Superconductivity mediated by spin fluctuations in weak and nearly ferromagnetic metals is studied close to the zero-temperature magnetic transition. We solve analytically the Eliashberg equations for $p$-wave pairing and obtain the quasiparticle self-energy and the superconducting transition temperature $T_c$ as a function of the distance to the quantum critical point (QCP). We show that the reduction of quasiparticle coherence and lifetime due to scattering by quasistatic spin fluctuations is the dominant pair-breaking process, which leads to a rapid suppression of $T_c$ to a nonzero value near the QCP. We point out the differences and similarities of the problem to that of paramagnetic impurities in superconductors.

• Received 2 April 2001

DOI:https://doi.org/10.1103/PhysRevLett.87.257001