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A $^{59}$Co nuclear quadrupole resonance (NQR) was performed on asingle-crystalline ferromagnetic (FM) superconductor UCoGe under pressure. TheFM phase vanished at a critical pressure $P_c$, and the NQR spectrum just below$P_c$ showed phase separation of the FM and paramagnetic (PM) phases belowCurie temperature $T_{\textrm{Curie}}$, suggesting first-order FM quantum phasetransition (QPT). We found that the internal field was absent above $P_c$, butthe superconductivity is almost unchanged. This result suggests the existenceof the nonunitary to unitary transition of the superconductivity around $P_c$.Nuclear spin-lattice relaxation rate $1/T_1$ showed the FM criticalfluctuations around $P_c$, which persist above $P_c$ and are clearly related tosuperconductivity in the PM phase. This FM QPT is understood to be a weak firstorder with critical fluctuations. $1/T_1$ sharply decreased in thesuperconducting (SC) state above $P_c$ with a single component, in contrast tothe two-component $1/T_1$ in the FM SC state, indicating that the inhomogeneousSC state is a characteristic feature of the FM SC state in UCoGe.

Enhancement of superconductivity by pressure-induced critical ferromagnetic fluctuations in UCoGe