, unexpectedly, this compound is quantum critical without tuning. The dynamical energy over temperature scaling in the neutron response throughout the Brillouin zone and the temperature dependence of the static uniform susceptibility, indicate that temperature is the only energy scale in the criticality. Such behavior, which has been associated with Kondo destruction quantum criticality in metallic systems, could be generic in the semimetal setting.

Quantum Criticality inside the Anomalous Metallic State of a Disordered Superconducting Thin Film

The field-induced superconductor-insulator transition (SIT) in two-dimensional (2D) systems is a famous example of a quantum phase transition. However, an emergence of an anomalous metallic state induced by field has been a long-standing problem in 2D superconductors. While theories predicted that the emergence is attributed to strong phase fluctuations of the superconducting order parameter due to quantum fluctuations, usual resistance measurements have not probed them directly. Here, using Nernst effect measurements, we uncover superconducting fluctuations in the vicinity of the field-induced metallic state in an amorphous Mo_{x}Ge_{1-x} thin film. The field range where the vortex Nernst signals are detectable remains nonzero toward zero temperature, and it locates inside the metallic state defined by the magnetoresistance, indicating that the metallic state results from quantum vortex liquid (QVL) with phase fluctuations due to quantum fluctuations. Slow decay of transport entropy of vortices in the QVL with decreasing temperature suggests that the metallic state originates from broadening of a quantum critical point in SIT.

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.

Unveiling the Physics of the Mutual Interactions in Paramagnets

In real paramagnets, there is always a subtle many-body contribution to the system's energy, which can be regarded as a small effective local magnetic field (Bloc). Usually, it is neglected, since it is very small when compared with thermal fluctuations and/or external magnetic fields (B). Nevertheless, as both the temperature (T) → 0 K and B → 0 T, such many-body contributions become ubiquitous. Here, employing the magnetic Grüneisen parameter (Γmag) and entropy arguments, we report on the pivotal role played by the mutual interactions in the regime of ultra-low-T and vanishing B. Our key results are: i) absence of a genuine zero-field quantum phase transition due to the presence of Bloc; ii) connection between the canonical definition of temperature and Γmag; and iii) possibility of performing adiabatic magnetization by only manipulating the mutual interactions. Our findings unveil unprecedented aspects emerging from the mutual interactions.

Anomaly Matching and Symmetry-Protected Critical Phases in SU(N) Spin Systems in 1+1 Dimensions

We study (1+1)-dimensional SU(N) spin systems in the presence of global SU(N) rotation and lattice translation symmetries. Knowing the mixed anomaly of the two symmetries at low energy, we identify, by the anomaly matching argument, a topological index for the spin model-the total number of Young-tableau boxes of spins per unit cell modulo N-characterizing the "ingappability" of the system. A nontrivial index implies either a ground-state degeneracy in a gapped phase, which can be thought of as a field-theory version of the Lieb-Schultz-Mattis theorem, or a restriction of the possible universality classes in a critical phase, regarded as the symmetry-protected critical phases. As an example of the latter case, we show that only a class of SU(N) Wess-Zumino-Witten theories can be realized in the low-energy limit of the given lattice model in the presence of the symmetries. Similar constraints also apply when a higher global symmetry emerges in the model with a lower symmetry. Our results agree with several examples known in previous studies of SU(N) models, and predict a general constraint on the structure factor which is measurable in experiments.

Theory of angle-dependent marginal Fermi liquid self-energy and its existence at all dopings in cuprates

Various angle-dependent measurements in hole-doped cuprates suggested that non-Fermi liquid (NFL) and Fermi-liquid (FL) self-energies coexist in the Brillouin zone. Moreover, it is also found that NFL self-energies survive up to the overdoped region where the resistivity features a global FL-behavior. To address this problem, we compute the momentum dependent self-energy from a single band Hubbard model. The self-energy is calculated self-consistently by using a momentum-dependent density-fluctuation (MRDF) method. One of our main results is that the computed self-energy exhibits a marginal-FL (MFL)-like frequency dependence only in the antinodal region, and FL-like behavior elsewhere at all dopings. The MFL self-energy stems from the fluctuations between the itinerant and localized densities-a result that appears when self-energy is calculated self-consistently and features an intermediate coupling behavior of cuprates. We also calculate the DC conductivity by including the full momentum dependent self-energy. We find that the resistivity-temperature exponent n becomes 1 near the optimal doping, while the MFL self-energy occupies largest momentum-space volume. Surprisingly, even in the NFL state near the optimal doping, the nodal region contains FL-like self-energies; while in the under- and over-dopings ([Formula: see text]), the antinodal region remains NFL-like. These results highlight the non-local correlation physics in cuprates and in other similar intermediately correlated materials, where a direct link between the microscopic single-particle spectral properties and the macroscopic transport behavior can not be well established.

