The magnon exchange mechanism of ferromagnetic superconductivity
(FM-superconductivity) was developed to explain in a natural way the fact that
the superconductivity in UGe2​, ZrZn2​ and URhGe is confined to the
ferromagnetic phase.The order parameter is a spin anti-parallel 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 ZrZn2​ 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
γ=TC​ 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 ZrZn2​ 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.Comment: 9 pages, 7 figures, accepted for publication in Phys.Rev.