  It is demonstrated both theoretically and experimentally that the spin
chirality associated with a noncoplanar spin configuration produces a
magneto-optical effect. Numerical study of the two-band Hubbard model on a
triangle cluster shows that the optical Hall conductivity $\sigma_{xy}(\omega)$
is proportional to the spin chirality. The detailed comparative experiments on
pyrochlore-type molybdates $R_2$Mo$_2$O$_7$ with $R=$Nd (Ising-like moments)
and $R=$Gd (Heisenberg-like ones) clearly distinguishes the two mechanisms,
i.e., spin chirality and spin-orbit interactions. It is concluded that for
$R$=Nd, $\sigma_{xy}(\omega)$ is dominated by the spin chirality for the dc
($\omega=0$) and the $d \to d$ incoherent intraband optical transitions between
Mo atoms.