Effect of Anisotropic Hybridization in YbAlB_{4} Probed by Linear Dichroism in Core-Level Hard X-Ray Photoemission Spectroscopy

We have probed the crystalline electric-field ground states of pure |J=7/2,J_{z}=±5/2⟩ as well as the anisotropic c-f hybridization in both valence fluctuating systems α- and β-YbAlB_{4} by linear polarization dependence of angle-resolved core level photoemission spectroscopy. Interestingly, the small but distinct difference between α- and β-YbAlB_{4} was found in the polar angle dependence of linear dichroism, indicating the difference in the anisotropy of c-f hybridization, which may be a key to understanding a heavy Fermi liquid state in α-YbAlB_{4} and a quantum critical state in β-YbAlB_{4}.

Tomonaga-Luttinger liquid behavior and spinon confinement in YbAlO3

Low dimensional quantum magnets are interesting because of the emerging collective behavior arising from strong quantum fluctuations. The one-dimensional (1D) S = 1/2 Heisenberg antiferromagnet is a paradigmatic example, whose low-energy excitations, known as spinons, carry fractional spin S = 1/2. These fractional modes can be reconfined by the application of a staggered magnetic field. Even though considerable progress has been made in the theoretical understanding of such magnets, experimental realizations of this low-dimensional physics are relatively rare. This is particularly true for rare-earth-based magnets because of the large effective spin anisotropy induced by the combination of strong spin-orbit coupling and crystal field splitting. Here, we demonstrate that the rare-earth perovskite YbAlO3 provides a realization of a quantum spin S = 1/2 chain material exhibiting both quantum critical Tomonaga-Luttinger liquid behavior and spinon confinement-deconfinement transitions in different regions of magnetic field-temperature phase diagram.

Local quantum phase transition in YFe2Al10

A phase transition occurs when correlated regions of a new phase grow to span the system and the fluctuations within the correlated regions become long lived. Here, we present neutron scattering measurements showing that this conventional picture must be replaced in YFe₂Al₁₀, a compound that forms naturally very close to a [Formula: see text] quantum phase transition. Fully quantum mechanical fluctuations of localized moments are found to diverge at low energies and temperatures; however, the fluctuating moments are entirely without spatial correlations. Zero temperature order in YFe₂Al₁₀ is achieved by an entirely local type of quantum phase transition that may originate with the creation of the moments themselves.

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.

Model for a Ferromagnetic Quantum Critical Point in a 1D Kondo Lattice

Motivated by recent experiments, we study a quasi-one-dimensional model of a Kondo lattice with ferromagnetic coupling between the spins. Using bosonization and dynamical large-N techniques, we establish the presence of a Fermi liquid and a magnetic phase separated by a local quantum critical point, governed by the Kondo breakdown picture. Thermodynamic properties are studied and a gapless charged mode at the quantum critical point is highlighted.

Relaxation calorimetry at very low temperatures for systems with internal relaxation

We present the detailed introduction of our relaxation calorimetry designed for tiny samples down to very low temperatures of 0.03 K. In particular, we discuss how to analyze the data that are modified by an internal thermal relaxation in the sample or in the sample stage of the specific heat cell. We demonstrate that the correct heat capacity is obtained even when the relaxation curve has a triple exponential decay, rather than a double exponential decay which has usually been discussed. As an example, we discuss the measurements performed for α-YbAlB₄ in a magnetic field of 5 T, where we found the triple exponential decay due to a thermal relaxation between electron and nuclear contributions at relatively high temperature well above 0.1 K. Our modified analysis provides the best solution in such a case.

Quantum valence criticality in a correlated metal

A valence critical end point existing near the absolute zero provides a unique case for the study of a quantum version of the strong density fluctuation at the Widom line in the supercritical fluids. Although singular charge and orbital dynamics are suggested theoretically to alter the electronic structure significantly, breaking down the standard quasi-particle picture, this has never been confirmed experimentally to date. We provide the first empirical evidence that the proximity to quantum valence criticality leads to a clear breakdown of Fermi liquid behavior. Our detailed study of the mixed valence compound α-YbAlB₄ reveals that a small chemical substitution induces a sharp valence crossover, accompanied by a pronounced non-Fermi liquid behavior characterized by a divergent effective mass and unusual T/B scaling in the magnetization.

