  We report that a novel type of superconducting order parameter has been
realized in the ferromagnetic states in UGe$_2$ via $^{73}$Ge
nuclear-quadrupole-resonance (NQR) experiments performed under pressure ($P$).
Measurements of the nuclear spin-lattice relaxation rate $(1/T_1)$ have
revealed an unconventional nature of superconductivity such that the up-spin
band is gapped with line nodes, but the down-spin band remains gapless at the
Fermi level. This result is consistent with that of a ferromagnetic
spin-pairing model in which Cooper pairs are formed among ferromagnetically
polarized electrons. The present experiment has shed new light on a possible
origin of ferromagnetic superconductivity, which is mediated by ferromagnetic
spin-density fluctuations relevant to the first-order transition inside the
ferromagnetic states.
