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

## TL;DR

This review compares UGe2, URhGe, and UCoGe ferromagnetic superconductors, highlighting their phase diagrams, magnetic fluctuations, and the role of FM fluctuations in mediating superconductivity, with insights into experimental and theoretical perspectives.

## Contribution

It provides a comprehensive comparison of three U-based ferromagnetic superconductors, emphasizing their phase diagrams, magnetic fluctuations, and the mechanisms behind superconductivity.

## Key findings

- Superconductivity coexists with ferromagnetism in UGe2, URhGe, and UCoGe.
- FM fluctuations are key to the emergence of superconductivity in these materials.
- Experimental evidence supports spin-triplet pairing mediated by FM fluctuations.

## Abstract

The discovery in 2000 that the ferromagnetic (FM) compound UGe2 (T_Curie = 52 K at ambient pressure) becomes superconducting under a pressure of P = 1.1 GPa until 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 of the coexistence of superconductivity (SC) and ferromagnetism at ambient pressure. Furthermore in UCoGe, it was found that SC survives in the PM regime from P_c = 1.1 to 4 GPa. Focus has been on low-temperature experiments under extreme conditions of magnetic field (H), pressure, and uniaxial stress. In UGe2, strong interplay exists between Fermi surface (FS) reconstructions in the cascade of different FM and PM ground states and their magnetic fluctuations. Similar phenomena occur in URhGe and UCoGe but, at first glance, the SC seems to be driven by the FM fluctuations. In UCoGe, a longitudinal field scan leads to a drastic decrease in the FM fluctuations, while a transverse field scan leads to suppression of the Curie temperature, T_Curie; the consequence is a boost in FM fluctuations, leading to a reinforcement of SC. The singularity in URhGe is the weakness of the anisotropy between c- and b-axes; the most noteworthy feature is the detection of reentrant SC near H_R. All the experimental results give evidence that the SC in these three materials originates from the FM fluctuations, which are amplitude modes of magnetic excitations in the FM state. Spin-triplet pairing has been anticipated in the FM superconductors and was actually observed by Knight-shift measurements in the SC state of UCoGe. Their fascinating (p, T, H) phase diagrams are now well established. Discussion is presented on how different theoretical approaches can describe the various phenomena discovered by experimentalists.