Session R56: Cerium-Based Heavy Fermion Metals

Interplay of CEF effects and RKKY interaction in Ce- and Yb-based heavy-fermion compounds

We calculate the influence of Crystalline Electric Field (CEF) effects on the indirect Ruderman-Kittel-Kasuya-Yoshida (RKKY) exchange interaction between local 4f moments in Ce- and Yb-compounds. Starting from a periodic Anderson model and neglecting spin-orbit effects among the conduction states, we show that the anisotropy of the CEF ground state manifests itself in the anisotropy of the effective exchange coupling constant J(R, R’) between two moments at sites R and R’ while the interaction between two Kramers doublets is isotropic in pseudo-spin space. We evaluate the exchange constant for various models of the conduction states in tetragonal Ce- and Yb-122 compounds. The influence of spin-orbit interaction among the conduction electrons is discussed.   

Crystal-field excitations and magnetic fluctuations of heavy-fermion metal CeB6

CeB₆ enters an antiferro-quadrupolar (AFQ) phase below T_AFQ=3.2K, in which the T_2g-symmetry quadrupoles order at a finite wave vector [Rep. Prog. Phys. 79, 066502 (2016)]. With its cubic lattice structure and 4f¹ Ce³⁺ electronic configuration, this compound is considered a prototypical example of heavy-fermion metal with quadrupolar ordering. We study the crystal-field (CF) excitations and magnetic fluctuations at Ce³⁺ sites by Raman scattering [Phys. Rev. Materials 3, 065003 (2019)]. The spectral linewidth of the CF transitions increases on cooling below 80K, at which the electric resistivity shows its maximum. This coincidence points to the relationship between the broadening of linewidth and Kondo physics. For quasi-elastic fluctuations, the temperature dependence of the static Raman susceptibility in the magnetic channel is consistent with the previously-reported magnetic susceptibility data. Such behavior implies that above T_AFQ, the tendency towards AFQ ordering induces ferromagnetic correlations which manifest as long-wavelength magnetic fluctuations.   

Large Fermi surface expansion through anisotropic mixing of conduction and f electrons in the semimetallic Kondo lattice CeBi

Using angle-resolved photoemission spectroscopy (ARPES) and resonant ARPES, we report evidence of strong anisotropic conduction-f electron mixing (c-f mixing) in CeBi by observing a largely expanded Ce-5d pocket at low temperature, with no change in the Bi-6p bands. The anisotropic Fermi surface (FS) expansion is accompanied by a pronounced spectral weight transfer from the local 4f ⁰ peak of Ce (corresponding to Ce³⁺) to the itinerant conduction bands near the Fermi level. Careful analysis suggests that the observed large FS change (with a volume expansion of the electron pocket up to 40%) can most naturally be explained by a small valence change (~ 1%) of Ce, which coexists with a very weak Kondo screening. Our work therefore provides evidence for a FS change driven by real charge fluctuations deep in the Kondo limit, which is highly dependent on the orbital character and momentum and is made possible by the low carrier density.   

Vanishing Hall number at a quantum critical point

Certain types of quantum critical points, phase transitions at zero-temperature, have long been thought to underlie unconventional superconductivity in a variety of systems. We study the effect of particle-hole dilution in the unconventional superconductor CeCoIn₅, and discover an unusual critical point that connects two distinct Fermi liquids with different Fermi surface volumes without any apparent symmetry breaking. The signature of this transition is pronounced in the Hall number, which nearly vanishes at the phase boundary between the two Fermi liquids and exhibits a strong dependence on the applied magnetic field. The experiment provides evidence for a type of quantum critical point that fractionalizes conventional metallic quasiparticles into gapless spin excitations and gapped charge carrying excitations. Calculations are presented which suggest that the experimentally measured Hall resistivity in this material reflects the motion of charged particles in the fractionalized Fermi fluid.
  

