Triplet superconductivity in ferromagnets due to magnon exchange

Abstract

We consider the superconducting pairing induced by spin-wave exchange in a ferromagnet with both conduction and localized electrons, the latter being described as spins. We use the microscopic Eliashberg theory to describe the pairing of conducting electrons and the random phase approximation approach to treat the localized spins assuming an exchange coupling between the conducting electrons and spins. In the framework of a nonrelativistic Hamiltonian, we found that the spin-wave exchange results in equal spin electron pairing described by the two components of the order parameter, Δ↑ (both spins up) and Δ↓ (both spins down). Due to the conservation of total spin projection on the axis of the spontaneous ferromagnetic moment, the spin-wave exchange at low temperatures includes an emission of magnons and an absorption of thermal magnons by the conduction electrons. The absorption and emission processes depend differently on the temperature, with the absorption being progressively suppressed as the temperature drops. As a result, the superconducting pairing exists only if the electron–spin-wave exchange parameter g exceeds some critical value gc. At g > gc, pairing vanishes if the temperature drops below the lowest point Tcl or increases above the upper critical point Tch ≈ Tm (the Curie temperature) where the spin waves cease to exist. This behavior inherent to the spin-carrying glue is in an obvious disagreement with the results of the conventional BCS approach, which assumes that the effective electron-electron attraction is simply proportional to the static magnetic susceptibility.