The phase separation of the ferromagnetic (FM) and paramagnetic (PM) phases in the superconducting (SC) state of UCoGe at the FM critical region was investigated using $^{59}$Co nuclear quadrupole resonance (NQR) technique by taking advantage of its site-selective feature. The NQR measurements revealed that the first-order quantum phase transition occurs between the FM and the PM states. The nuclear spin-lattice relaxation rate $1/T_1$ exhibited a clear drop at the SC state in the PM phase, whereas it was not detected in the FM phase, which indicates that the superconductivity in the FM phase becomes weaker at the FM critical region due to the presence of the PM SC state. This result suggests that the SC condensation energy of the PM SC state is equal or larger than that of the FM SC state in this region. The pressure-temperature phase diagram of UCoGe was modified by taking the results from this study into account.
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