Quantum Critical Strange Metal and Fermi Surface Reconstruction in a large-N Kondo Lattice Model

Quantum critical points in heavy Fermion materials, involving a change of the Fermi surface volume, have presented a long standing puzzle. One way to describe such a transition within a Kondo lattice model is through condensation of a slave Boson. However, this approach leads to a weakly coupled critical point, which fails to describe non-Fermi liquid behavior, such as the ubiquitously observed T-linear resistivity at criticality. We present a modified large-N Kondo lattice model, which also describes a transition from a small Fermi surface to a heavy Fermi liquid with a large Fermi surface, but gives rise to T-linear resistivity at the critical point. In the large-N limit we also compute the behavior of the Hall transport properties across the transition and compare the results to recent experiments with CeCoIn₅. We show under what conditions a strong enhancement of the Hall coefficient, seen in the experiment, is expected.   

Spectroscopic evidence for pre-formed heavy electron pairs and novel pairing mechanism in CeCoIn5 (Part 1/2)

The heavy-fermion compound CeCoIn₅ shows unconventional superconductivity (T_c=2.3 K) with d_x²_-y²–wave pairing symmetry[1]. Despite evidence for pseudogap in the normal state[2], their spectroscopic nature remains to be unraveled. Here, we present results from planar tunneling spectroscopy measurements on CeCoIn₅ along [001], [100], and [110] directions. While the nodal junction exhibits only a zero-bias conductance peak, the non-nodal junctions show sharp double peaks corresponding to the superconducting gap. Interestingly, they evolve continuously crossing the T_c, merging into a single broad peak at T_p=5K. From quantitative analyses of the conductance spectra, we have found that the gap persistent in the normal state originates from the formation of heavy electron pairs that condense into a coherent state below T_c. We will discuss the implications of our findings in the context of other measurement results in the literature along with the underlying pairing mechanism.

[1]Park,et al,PRL100,177001(2008);Thompson,et al,JPSJ 81,011002(2012).
[2]Ernst,et al,Phys. Stat. Sol. B 247,624(2010);Fasano,et al,Physica B 536,798(2018).   

Spectroscopic evidence for pre-formed heavy electron pairs and novel pairing mechanism in CeCoIn5 (Part 2/2)

The glue that binds heavy electrons into pairs in CeCoIn₅(T_c=2.3K) is not known unambiguously yet. The origin of the neutron resonance peak[1] is still controversial[2] despite the original interpretation as evidence for the spin fluctuation mechanism. Also, the hump-dip feature expected in tunneling conductance is missing in scanning tunneling spectroscopy measurements[3]. Here, we present results from planar tunneling spectroscopy on CeCoIn₅, revealing the pairing gap opens at T_p~5K. Interestingly, under a magnetic field, the pairing gap turns into a field-induced gap-like feature (FIG). The FIG increases linearly with the field and is observed only below T_p. This concomitance of the FIG with the pairing along with its linear field dependence strongly suggests that it is intimately tied to the underlying pairing mechanism. We will discuss these findings in the context of the composite pairing mechanism based on the cooperative two-channel Kondo effect[4].

[1]Stock,et al,PRL100,087001(2008).
[2]Song,et al,Nat.Comm.7,12774(2016).
[3]Fasano,et al,Physica B536,798(2018);Allan,et al,Nat.Phys.9,468(2013).
[4]Flint,et al,Nat.Phys.4,643(2008)   

Resonances in thermal conductivity of superconducting CeCoIn5 in rotating magnetic field

We performed thermal conductivity measurements of d-wave superconducting CeCoIn₅ in magnetic field up to 12 Tesla rotating in the a-b plane of this tetragonal compound, in a dilution refrigerator. The heat current J was applied along the [100] direction, antinodal of the superconducting order parameter. In similar previous measurements we observed sharp field-magnitude independent resonances in thermal conductivity for field direction Θ = ± 33° away from the direction of the heat current J applied along [110], the direction of the nodes. For heat current J||[100] we observe the resonances at Θ = ± 12°, complimentary to previous 33° resonances, also independent of the magnitude of the magnetic field. The field direction with respect to the crystallographic direction, not the direction of the heat current, is therefore of importance. Our model calculation of the density of state in the normal CeCoIn₅ in magnetic field show sharp resonances as function of the field orientation. This suggests that the sharp resonances in thermal conductivity in superconducting CeCoIn₅ should be attributed to normal parts of the Fermi surface, which were suggested to exist in magnetic field.   

