Since the discovery of superconductivity, there has been a drive to understand the mechanisms by which it occurs. The BCS (Bardeen-Cooper-Schrieffer) model successfully treats the electrons in conventional superconductors as pairs coupled by phonons (vibrational modes of oscillation) moving through the material, but there is as yet no accepted model for high-transition-temperature, organic or 'heavy fermion' superconductivity. Experiments that reveal unusual properties of those superconductors could therefore point the way to a deeper understanding of the underlying physics. In particular, the response of a material to a magnetic field can be revealing, because this usually reduces or quenches superconductivity. Here we report measurements of the heat capacity and magnetization that show that, for particular orientations of an external magnetic field, superconductivity in the heavy-fermion material CeCoIn(5) is enhanced through the magnetic moments (spins) of individual electrons. This enhancement occurs by fundamentally altering how the superconducting state forms, resulting in regions of superconductivity alternating with walls of spin-polarized unpaired electrons; this configuration lowers the free energy and allows superconductivity to remain stable. The large magnetic susceptibility of this material leads to an unusually strong coupling of the field to the electron spins, which dominates over the coupling to the electron orbits.

To understand the origin of superconductivity, it is crucial to ascertain the nature and origin of the primary carriers available to participate in pairing. Recent quantum oscillation experiments on high-transition-temperature (high-T(c)) copper oxide superconductors have revealed the existence of a Fermi surface akin to that in normal metals, comprising fermionic carriers that undergo orbital quantization. The unexpectedly small size of the observed carrier pocket, however, leaves open a variety of possibilities for the existence or form of any underlying magnetic order, and its relation to d-wave superconductivity. Here we report experiments on quantum oscillations in the magnetization (the de Haas-van Alphen effect) in superconducting YBa(2)Cu(3)O(6.51) that reveal more than one carrier pocket. In particular, we find evidence for the existence of a much larger pocket of heavier mass carriers playing a thermodynamically dominant role in this hole-doped superconductor. Importantly, characteristics of the multiple pockets within this more complete Fermi surface impose constraints on the wavevector of any underlying order and the location of the carriers in momentum space. These constraints enable us to construct a possible density-wave model with spiral or related modulated magnetic order, consistent with experimental observations.

Measurements of the de Haas-van Alphen effect in the normal state of the heavy-fermion superconductor CeCoIn 5 have been carried out using a torque cantilever at temperatures ranging from 20 to 500 mK and in fields up to 18 T. Angular-dependent measurements of the extremal Fermi surface areas reveal a more extreme two-dimensional sheet than is found in either CeRhIn 5 or CeIrIn 5 . The effective masses of the measured frequencies range from 9 to 20m*/m 0 .

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