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Register a new userReview of U-based Ferromagnetic Superconductors: Comparison between UGe2, URhGe, and UCoGe
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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.
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We review our recent studies on ferromagnetic superconductors, UGe2, URhGe and UCoGe, where the spin-triplet state with the so-called equal spin pairing is realized. We focus on experimental results of URhGe and UCoGe in which the superconductivity occurs already at ambient pressure. The huge upper critical field Hc2 on UCoGe for the field along the hard magnetization axis (b-axis) is confirmed by the AC susceptibility measurements by the fine tuning of field angle. Contrary to the huge Hc2 along the hard-magnetization axis, Hc2 along the easy-magnetization axis (c-axis) is relatively small in value. However, the initial slope of Hc2, namely dHc2/dT (H -> 0) both in UCoGe and in URhGe indicates the large value, which can be explained by the magnetic domain effect detected in the magnetization measurements. The specific heat measurements using a high quality single crystal of UCoGe demonstrate the bulk superconductivity, which is extended under magnetic field for the field along c-axis.
The field-angular dependence of Co-NMR spin-lattice relaxation rate 1/T1 has been measured for a 10% Co-doped single crystal of URhGe. The experiment revealed that spin fluctuations in ferromagnetic (FM) state of URhGe are robust against magnetic field below about 4 T, applied along any direction in the bc crystal plane. This is in clear contrast with the sister compound UCoGe, in which FM spin fluctuations are rapidly suppressed by a tiny applied field along the c axis. We show that such a difference in the character of the spin fluctuations is reflected in their two distinct phase diagrams for the upper critical field Hc2, providing further support to the mechanism of superconductivity mediated by spin fluctuations in these materials.
The field-reentrant (field-reinforced) superconductivity on ferromagnetic superconductors is one of the most interesting topics in unconventional superconductivity. The enhancement of effective mass and the induced ferromagnetic fluctuations play key roles for reentrant superconductivity. However, the associated change of the Fermi surface, which is often observed at (pseudo-) metamagnetic transition, can also be a key ingredient. In order to study the Fermi surface instability, we performed Hall effect measurements in the ferromagnetic superconductor URhGe. The Hall effect of URhGe is well explained by two contributions, namely by the normal Hall effect and by the large anomalous Hall effect due to skew scattering. The large change in the Hall coefficient is observed at low fields between the paramagnetic and ferromagnetic states for H // c-axis (easy-magnetization axis) in the orthorhombic structure, indicating that the Fermi surface is reconstructed in the ferromagnetic state below the Curie temperature (T_Curie=9.5K). At low temperatures (T << T_Curie), when the field is applied along the b-axis, the reentrant superconductivity was observed in both the Hall resistivity and the magnetoresistance below 0.4K. Above 0.4K, a large jump with the first-order nature was detected in the Hall resistivity at a spin-reorientation field H_R ~ 12.5T, demonstrating that the marked change of the Fermi surface occurs between the ferromagnetic state and the polarized state above H_R. The results can be understood by the Lifshitz-type transition, induced by the magnetic field or by the change of the effective magnetic field.
We have performed 59Co NMR experiments on the ferromagnetic superconductor UCoGe under magnetic fields (H) along the a- and b- axes to investigate the relationship between ferromagnetic properties and superconductivity. The ferromagnetic ordering temperature TCurie is suppressed and the nuclear spin-lattice relaxation rate 1/T1 at 2 K is enhanced in H || b, although TCurie and 1/T1 are unchanged in H || a, indicating that the ferromagnetic criticality is induced only when H is applied along the b axis. We show the close relationship between the magnetic anisotropies and the superconducting ones reported by Aoki et al.: the superconductivity is gradually suppressed in H || a, but enhanced in H || b above 5 T. We strongly suggest that the enhancement of the superconductivity observed in H || b originates from the field induced ferromagnetic criticality, as pointed out by Aoki et al and Mineev.
We have performed ^{59}Co-nuclear quadrupole resonance (NQR) and nuclear magnetic resonance (NMR) studies on YCoGe, which is a reference compound of ferromagnetic superconductor UCoGe, in order to investigate the magnetic properties at the Co site. Magnetic and superconducting transitions were not observed down to 0.3 K, but a conventional metallic behavior was found in YCoGe, although its crystal structure is similar to that of UCoGe. From the comparison between experimental results of two compounds, the ferromagnetism and superconductivity observed in UCoGe originate from the U-5f electrons.
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