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.
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