  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.
