Strong magnetic fluctuations can provide a coupling mechanism for electrons that leads to unconventional superconductivity. Magnetic order and superconductivity have been found to coexist in a number of magnetically mediated superconductors, but these order parameters generally compete. We report that close to the upper critical field, CeCoIn5 adopts a multicomponent ground state that simultaneously carries cooperating magnetic and superconducting orders. Suppressing superconductivity in a first-order transition at the upper critical field leads to the simultaneous collapse of the magnetic order, showing that superconductivity is necessary for the magnetic order. A symmetry analysis of the coupling between the magnetic order and the superconducting gap function suggests a form of superconductivity that is associated with a nonvanishing momentum.

Many superconducting materials allow the penetration of magnetic fields in a mixed state in which the superfluid is threaded by a regular lattice of Abrikosov vortices, each carrying one quantum of magnetic flux. The phenomenological Ginzburg-Landau theory, based on the concept of characteristic length scales, has generally provided a good description of the Abrikosov vortex lattice state. We conducted neutron-scattering measurements of the vortex lattice form factor in the heavy-fermion superconductor cerium-cobalt-indium (CeCoIn 5 ) and found that this form factor increases with increasing field—opposite to the expectations within the Abrikosov-Ginzburg-Landau paradigm. We propose that the anomalous field dependence of the form factor arises from Pauli paramagnetic effects around the vortex cores and from the proximity of the superconducting state to a quantum critical point.