Quantum critical Kondo quasiparticles probed by ESR in β-YbAlB₄

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.

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.

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.

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.

Mean field theory of electron spin resonance g-factors in β-YbAlB4

We present a mean-field theory of the conduction electron spin resonance g-factors in β-YbAlB4. The temperature-dependent shift in the g-factors is attributed to an isotropic exchange interaction between the spin of the conduction electrons and the spin of the Yb(3+) ion. In the mean field approximation, the difference between the parallel and perpendicular g-factors is proportional to the difference between the parallel and perpendicular susceptibilities. Using experimental values for the susceptibilities, and fitting the data at 4.2 K, we predict the temperature dependence of the g-shifts at higher temperatures.

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.

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.

β-YbAlB4: a critical nodal metal

We propose a model for the intrinsic quantum criticality of β-YbAlB(4), in which a vortex in momentum space gives rise to a new type of Fermi surface singularity. The unquenched angular momentum of the |J=7/2,m(J)=±5/2> Yb 4f states generates a momentum-space line defect in the hybridization between 4f and conduction electrons, leading to a quasi-two-dimensional Fermi surface with a k(⊥)(4) dispersion and a singular density of states proportional to E(-1/2). We discuss the implications of this line node in momentum space for our current understanding of quantum criticality and its interplay with topology.

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).