4f-electron localization in CexLa 1-xM In5 with M=Co, Rh, or Ir

An emerging global picture of heavy fermion physics

Recent progresses using state-of-the-art experimental techniques have motivated a number of new insights on heavy fermion physics. This article gives a brief summary of the author's research along this direction. We discuss five major topics including: (1) development of phase coherence and two-stage hybridization; (2) two-fluid behavior and hidden universal scaling; (3) quantum phase transitions and fractionalized heavy fermion liquid; (4) quantum critical superconductivity; (5) material-specific properties. These cover the most essential parts of heavy fermion physics and lead to an emerging global picture beyond conventional theories based on mean-field or local approximations.

Localized 4f-electrons in the quantum critical heavy fermion ferromagnet CeRh6Ge4

Ferromagnetic quantum critical points were predicted to be prohibited in clean itinerant ferromagnetic systems, yet such a phenomenon was recently revealed in CeRh₆Ge₄, where the Curie temperature can be continuously suppressed to zero under a moderate hydrostatic pressure. Here we report the observation of quantum oscillations in CeRh₆Ge₄ from measurements using the cantilever and tunnel-diode oscillator methods in fields up to 45 T, clearly demonstrating that the ferromagnetic quantum criticality occurs in a clean system. In order to map the Fermi surface of CeRh₆Ge₄, we performed angle-dependent measurements of quantum oscillations at ambient pressure, and compared the results to density functional theory calculations. The results are consistent with the Ce 4f electrons remaining localized and not contributing to the Fermi surface, suggesting that localized ferromagnetism is a key factor for the occurrence of a ferromagnetic quantum critical point in CeRh₆Ge₄.

Anisotropic c-f Hybridization in the Ferromagnetic Quantum Critical Metal CeRh_{6}Ge_{4}

Heavy fermion compounds exhibiting a ferromagnetic quantum critical point have attracted considerable interest. Common to two known cases, i.e., CeRh_{6}Ge_{4} and YbNi_{4}P_{2}, is that the 4f moments reside along chains with a large interchain distance, exhibiting strong magnetic anisotropy that was proposed to be vital for the ferromagnetic quantum criticality. Here, we report an angle-resolved photoemission study on CeRh_{6}Ge_{4} in which we observe sharp momentum-dependent 4f bands and clear bending of the conduction bands near the Fermi level, indicating considerable hybridization between conduction and 4f electrons. The extracted hybridization strength is anisotropic in momentum space and is obviously stronger along the Ce chain direction.The hybridized 4f bands persist up to high temperatures, and the evolution of their intensity shows clear band dependence. Our results provide spectroscopic evidence for anisotropic hybridization between conduction and 4f electrons in CeRh_{6}Ge_{4}, which could be important for understanding the electronic origin of the ferromagnetic quantum criticality.

Robust Fermi-Surface Morphology of CeRhIn_{5} across the Putative Field-Induced Quantum Critical Point

We report a comprehensive de Haas-van Alphen (dHvA) study of the heavy-fermion material CeRhIn_{5} in magnetic fields up to 70 T. Several dHvA frequencies gradually emerge at high fields as a result of magnetic breakdown. Among them is the thermodynamically important β_{1} branch, which has not been observed so far. Comparison of our angle-dependent dHvA spectra with those of the non-4f compound LaRhIn_{5} and with band-structure calculations evidences that the Ce 4f electrons in CeRhIn_{5} remain localized over the whole field range. This rules out any significant Fermi-surface reconstruction, either at the suggested nematic phase transition at B^{*}≈30  T or at the putative quantum critical point at B_{c}≃50  T. Our results rather demonstrate the robustness of the Fermi surface and the localized nature of the 4f electrons inside and outside of the antiferromagnetic phase.

