Odd-parity superconductivity and the ferromagnetic quantum critical point

The study of the emergence of superconductivity close to quantum critical points affords a powerful means to identify the mechanism that drives the formation of unconventional superconductivity in heavy fermion materials. The recent discovery of superconducting states close to quantum critical points in ferromagnets UGe2 and URhGe is reviewed in this light. For URhGe we examine whether the predominant type of magnetic excitations involved are longitudinal excitations, hitherto considered theoretically to be the most promising candidate to mediate equal-spin-paired superconductivity.