Magnon exchange mechanism of ferromagnetic superconductivity

Abstract

The magnon exchange mechanism of ferromagnetic superconductivity (FM superconductivity) was developed to explain in a natural way the fact that the superconductivity in ${\mathrm{UGe}}_{2},$ ${\mathrm{ZrZn}}_{2},$ and URhGe is confined to the ferromagnetic phase. The order parameter is a spin antiparallel component of a spin-1 triplet with zero spin projection. The transverse spin fluctuations are pair forming and the longitudinal ones are pair breaking. In the present paper, a superconducting solution, based on the magnon exchange mechanism, is obtained which closely matches the experiments with ${\mathrm{ZrZn}}_{2}$ and URhGe. The onset of superconductivity leads to the appearance of complicated Fermi surfaces in the spin-up and spin-down momentum distribution functions. Each of them consist of two pieces, but they are simple connected and can be made very small by varying the microscopic parameters. As a result, it is obtained that the specific heat depends on the temperature linearly, at low temperature, and the coefficient $\ensuremath{\gamma}=C/T$ is smaller in the superconducting phase than in the ferromagnetic one. The absence of a quantum transition from ferromagnetism to ferromagnetic superconductivity in a weak ferromagnets ${\mathrm{ZrZn}}_{2}$ and URhGe is explained accounting for the contribution of magnon self-interaction to the spin fluctuations' parameters. It is shown that in the presence of an external magnetic field the system undergoes a first-order quantum phase transition.