  We show theoretically that the nuclear spin-lattice relaxation rate
(T_1T)^{-1} and the spin susceptibility exhibit divergent behaviors toward zero
temperature at the quantum critical point (QCP) of the first-order valence
transition. Remarkable enhancement in (T_1T)^{-1} and the spin susceptibility
is induced by valence fluctuations even at the valence-crossover temperature
far away from the QCP. This mechanism well explains peculiar behaviors observed
recently in YbAuCu_4 and also gives a systematic explanation for YbXCu_4 for
X=In, Au, Ag, Tl, and Pd from the viewpoint of the closeness to the QCP. This
also explains anomalously enhanced Wilson ratio observed in the paramagnetic Ce
and Yb based compounds. This offers a new concept that spin fluctuations are
induced via relative charge fluctuations, which can be generally applied to the
systems with valence instabilities.
