  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.
