Superconductivity develops from an attractive interaction between itinerant electrons that creates electron pairs, which condense into a macroscopic quantum state-the superconducting state. On the other hand, magnetic order in a metal arises from electrons localized close to the ionic core and whose interaction is mediated by itinerant electrons. The dichotomy between local moment magnetic order and superconductivity raises the question of whether these two states can coexist and involve the same electrons. Here, we show that the single 4f electron of cerium in CeRhIn 5 simultaneously produces magnetism, characteristic of localization, and superconductivity that requires itinerancy. The dual nature of the 4f-electron allows microscopic coexistence of antiferromagnetic order and superconductivity whose competition is tuned by small changes in pressure and magnetic field. Electronic duality contrasts with conventional interpretations of coexisting spin-density magnetism and superconductivity and offers a new avenue for understanding complex states in classes of materials.4f electrons ͉ local moment magnetism ͉ strongly correlated systems ͉ superconductivity T he possibility that the same electrons might exhibit simultaneously localized and itinerant characters has been raised in the context of materials in which strong Coulomb interactions nominate physical properties (1). UPd 2 Al 3 is one such correlated electron material in which coexisting antiferromagnetism and superconductivity may be interpreted if two of uranium's three 5f electrons are localized spatially close to the ionic core and produce antiferromagnetic order, whereas the remaining f electron is spatially delocalized and participates in creating superconductivity (2). In elemental Pu metal, the volume and electronic spectrum of its ␦-phase could be described ad hoc if one of Pu's five 5f electrons were itinerant and four of the 5f electrons were localized (3, 4). Theoretically, the competition between intra-atomic Coulomb interactions and anisotropic hybridization of f electrons with their chemical environment is one potential route to the division of 5f orbitals into localized and delocalized components (5). A more perplexing situation is presented if a single f electron, such as in Ce, were to display localized and itinerant natures simultaneously. Like UPd 2 Al 3 , CeRhIn 5 is a strongly correlated metal in which antiferromagnetic order and superconductivity coexist (6), and as we will show, this coexistence necessitates the concept of electronic duality.Within the resolution of electronic structure calculations and measurements, the single 4f electron of Ce in CeRhIn 5 is localized (7), consistent with the observation of antiferromagnetic ordering of the nearly full magnetic moment carried by a localized 4f 1 electron in a crystalline electric-field doublet ground state (8). A slight (Ϸ10%) reduction of the ordered moment from its full value is due to weak hybridization of the 4f electron with ligand electrons, which transfers some spectral weigh...

a b s t r a c tMeasurements of the upper critical field H c2 of the Pu-based heavy-fermion superconductor PuRhGa 5 have been made using a torque magnetometer at temperatures down to 0.6 K and magnetic fields up to 17 T along the principal axes of the tetragonal structure. A linear temperature dependence of H c2 down to T c /10 for H||c and to T c /2 for H||ab is observed. While the data appear to be inconsistent with both purely Pauli limiting or orbital effects governing the upper critical field, the linear T-dependence of H c2 is well described by a two-band model of superconductivity involving coupled bands of heavy and light electrons. A close similarity between PuRhGa 5 and the pressure-induced antiferromagnetic isostructural superconductor CeRhIn 5 is also found.Published by Elsevier B.V.

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