Superconductivity in a Strong Spin-Exchange Field

TLDR

A strong exchange field from ferromagnetically aligned impurities polarizes conduction electron spins. In a superconductor, such a field must exceed the energy gap to influence the system. When the exchange field surpasses the superconducting gap, the self‑consistent gap equation produces a depaired ground state with a spatially varying complex order parameter, nonzero pairing momentum, suppressed supercurrent, spin polarization, normal‑like specific heat, anisotropic electrodynamics, and a degenerate ground state supporting low‑lying collective excitations. Scattering effects in real superconducting ferromagnets remain unstudied and may affect experimental verification of these idealized predictions.

Abstract

A strong exchange field, such as produced by ferromagnetically aligned impurities in a metal, will tend to polarize the conduction electron spins. If the metal is a superconductor, this will happen only if the spin-exchange field is sufficiently strong compared to the energy gap. When the field is strong enough to break many electron pairs, the self-consistent gap equation is modified and a new type of depaired superconducting ground state occurs. In the idealization of a spatially uniform exchange field with no scattering, it is found that the depaired state has a spatially dependent complex Gorkov field, corresponding to a nonzero pairing momentum in the BCS model. The presence of the "normal" electrons from the broken pairs reduces the total current to zero, gives the depaired state some spin polarization, and results in almost normal Sommerfeld specific heat and single-electron tunneling characteristics. The nonzero value of the pairing momentum also gives rise to an unusual anisotropic electrodynamic behavior of the superconductor, as well as to a degenerate ground state and low-lying collective excitations, in accordance with Goldstone's theorem. The effects of scattering in an actual superconducting ferromagnetic alloy have not been studied and may interfere with experimental investigation of the theoretical results found in this paper for the idealized model.