Giant Isotropic Nernst Effect in an Anisotropic Kondo Semimetal

The "failed Kondo insulator" CeNiSn has long been suspected to be a nodal metal, with a node in the hybridization matrix elements. Here we carry out a series of Nernst effect experiments to delineate whether the severely anisotropic magnetotransport coefficients do indeed derive from a nodal metal or can simply be explained by a highly anisotropic Fermi surface. Our experiments reveal that despite an almost twentyfold anisotropy in the Hall conductivity, the large Nernst signal is isotropic. Taken in conjunction with the magnetotransport anisotropy, these results provide strong support for an isotropic Fermi surface with a large anisotropy in quasiparticle mass derived from a nodal hybridization.

Quantum criticality in an organic spin-liquid insulator κ-(BEDT-TTF)2Cu2(CN)3

A quantum spin-liquid state, an exotic state of matter, appears when strong quantum fluctuations enhanced by competing exchange interactions suppress a magnetically ordered state. Generally, when an ordered state is continuously suppressed to 0 K by an external parameter, a quantum phase transition occurs. It exhibits critical scaling behaviour, characterized only by a few basic properties such as dimensions and symmetry. Here we report the low-temperature magnetic torque measurements in an organic triangular-lattice antiferromagnet, κ-(BEDT-TTF)₂Cu₂(CN)₃, where BEDT-TTF stands for bis(ethylenedithio)tetrathiafulvalene. It is found that the magnetic susceptibilities derived from the torque data exhibit a universal critical scaling, indicating the quantum critical point at zero magnetic field, and the critical exponents, γ=0.83(6) and νz=1.0(1). These exponents greatly constrain the theoretical models for the quantum spin liquid, and at present, there is no theory to explain the values, to the best of our knowledge.

Quantum spin liquids emerge when quantum fluctuations suppress a magnetically ordered state. Here the authors measure magnetic torque in κ-(BEDT-TTF)₂Cu₂(CN)₃, showing universal critical scaling in the magnetic susceptibilities, with critical exponents incompatible with known models for quantum spin liquids.

Metal Flux Growth, Structural Relations, and Physical Properties of EuCu2Ge2 and Eu3T2In9 (T = Cu and Ag)

Single crystals (SCs) of the compounds Eu₃Ag₂In₉ and EuCu₂Ge₂ were synthesized through the reactions run in liquid indium. Eu₃Ag₂In₉ crystallizes in the La₃Al₁₁ structure type [orthorhombic space group (SG) Immm] with the lattice parameters: a = 4.8370(1) Å, b = 10.6078(3) Å, and c = 13.9195(4) Å. EuCu₂Ge₂ crystallizes in the tetragonal ThCr₂Si₂ structure type (SG I4/mmm) with the lattice parameters: a = b = 4.2218(1) Å, and c = 10.3394(5) Å. The crystal structure of Eu₃Ag₂In₉ is comprised of edge-shared hexagonal rings consisting of indium. The one-dimensional chains of In₆ rings are shared through the edges, which are further interconnected with other six-membered rings forming a three-dimensional (3D) stable crystal structure along the bc plane. The crystal structure of EuCu₂Ge₂ can be explained as the complex [CuGe]^(2+δ)- polyanionic network embedded with Eu ions. These polyanionic networks present in the crystal structure of EuCu₂Ge₂ are shared through the edges of the 011 plane containing Cu and Ge atoms, resulting in a 3D network. The structural relationship between Eu₃T₂In₉ and EuCu₂Ge₂ has been discussed in detail, and we conclude that Eu₃T₂In₉ is the metal deficient variant of EuCu₂Ge₂. The magnetic susceptibilities of Eu₃T₂In₉ (T = Cu and Ag) and EuCu₂Ge₂ were measured between 2 and 300 K. In all cases, magnetic susceptibility data followed Curie-Weiss law above 150 K. Magnetic moment values obtained from the measurements indicate the probable mixed/intermediate valent behavior of the europium atoms, which was further confirmed by X-ray absorption studies and bond distances around the Eu atoms. Electrical resistivity measurements suggest that Eu₃T₂In₉ and EuCu₂Ge₂ are metallic in nature.

