Mutual enhancement of magnetism and Fulde-Ferrell-Larkin-Ovchinnikov superconductivity in CeCoIn5

Recent experiments on CeCoIn5 suggest an unusual interplay between superconducting and magnetic orders that gives rise to a multicomponent (magnetosuperconducting) phase. We demonstrate that characteristics of CeCoIn5 make this system particularly well suited for the onset of such a phase. Based on general considerations, we show that superconductivity with nonzero Cooper-pair momentum may lead to an enhancement of the spin-spin response function and, simultaneously, incommensurate spin-density wave may enhance the Cooper-pair susceptibility.