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The discovery in 2000 that the ferromagnetic (FM) compound UGe2 (T_Curie = 52K at ambient pressure) becomes superconducting under a pressure of P = 1.1 GPauntil it enters the paramagnetic (PM) phase above Pc = 1.6 GPa was a surprise.Successive searches for new materials (URhGe and UCoGe) led to the discovery ofthe coexistence of superconductivity (SC) and ferromagnetism at ambientpressure. Furthermore in UCoGe, it was found that SC survives in the PM regimefrom P_c = 1.1 to 4 GPa. Focus has been on low-temperature experiments underextreme conditions of magnetic field (H), pressure, and uniaxial stress. InUGe2, strong interplay exists between Fermi surface (FS) reconstructions in thecascade of different FM and PM ground states and their magnetic fluctuations.Similar phenomena occur in URhGe and UCoGe but, at first glance, the SC seemsto be driven by the FM fluctuations. In UCoGe, a longitudinal field scan leadsto a drastic decrease in the FM fluctuations, while a transverse field scanleads to suppression of the Curie temperature, T_Curie; the consequence is aboost in FM fluctuations, leading to a reinforcement of SC. The singularity inURhGe is the weakness of the anisotropy between c- and b-axes; the mostnoteworthy feature is the detection of reentrant SC near H_R. All theexperimental results give evidence that the SC in these three materialsoriginates from the FM fluctuations, which are amplitude modes of magneticexcitations in the FM state. Spin-triplet pairing has been anticipated in theFM superconductors and was actually observed by Knight-shift measurements inthe SC state of UCoGe. Their fascinating (p, T, H) phase diagrams are now wellestablished. Discussion is presented on how different theoretical approachescan describe the various phenomena discovered by experimentalists.

Review of U-based Ferromagnetic Superconductors: Comparison between UGe2, URhGe, and UCoGe