Emergent spin-valley-orbital physics by spontaneous parity breaking

The spin-orbit coupling in the absence of spatial inversion symmetry plays an important role in realizing intriguing electronic states in solids, such as topological insulators and unconventional superconductivity. Usually, the inversion symmetry breaking is inherent in the lattice structures, and hence, it is not easy to control these interesting properties by external parameters. We here theoretically investigate the possibility of generating the spin-orbital entanglement by spontaneous electronic ordering caused by electron correlations. In particular, we focus on the centrosymmetric lattices with local asymmetry at the lattice sites, e.g. zigzag, honeycomb, and diamond structures. In such systems, conventional staggered orders, such as charge order and antiferromagnetic order, break the inversion symmetry and activate the antisymmetric spin-orbit coupling, which is hidden in a sublattice-dependent form in the paramagnetic state. Considering a minimal two-orbital model on a honeycomb structure, we scrutinize the explicit form of the antisymmetric spin-orbit coupling for all the possible staggered charge, spin, orbital, and spin-orbital orders. We show that the complete table is useful for understanding of spin-valley-orbital physics, such as spin and valley splitting in the electronic band structure and generalized magnetoelectric responses in not only spin but also orbital and spin-orbital channels, reflecting in peculiar magnetic, elastic, and optical properties in solids.

Crossover from a heavy fermion to intermediate valence state in noncentrosymmetric Yb2Ni12(P,As)7

We report measurements of the physical properties and electronic structure of the hexagonal compounds Yb₂Ni₁₂Pn₇ (Pn = P, As) by measuring the electrical resistivity, magnetization, specific heat and partial fluorescence yield x-ray absorption spectroscopy (PFY-XAS). These demonstrate a crossover upon reducing the unit cell volume, from an intermediate valence state in Yb₂Ni₁₂As₇ to a heavy-fermion paramagnetic state in Yb₂Ni₁₂P₇, where the Yb is nearly trivalent. Application of pressure to Yb₂Ni₁₂P₇ suppresses T_FL, the temperature below which Fermi liquid behavior is recovered, suggesting the presence of a quantum critical point (QCP) under pressure. However, while there is little change in the Yb valence of Yb₂Ni₁₂P₇ up to 30 GPa, there is a strong increase for Yb₂Ni₁₂As₇ under pressure, before a near constant value is reached. These results indicate that any magnetic QCP in this system is well separated from strong valence fluctuations. The pressure dependence of the valence and lattice parameters of Yb₂Ni₁₂As₇ are compared and at 1 GPa, there is an anomaly in the unit cell volume as well as a change in the slope of the Yb valence, indicating a correlation between structural and electronic changes.

Synthesis, crystal structure and properties of the new superconductors TaRuB and NbOsB

Two new ternary compounds TaRuB and NbOsB were synthesized by arc-melting and annealing at 1500-1850 °C. They crystallize in orthorhombic primitive structures with space group Pbam. Magnetic susceptibility, electrical resistivity, and specific heat measurements reveal bulk superconductivity for metallic TaRuB with a T(c) ≈ 4 K. Electronic structure calculations by DFT methods show that 4d and 5d transition-metal states dominate the density of states (DOS) at the Fermi level E(F) with a pronounced quasi one-dimensional behaviour along the [0 0 1] direction. Comparison of the calculated DOS at E(F) with specific heat data reveals a moderate electron-phonon coupling. Possible small boron vacancies could significantly reduce the DOS at E(F), hence decrease T(c) for samples annealed at higher temperatures. For NbOsB, the DOS(E(F)) is strongly reduced due to an increase of covalent bonding interactions between Os and B. Accordingly, a lower T(c) ≈ 1 K is observed.

Heavy fermions. Unconventional Fermi surface in an insulating state

Insulators occur in more than one guise; a recent finding was a class of topological insulators, which host a conducting surface juxtaposed with an insulating bulk. Here, we report the observation of an unusual insulating state with an electrically insulating bulk that simultaneously yields bulk quantum oscillations with characteristics of an unconventional Fermi liquid. We present quantum oscillation measurements of magnetic torque in high-purity single crystals of the Kondo insulator SmB6, which reveal quantum oscillation frequencies characteristic of a large three-dimensional conduction electron Fermi surface similar to the metallic rare earth hexaborides such as PrB6 and LaB6. The quantum oscillation amplitude strongly increases at low temperatures, appearing strikingly at variance with conventional metallic behavior.

