β-YbAlB4: a critical nodal metal

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.

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.

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.

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.

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}.

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.

Multiband electronic transport in α-Yb1-x Sr x AlB4 [x = 0, 0.19(3)] single crystals

We report on the evidence for the multiband electronic transport in α-YbAlB4 and α-Yb0.81(2)Sr0.19(3)AlB4. Multiband transport reveals itself below 10 K in both compounds via Hall effect measurements, whereas anisotropic magnetic ground state sets in below 3 K in α-Yb0.81(2)Sr0.19(3)AlB4. Our results show that Sr(2+) substitution enhances conductivity, but does not change the quasiparticle mass of bands induced by heavy fermion hybridization.

Conduction electron spin resonance in the α-Yb1-xFexAlB4 (0 ⩽ x ⩽ 0.50) and α-LuAlB4 compounds

β-YbAlB4 has become one of the most studied heavy fermion systems since its discovery due to its remarkable physical properties. This system is the first reported Yb-based heavy-fermion superconductor (HFS) for which the low-T superconducting state emerges from a non-fermi-liquid (NFL) normal state associated with quantum criticality Nakatsuji et al 2008 Nature 4 603. Additionally, it presents a striking and unprecedented electron spin resonance (ESR) signal which behaves as a conduction electron spin resonance (CESR) at high temperatures and acquires features of the Yb(3+) local moment ESR at low temperatures. The latter, also named Kondo quasiparticles spin resonance (KQSR), has been defined as a 4f-ce strongly coupled ESR mode that behaves as a local probe of the Kondo quasiparticles in a quantum critical regime, Holanda et al 2011 Phys. Rev. Lett. 107 026402. Interestingly, β-YbAlB4 possesses a previously known structural variant, namely the α-YbAlB4, phase which is a paramagnetic Fermi liquid (FL) at low temperatures Macaluso et al 2007 Chem. Mater. 19 1918. However, it has been recently suggested that the α-YbAlB4 phase may be tuned to NFL behavior and/or magnetic ordering as the compound is doped with Fe. Here we report ESR studies on the α-Yb1-xFexAlB4 (0 ⩽ x ⩽ 0.50) series as well as on the reference compound α-LuAlB4. For all measured samples, the observed ESR signal behaves as a CESR in the entire temperature range (10 K ≲ T ≲ 300 K) in clear contrast with what has been observed for β-YbAlB4. This striking result indicates that the proximity to a quantum critical point is crucial to the occurrence of a KQSR signal.

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.

Conduction electron spin resonance in AlB2

This work reports on electron spin resonance experiments in oriented single crystals of the hexagonal AlB2 diboride compound (P6/mmm, D16h structure) which display conduction electron spin resonance. The X-band electron spin resonance spectra showed a metallic Dysonian resonance with g-value and intensity independent of temperature. The thermal broadening of the anisotropic electron spin resonance linewidth ΔH tracks the T-dependence of the electrical resistivity below T is approximately equal to 100 K. These results confirm the observation of a conduction electron spin resonance in AlB2 and are discussed in comparison with other boride compounds. Based on our main findings for AlB2 and the calculated electronic structure of similar layered honeycomb-like structures, we conclude that any array of covalent B-B layers potentially results in a conduction electron spin resonance signal. This observation may shed new light on the nature of the non-trivial conduction electron spin resonance-like signals of complex f-electron systems such as β-YbAlB4.

Evolution of c-f hybridization and two-component Hall effect in β-YbAlB4

β-YbAlB(4) is the unique heavy fermion superconductor that exhibits unconventional quantum criticality without tuning in a strongly intermediate valence state. Despite the large coherence temperature, set by the peak of the longitudinal resistivity, our Hall effect measurements reveal that resonant skew scattering from incoherent local moments persists down to at least ~40 K, where the Hall coefficient exhibits a distinct minimum signaling another formation of coherence. The observation strongly suggests that the hybridization between f moments and conduction electrons has a two-component character with distinct Kondo or coherence scales T(K) of ~40 K and 200 K; this is confirmed by the magnetic field dependence of ρ(xy).