Effect of Ferromagnetic Spin Correlations on Superconductivity in Ferromagnetic Metals

We study the renormalization of the quasiparticle properties in weak ferromagnetic metals, due to spin fluctuations, away from the quantum critical point for small magnetic moment. We explain the origin of the s-wave superconducting instability in the ferromagnetic phase and find that the vertex corrections are small and Migdal's theorem is satisfied away from the quantum critical point.