Characteristic signatures of quantum criticality driven by geometrical frustration

Geometrical frustration describes situations where interactions are incompatible with the lattice geometry and stabilizes exotic phases such as spin liquids. Whether geometrical frustration of magnetic interactions in metals can induce unconventional quantum critical points is an active area of research. We focus on the hexagonal heavy fermion metal CeRhSn, where the Kondo ions are located on distorted kagome planes stacked along the c axis. Low-temperature specific heat, thermal expansion, and magnetic Grüneisen parameter measurements prove a zero-field quantum critical point. The linear thermal expansion, which measures the initial uniaxial pressure derivative of the entropy, displays a striking anisotropy. Critical and noncritical behaviors along and perpendicular to the kagome planes, respectively, prove that quantum criticality is driven be geometrical frustration. We also discovered a spin flop-type metamagnetic crossover. This excludes an itinerant scenario and suggests that quantum criticality is related to local moments in a spin liquid-like state.

Yb7Ni4InGe12: a quaternary compound having mixed valent Yb atoms grown from indium flux

The new intermetallic compound Yb7Ni4InGe12 was obtained as large silver needle shaped single crystals from reactive indium flux. Single crystal X-ray diffraction suggests that Yb7Ni4InGe12 crystallizes in the Yb7Co4InGe12 structure type, and tetragonal space group P4/m and lattice constants are a = b = 10.291(2) Å and c = 4.1460(8) Å. The crystal structure of Yb7Ni4InGe12 consists of columnar units of three different types of channels filled with the Yb atoms. The crystal structure of Yb7Ni4InGe12 is closely related to Yb5Ni4Ge10. The effective magnetic moment obtained from the magnetic susceptibility measurements in the temperature range 200-300 K is 3.66μB/Yb suggests mixed/intermediate valence behavior of ytterbium atoms. X-ray absorption near edge spectroscopy (XANES) confirms that Yb7Ni4InGe12 exhibits mixed valence.

Targeted crystal growth of rare Earth intermetallics with synergistic magnetic and electrical properties: structural complexity to simplicity

The single-crystal growth of extended solids is an active area of solid-state chemistry driven by the discovery of new physical phenomena. Although many solid-state compounds have been discovered over the last several decades, single-crystal growth of these materials in particular enables the determination of physical properties with respect to crystallographic orientation and the determination of properties without possible secondary inclusions. The synthesis and discovery of new classes of materials is necessary to drive the science forward, in particular materials properties such as superconductivity, magnetism, thermoelectrics, and magnetocalorics. Our research is focused on structural characterization and determination of physical properties of intermetallics, culminating in an understanding of the structure-property relationships of single-crystalline phases. We have prepared and studied compounds with layered motifs, three-dimensional magnetic compounds exhibiting anisotropic magnetic and transport behavior, and complex crystal structures leading to intrinsically low lattice thermal conductivity. In this Account, we present the structural characteristics and properties that are important for understanding the magnetic properties of rare earth transition metal intermetallics grown with group 13 and 14 metals. We present phases adopting the HoCoGa5 structure type and the homologous series. We also discuss the insertion of transition metals into the cuboctahedra of the AuCu3 structure type, leading to the synthetic strategy of selecting binaries to relate to ternary intermetallics adopting the Y4PdGa12 structure type. We provide examples of compounds adopting the ThMn12, NaZn13, SmZn11, CeCr2Al20, Ho6Mo4Al43, CeRu2Al10, and CeRu4Al16-x structure types grown with main-group-rich self-flux methods. We also discuss the phase stability of three related crystal structures containing atoms in similar chemical environments: ThMn12, CaCr2Al10, and YbFe2Al10. In addition to dimensionality and chemical environment, complexity is also important in materials design. From relatively common and well-studied intermetallic structure types, we present our motivation to work with complex stannides adopting the Dy117Co57Sn112 structure type for thermoelectric applications and describe a strategy for the design of new magnetic intermetallics with low lattice thermal conductivity. Our quest to grow single crystals of rare-earth-rich complex stannides possessing low lattice thermal conductivity led us to discover the new structure type Ln30Ru4+xSn31-y (Ln = Gd, Dy), thus allowing the correlation of primitive volumes with lattice thermal conductivities. We highlight the observation that Ln30Ru4+xSn31-y gives rise to highly anisotropic magnetic and transport behavior, which is unexpected, illustrating the need to measure properties on single crystals.

