Strong Enhancement of SuperconductingTcin Ferromagnetic Phases

It is shown that the critical temperature for spin-triplet, $p$-wave superconductivity mediated by spin fluctuations is generically much higher in a Heisenberg ferromagnetic phase than in a paramagnetic one, due to the coupling of the magnons to the longitudinal magnetic susceptibility. Together with the tendency of the low-temperature ferromagnetic transition in very clean Heisenberg magnets to be of first order, this qualitatively explains the phase diagram recently observed in ${\mathrm{UGe}}_2$.