Band Dependent Interlayer f-Electron Hybridization in CeRhIn_{5}

A key issue in heavy fermion research is how subtle changes in the hybridization between the 4f (5f) and conduction electrons can result in fundamentally different ground states. CeRhIn_{5} stands out as a particularly notable example: when replacing Rh with either Co or Ir, antiferromagnetism gives way to superconductivity. In this photoemission study of CeRhIn_{5}, we demonstrate that the use of resonant angle-resolved photoemission spectroscopy with polarized light allows us to extract detailed information on the 4f crystal field states and details on the 4f and conduction electron hybridization, which together determine the ground state. We directly observe weakly dispersive Kondo resonances of f electrons and identify two of the three Ce 4f_{5/2}^{1} crystal-electric-field levels and band-dependent hybridization, which signals that the hybridization occurs primarily between the Ce 4f states in the CeIn_{3} layer and two more three-dimensional bands composed of the Rh 4d and In 5p orbitals in the RhIn_{2} layer. Our results allow us to connect the properties observed at elevated temperatures with the unusual low-temperature properties of this enigmatic heavy fermion compound.

Multiple quantum phase transitions and superconductivity in Ce-based heavy fermions

Heavy fermions have served as prototype examples of strongly-correlated electron systems. The occurrence of unconventional superconductivity in close proximity to the electronic instabilities associated with various degrees of freedom points to an intricate relationship between superconductivity and other electronic states, which is unique but also shares some common features with high temperature superconductivity. The magnetic order in heavy fermion compounds can be continuously suppressed by tuning external parameters to a quantum critical point, and the role of quantum criticality in determining the properties of heavy fermion systems is an important unresolved issue. Here we review the recent progress of studies on Ce based heavy fermion superconductors, with an emphasis on the superconductivity emerging on the edge of magnetic and charge instabilities as well as the quantum phase transitions which occur by tuning different parameters, such as pressure, magnetic field and doping. We discuss systems where multiple quantum critical points occur and whether they can be classified in a unified manner, in particular in terms of the evolution of the Fermi surface topology.

Evidence for Coexistence of Bulk Superconductivity and Itinerant Antiferromagnetism in the Heavy Fermion System CeCo(In(1-x)Cdx)5

In the generic phase diagram of heavy fermion systems, tuning an external parameter such as hydrostatic or chemical pressure modifies the superconducting transition temperature. The superconducting phase forms a dome in the temperature—tuning parameter phase diagram, which is associated with a maximum of the superconducting pairing interaction. Proximity to antiferromagnetism suggests a relation between the disappearance of antiferromagnetic order and superconductivity. We combine muon spin rotation, neutron scattering, and x-ray absorption spectroscopy techniques to gain access to the magnetic and electronic structure of CeCo(In_1−xCd_x)₅ at different time scales. Different magnetic structures are obtained that indicate a magnetic order of itinerant character, coexisting with bulk superconductivity. The suppression of the antiferromagnetic order appears to be driven by a modification of the bandwidth/carrier concentration, implying that the electronic structure and consequently the interplay of superconductivity and magnetism is strongly affected by hydrostatic and chemical pressure.

Correlation between ground state and orbital anisotropy in heavy fermion materials

The interplay of structural, orbital, charge, and spin degrees of freedom is at the heart of many emergent phenomena, including superconductivity. Unraveling the underlying forces of such novel phases is a great challenge because it not only requires understanding each of these degrees of freedom, it also involves accounting for the interplay between them. Cerium-based heavy fermion compounds are an ideal playground for investigating these interdependencies, and we present evidence for a correlation between orbital anisotropy and the ground states in a representative family of materials. We have measured the 4f crystal-electric field ground-state wave functions of the strongly correlated materials CeRh1-xIrxIn5 with great accuracy using linear polarization-dependent soft X-ray absorption spectroscopy. These measurements show that these wave functions correlate with the ground-state properties of the substitution series, which covers long-range antiferromagnetic order, unconventional superconductivity, and coexistence of these two states.