Thermal expansion of heavy-fermion CeRhIn5 under pressure

Antiferromagnetic CeRhIn₅ is a prototypical heavy-fermion compound. With applied pressure, the antiferromagnetic ordering of CeRhIn₅ disappears and an unconventional superconducting state emerges. Crystalline electric field (CEF) effects are known to be important in the determination of the ground state of heavy-fermion materials. However, CEF effects in CeRhIn₅ have not been studied under pressure because of the limiting volume and background of pressure cells. Here we probe the CEF scheme of CeRhIn₅ via thermal expansion measurements under pressure using the strain gauge method at high temperature and optical fiber sensors at low temperature. We report the temperature dependence of the linear thermal-expansion coefficient of CeRhIn₅ under pressure. Our results allow us to determine CEF splitting energies from the ground state to the excited state and observe the evolution of the phase transitions under pressure. We will discuss the pressure dependence of CEF effects in CeRhIn₅ in comparison with other 115 compounds.   

Ferromagetic quantum critical point in heavy fermion compound CeRh6Ge4

Due to the low energy scales, the ground state of heavy fermion compounds can be readily tuned by parameters such as pressure, magnetic fields or doping. There have been numerous studies into antiferromagnetic quantum criticality and unconventional superconductivity, which have been revealed a possible role for spin fluctuations in the superconducting pairing [1, 2]. However, ferromagnetism in heavy fermion systems has been less investigated and there is still short of evidence for the presence of ferromagnetic quantum critical point in a pure system [3]. Here we report various measurements of the ferromagnetic compound CeRh₆Ge₄ under pressure, which provide clear evidence for the existence of a ferromagnetic critical point, at which strange metal behavior is also observed [4].

References:
[1] N. D. Mathur et al., Nature 394, 39 (1998).
[2] Z. F. Weng et al., Rep. Prog. Phys. 79, 094503 (2016)
[3] M. Brando et al., Rev. Mod. Phys. 88, 025006 (2016).
[4] B. Shen et al., arXiv: 1907.10470.   

Theoretical investigation of mixed valence compound CeRh3 by means of 3d-4f resonant inelastic X-ray scattering

Ce intermetallics, which are typical strongly correlated system, show the various phenomena, Kondo effects, magnetic ordering and so on. This variety is caused to the 4f electron behavior of Ce atoms, and the electron state needs to be investigated for the understanding of the phenomena.
X-ray core-level spectroscopy is an efficient technique to investigate the electronic state of strongly correlated systems. Recent years, experimental techniques have been rapidly developing and, especially, the progress in experimental resolution has enabled us to observe fine spectral features, which were not formerly observed. These advantages will enable us to observe spectral fine features related with the electron state related to Kondo effects and/or magnetic ordering of the Ce intermetallics.
In this study, the spectral calculation for 3d-4f resonant inelastic X-ray scattering (RIXS) of CeRh₃ is shown, and the character of the final state for 3d-4f RIXS is clarified by paying attention to the incident X-ray energy and polarization. This calculation is performed with an impurity Anderson model considering full multiplet effects in addition to a realistic band effect based on a local density approximation calculation.
  