Pressure-induced valence crossover and novel metamagnetic behavior near the antiferromagnetic quantum phase transition of YbNi_{3}Ga_{9}

We report electrical resistivity, ac magnetic susceptibility, and x-ray absorption spectroscopy measurements of intermediate valence YbNi_{3}Ga_{9} under pressure and magnetic field. We have revealed a characteristic pressure-induced Yb valence crossover within the temperature-pressure phase diagram, and a first-order metamagnetic transition is found below P_{c}∼9  GPa where the system undergoes a pressure-induced antiferromagnetic transition. As a possible origin of the metamagnetic behavior, a critical valence fluctuation emerging near the critical point of the first-order valence transition is discussed on the basis of the temperature-field-pressure phase diagram.

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.

Contiguous 3d and 4f magnetism: strongly correlated 3d electrons in YbFe2Al10

We present magnetization, specific heat, and (27)Al NMR investigations on YbFe2Al10 over a wide range in temperature and magnetic field. The magnetic susceptibility at low temperatures is strongly enhanced at weak magnetic fields, accompanied by a ln(T0/T) divergence of the low-T specific heat coefficient in zero field, which indicates a ground state of correlated electrons. From our hard-x-ray photoemission spectroscopy study, the Yb valence at 50 K is evaluated to be 2.38. The system displays valence fluctuating behavior in the low to intermediate temperature range, whereas above 400 K, Yb(3+) carries a full and stable moment, and Fe carries a moment of about 3.1 μB. The enhanced value of the Sommerfeld-Wilson ratio and the dynamic scaling of the spin-lattice relaxation rate divided by T[(27)(1/T1T)] with static susceptibility suggests admixed ferromagnetic correlations. (27)(1/T1T) simultaneously tracks the valence fluctuations from the 4f Yb ions in the high temperature range and field dependent antiferromagnetic correlations among partially Kondo screened Fe 3d moments at low temperature; the latter evolve out of an Yb 4f admixed conduction band.

Crossover between Fermi liquid and non-Fermi liquid behavior in the non-centrosymmetric compound Yb2Ni12P7

A crossover from a non-Fermi liquid to a Fermi liquid phase in Yb2Ni12P7 is observed by analyzing electrical resistivity ρ(T), magnetic susceptibility χ(T), specific heat C(T), and thermoelectric power S(T) measurements. The electronic contribution to specific heat, Ce(T), behaves as Ce(T)/T∼-ln(T) for 5 K<T<15 K, which is consistent with non-Fermi liquid behavior. Below T∼4 K, the upturn in Ce(T)/T begins to saturate, suggesting that the system crosses over into a Fermi-liquid ground state. This is consistent with robust ρ(T)-ρ0=AT2 behavior below T∼4 K, with the power-law exponent becoming sub-quadratic for T>4 K. A crossover between Fermi-liquid and non-Fermi liquid behavior suggests that Yb2Ni12P7 is in close proximity to a quantum critical point, in agreement with results from recent measurements of this compound under applied pressure.

Quantum critical fluctuations in layered YFe2Al10

The absence of thermal fluctuations at T = 0 makes it possible to observe the inherently quantum mechanical nature of systems where the competition among correlations leads to different types of collective ground states. Our high precision measurements of the magnetic susceptibility, specific heat, and electrical resistivity in the layered compound YFe2Al10 demonstrate robust field-temperature scaling, evidence that this system is naturally poised without tuning on the verge of ferromagnetic order that occurs exactly at T = 0, where magnetic fields drive the system away from this quantum critical point and restore normal metallic behavior.

Theory of the electron spin resonance in the heavy fermion metal β-YbAlB4

The heavy fermion metal β-YbAlB4 exhibits a bulk room temperature conduction electron spin resonance (ESR) signal which evolves into an Ising-anisotropic f-electron signal exhibiting hyperfine features at low temperatures. We develop a theory for this phenomenon based on the development of resonant scattering off a periodic array of Kondo centers. We show that the hyperfine structure arises from the scattering off the Yb atoms with nonzero nuclear spin, while the constancy of the ESR intensity is a consequence of the presence of crystal electric field excitations of the order of the hybridization strength.

