The origin of magnetic order in metals has two extremes: an instability in a liquid of local magnetic moments interacting through conduction electrons, and a spin-density wave instability in a Fermi liquid of itinerant electrons. This dichotomy between 'local-moment' magnetism and 'itinerant-electron' magnetism is reminiscent of the valence bond/molecular orbital dichotomy present in studies of chemical bonding. The class of heavy-electron intermetallic compounds of cerium, ytterbium and various 5f elements bridges the extremes, with itinerant-electron magnetic characteristics at low temperatures that grow out of a high-temperature local-moment state. Describing this transition quantitatively has proved difficult, and one of the main unsolved problems is finding what determines the temperature scale for the evolution of this behaviour. Here we present a simple, semi-quantitative solution to this problem that provides a basic framework for interpreting the physics of heavy-electron materials and offers the prospect of a quantitative determination of the physical origin of their magnetic ordering and superconductivity. It also reveals the difference between the temperature scales that distinguish the conduction electrons' response to a single magnetic impurity and their response to a lattice of local moments, and provides an updated version of the well-known Doniach diagram.

We report pressure-induced superconductivity in a single crystal of CaFe 2 As 2 . At atmospheric pressure, this material is antiferromagnetic below 170 K but under an applied pressure of 0.69 GPa becomes superconducting, with a transition temperature T c exceeding 10 K. The rate of T c suppression with applied magnetic field is −0.7 K T −1 , giving an extrapolated zero-temperature upper critical field of 10-14 T.

fruitful discussions, Guanghan Cao and Zhicheng Wang for assisting with 3 He-SQUID measurements, and Xiaoyan Xiao for assistance with single crystal x-ray diffraction.

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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 (B c0 ≈ 50 T) in the heavy-fermion metal CeRhIn 5 . A sharp, magnetic-field-induced change in Fermi surface is detected both in the dHvA effect and Hall resistivity at B * 0 ≈ 30 T, well inside the antiferromagnetic phase. Comparisons with band-structure calculations and properties of isostructural CeCoIn 5 suggest that the Fermi-surface change at B * 0 is associated with a localized-to-itinerant transition of the Ce-4f electrons in CeRhIn 5 . Taken in conjunction with pressure experiments, our results demonstrate that at least two distinct classes of QCP are observable in CeRhIn 5 , a significant step toward the derivation of a universal phase diagram for QCPs.heavy fermion | quantum phase transitions | superconductivity | Fermi surface reconstruction | localized-itinerant transition