Itinerant Ferromagnetism and Superconductivity

Superconductivity has again become a challenge following the discovery of unconventional superconductivity. Resistance-free currents have been observed in heavy-fermion materials, organic conductors and copper oxides. The discovery of superconductivity in a single crystal of $UGe_2$, $ZrZn_2$ and $URhGe$ revived the interest in the coexistence of superconductivity and ferromagnetism. The experiments indicate that: i)The superconductivity is confined to the ferromagnetic phase. ii)The ferromagnetic order is stable within the superconducting phase (neutron scattering experiments). iii) The specific heat anomaly associated with the superconductivity in these materials appears to be absent. The specific heat depends on the temperature linearly at low temperature. I present a review of the recent experimental results and the basic theoretical ideas concerning ferromagnetic superconductivity (FM-superconductivity) induced by the ferromagnetic spin fluctuations. A particular attention is paid to the magnon exchange mechanism of FM-superconductivity.