Quantum bicriticality in the heavy-fermion metamagnet YbAgGe

Bicritical points, at which two distinct symmetry-broken phases become simultaneously unstable, are typical for spin-flop metamagnetism. Interestingly, the heavy-fermion compound YbAgGe also possesses such a bicritical point (BCP) with a low temperature T(BCP)≈0.3  K at a magnetic field of μH(BCP)≈4.5  T. In its vicinity, YbAgGe exhibits anomalous behavior that we attribute to the influence of a quantum bicritical point that is close in parameter space yet can be reached by tuning T(BCP) further to zero. Using high-resolution measurements of the magnetocaloric effect, we demonstrate that the magnetic Grüneisen parameter ΓH indeed both changes sign and diverges as required for quantum criticality. Moreover, ΓH displays a characteristic scaling behavior but only on the low-field side H≲H(BCP), indicating a pronounced asymmetry with respect to the critical field. We speculate that the small value of T(BCP) is related to the geometric frustration of the Kondo lattice of YbAgGe.

Non-Fermi liquid regimes with and without quantum criticality in Ce(1-x)Yb(x)CoIn5

One of the greatest challenges to Landau's Fermi liquid theory--the standard theory of metals--is presented by complex materials with strong electronic correlations. In these materials, non-Fermi liquid transport and thermodynamic properties are often explained by the presence of a continuous quantum phase transition that happens at a quantum critical point (QCP). A QCP can be revealed by applying pressure, magnetic field, or changing the chemical composition. In the heavy-fermion compound CeCoIn5, the QCP is assumed to play a decisive role in defining the microscopic structure of both normal and superconducting states. However, the question of whether a QCP must be present in the material's phase diagram to induce non-Fermi liquid behavior and trigger superconductivity remains open. Here, we show that the full suppression of the field-induced QCP in CeCoIn5 by doping with Yb has surprisingly little impact on both unconventional superconductivity and non-Fermi liquid behavior. This implies that the non-Fermi liquid metallic behavior could be a new state of matter in its own right rather than a consequence of the underlying quantum phase transition.

Anomalous superfluid density in quantum critical superconductors

When a second-order magnetic phase transition is tuned to zero temperature by a nonthermal parameter, quantum fluctuations are critically enhanced, often leading to the emergence of unconventional superconductivity. In these "quantum critical" superconductors it has been widely reported that the normal-state properties above the superconducting transition temperature T(c) often exhibit anomalous non-Fermi liquid behaviors and enhanced electron correlations. However, the effect of these strong critical fluctuations on the superconducting condensate below T(c) is less well established. Here we report measurements of the magnetic penetration depth in heavy-fermion, iron-pnictide, and organic superconductors located close to antiferromagnetic quantum critical points, showing that the superfluid density in these nodal superconductors universally exhibits, unlike the expected T-linear dependence, an anomalous 3/2 power-law temperature dependence over a wide temperature range. We propose that this noninteger power law can be explained if a strong renormalization of effective Fermi velocity due to quantum fluctuations occurs only for momenta k close to the nodes in the superconducting energy gap Δ(k). We suggest that such "nodal criticality" may have an impact on low-energy properties of quantum critical superconductors.

New structure type in the mixed-valent compound YbCu4Ga8

The new compound YbCu(4)Ga(8) was obtained as large single crystals in high yield from reactions run in liquid gallium. Preliminary investigations suggest that YbCu(4)Ga(8) crystallizes in the CeMn(4)Al(8) structure type, tetragonal space group I4/mmm, and lattice constants are a = b = 8.6529(4) Å and c = 5.3976(11) Å. However, a detailed single-crystal XRD revealed a tripling of the c axis and crystallizing in a new structure type with lattice constants of a = b = 8.6529(4) Å and c = 15.465(1) Å. The structural model was further confirmed by neutron diffraction measurements on high-quality single crystal. The crystal structure of YbCu(4)Ga(8) is composed of pseudo-Frank-Kasper cages occupying one ytterbium atom in each ring which are shared through the corner along the ab plane, resulting in a three-dimensional network. The magnetic susceptibility of YbCu(4)Ga(8) investigated in the temperature range 2-300 K showed Curie-Weiss law behavior above 100 K, and the experimentally measured magnetic moment indicates mixed-valent ytterbium. Electrical resistivity measurements show the metallic nature of the compound. At low temperatures, variation of ρ as a function of T indicates a possible Fermi-liquid state at low temperatures.