Fermi surface reconstruction and multiple quantum phase transitions in the antiferromagnet CeRhIn5

Conventional, thermally driven continuous phase transitions are described by universal critical behavior that is independent of the specific microscopic details of a material. However, many current studies focus on materials that exhibit quantum-driven continuous phase transitions (quantum critical points, or QCPs) at absolute zero temperature. The classification of such QCPs and the question of whether they show universal behavior remain open issues. Here we report measurements of heat capacity and de Haas-van Alphen (dHvA) oscillations at low temperatures across a field-induced antiferromagnetic QCP (Bc0 ≈ 50 T) in the heavy-fermion metal CeRhIn5. A sharp, magnetic-field-induced change in Fermi surface is detected both in the dHvA effect and Hall resistivity at B0* ≈ 30 T, well inside the antiferromagnetic phase. Comparisons with band-structure calculations and properties of isostructural CeCoIn5 suggest that the Fermi-surface change at B0* is associated with a localized-to-itinerant transition of the Ce-4f electrons in CeRhIn5. Taken in conjunction with pressure experiments, our results demonstrate that at least two distinct classes of QCP are observable in CeRhIn5, a significant step toward the derivation of a universal phase diagram for QCPs.

Electronic inhomogeneity in a Kondo lattice

Inhomogeneous electronic states resulting from entangled spin, charge, and lattice degrees of freedom are hallmarks of strongly correlated electron materials; such behavior has been observed in many classes of d -electron materials, including the high-T c copper-oxide superconductors, manganites, and most recently the iron–pnictide superconductors. The complexity generated by competing phases in these materials constitutes a considerable theoretical challenge—one that still defies a complete description. Here, we report a manifestation of electronic inhomogeneity in a strongly correlated f -electron system, using CeCoIn5 as an example. A thermodynamic analysis of its superconductivity, combined with nuclear quadrupole resonance measurements, shows that nonmagnetic impurities (Y, La, Yb, Th, Hg, and Sn) locally suppress unconventional superconductivity, generating an inhomogeneous electronic “Swiss cheese” due to disrupted periodicity of the Kondo lattice. Our analysis may be generalized to include related systems, suggesting that electronic inhomogeneity should be considered broadly in Kondo lattice materials.

Unconventional quantum criticality in the pressure-induced heavy-fermion superconductor CeRhIn₅

The lack of superconductivity in several candidate materials that exhibit a non-spin density wave quantum critical point has raised the question of whether the associated spectra of quantum fluctuations are beneficial to forming superconducting electron pairs. Here we discuss the possibility that the prototypical heavy-fermion antiferromagnet CeRhIn5 may be the first example of unconventional superconductors where superconductivity arises from Kondo-breakdown quantum criticality.

Electronic structure of Ce(n)M(m)In(2m+3n), where n = 1, 2; m = 0, 1;M = Co, Rh or Ir: experiment and calculations

We present a detailed study of the electronic structure of the Ce(n)M(m)In(2m+3n) (M = Co, Rh, Ir; n = 1, 2 and m = 0, 1) series of Ce intermetallic compounds and of the reference LaIn(3) compound. The ground state of these heavy-fermion (HF) materials can be tuned between antiferromagnetic (AF) and superconducting (SC), with pressure or doping as the tuning parameter. Performing the x-ray photoelectron spectroscopy (XPS) measurements on the Ce 3d core levels as well as on the valence band states we analyse the dependence of both the Ce 4f band character and physical properties on the kind of transition metal atom M and on the number of CeIn(3) layers intervened by the MIn(2) layers in the investigated family of compounds. We draw a parallel between the XPS valence band spectra and ab initio band structure calculations based on the full-potential linearized augmented plane-wave (FP-LAPW) method. We analyse changes in valence band states within the whole family of materials. We compare the experimental magnetic moments on Ce atoms with the theoretical ones calculated within different approximations for exchange-correlation potential. Finally, we have shown that the Ce 4f electrons participate in bonding formation for all investigated compounds. Our study indicates that the observed changes in the 4f band on-site hybridization energy result from the reconstruction of the charge density distribution driven by transition metal atoms inserted into the CeIn(3) structure.

Evidence for a new magnetic field scale in CeCoIn5

The Nernst coefficient of displays two distinct anomalies in magnetic field. The feature detected at Hk approximately 23 T is similar to what is observed in CeRu2Si2 at Hm = 7.8 T where a metamagnetic transition occurs. In CeCoIn5, new frequencies are observed in de Haas-van Alphen oscillations when the field exceeds 23 T where the Dingle temperature decreases by about 30%. Based on the Nernst coefficient anomalies, the magnetic phase diagram of CeCoIn5 is revised.