Low temperature characterization of single crystalline Ce2Ni2In

Materials with the R₂T₂X (R = Ce,Yb; T=transition metal; X=main group element) stoichiometry span an extensive (~40) class of compounds. The underlying interactions of these tetragonal systems leads typically to dimerization of the 4f magnetic moments associated with the R ions. These materials feature a broad range of physics, ranging from valence fluctuations, non-Fermi liquid behavior and heavy fermion ground states. Most recently fractional excitations have been observed in inelastic neutron scattering experiments performed on Yb₂Pt₂Pb. In this talk we will introduce Ce₂Ni₂In, as a new single crystalline addition to the 221 family of materials. We will discuss its synthesis, general characterization, measurements of the specific heat as well as directional dependent measurements of the magnetic susceptibility and electrical transport from room temperature down to 50 mK.
  

Frist Principles Study of the Fermi Surface Topology of CeCu2Si2

Since the discovery of heavy-fermion superconductivity in CeCu₂Si₂, the material has attracted interest in the nature of superconducting pairing. So, it is essential to better understand the electronic Fermi surface topology and its role in strong antiferromagnetic fluctuations. We have performed electronic ground state calculations on CeCu₂Si₂ using the Gutzwiller approximation. This method captures the quasiparticle band renormalization from the strong onsite Coulomb repulsion. We have performed an analysis of the electronic structure and the Fermi surface topology by varying the interaction strength and taking into account the crystal-field splitting. Using the de Haas van Alphen effect, the extremal Fermi surface cross-sectional areas were calculated to quantify the quasiparticle mass renormalization in the energy bands. Our results confirm two Fermi surface sheets corresponding to the heavy and light quasiparticles, which is in agreement with the renormalized band method. We also discuss the connection of the Fermi surface topology to hot-spots in the magnetic susceptibility form factor measured by neutron scattering.   

Quantum Criticality from Sequential Destruction of SU(4) Spin-Orbital-coupled Kondo Effect*

Quantum criticality and the beyond-Landau physics of Kondo destruction [1,2] have recently been studied in systems with multipolar degrees of freedom. The compound Ce₃Pd₂₀Si₆ shows evidence of two consecutive Fermi surface collapsing quantum critical points (QCPs) as it is tuned from a paramagnetic to an antiferroquadrupolar and then to an antiferromagnetic state [3]. A theory was advanced [3] for a sequential destruction of spin-orbital-coupled Kondo entanglement in an SU(4) Bose-Fermi Kondo model, an effective model for a multipolar Kondo lattice. Here we report an analytical renormalization group calculation of the model with Ising anisotropy, using a Coulomb-gas representation. We show that a generic trajectory in the parameter space contains two QCPs associated with the destruction of the orbital and spin Kondo effects, respectively. Our work establishes a firm theoretical ground for the sequential Kondo destruction.

[1] Q. Si et al., Nature 413, 804 (2001).
[2] S. Paschen et al., Nature 432, 881 (2004).
[3] V. Martelli, A. Cai, E. M. Nica, M. Taupin, A. Prokofiev, C.-C. Liu, H.-H. Lai, R. Yu, K. Ingersent, R. Küchler, A. M. Strydom, D. Geiger, J. Haenel, J. Larrea, Q. Si, and S. Paschen, PNAS 116, 17701 (2019).   

X-ray and neutron-diffraction studies of the CeOs4Sb12 valence transition at low temperatures and high magnetic fields

CeOs₄Sb₁₂ exhibits a very unusual field- and temperature-driven valence transition that is accompanied by a drastic change in Fermi-surface topology. It is also a candidate heavy-fermion topological semimetal and sports a field-induced quantum-critical point at about 20 T. Single crystal x-ray diffraction in pulsed magnetic fields of up to 30 T using a unique instrumental combination at the Advanced Photon Source permitted a study of the change in unit-cell volume as the field swept through the valence transition. In addition, neutron-diffraction measurements probed the analogous structural changes as a function of temperature in zero magnetic field. Both measurements shed light on the unique “wedge-shaped” phase boundary that marks the valence transition in CeOs₄Sb₁₂.