Superconductivity and ferromagnetic quantum criticality in uranium compounds

We review our recent studies on ferromagnetic superconductors, UGe₂, URhGe, and UCoGe, together with the ferromagnetic quantum criticality and paramagnetic singularity on the Ising 5 f-itinerant system UCoAl. Thanks to the variety of ordered moment in ferromagnetic superconductors from 1.5 μ_B to 0.05 μ_B, interesting systematic changes or similarities are clarified. All ferromagnetic superconductors show large upper critical field H_c2, and the field-reentrant (-reinforced) phenomena are observed in the field-temperature phase diagram, when the pressure or field direction is tuned for particular conditions. These phenomena are well explained by the ferromagnetic longitudinal fluctuations, which are induced by the magnetic field in transverse configurations. The large H_c2 might be also associated with possible additional effects of Fermi surface instabilities, such as Lifshitz-type singularities.