  The mechanism of unconventional superconductivity, such as
high-temperature-cuprate, Fe-based, and heavy-fermion superconductors, has been
studied as a central issue in condensed-matter physics. Spin fluctuations,
instead of phonons, are considered to be responsible for the formation of
Cooper pairs, and many efforts have been made to confirm this mechanism
experimentally. Although a qualitative consensus seems to have been obtained,
experimental confirmation has not yet been achieved. This is owing to a lack of
the quantitative comparison between theory and experiments. Here, we show a
semi-quantitative comparison between the superconducting-transition temperature
($T_{\rm SC}$) and spin fluctuations derived from the nuclear magnetic
resonance (NMR) experiment on the ferromagnetic (FM) superconductor UCoGe, in
which the FM fluctuations and superconductivity are tunable by external fields.
The enhancement and abrupt suppression of $T_{\rm SC}$ by applied fields, as
well as the pressure variation of $T_{\rm SC}$ around the FM criticality are
well understood by the change in the FM fluctuations on the basis of the
single-band spin-triplet theoretical formalism. The present comparisons
strongly support the theoretical formalism of spin-fluctuation-mediated
superconductivity, particularly in UCoGe.
