  Spin scalar chiral ordering gives rise to nontrivial topological characters
and peculiar transport properties. We here examine how quantum spin
fluctuations affect the spin scalar chiral ordering in itinerant electron
systems. We take the Kondo lattice model on a triangular lattice, and perform
the linear spin wave analysis in the Chern insulator phases with spin scalar
chiral ordering obtained in the case that the localized spins are classical. We
find that, although the quantum fluctuation destabilizes the spin scalar chiral
phase at 3/4 filling that originates from the perfect nesting of Fermi surface,
it retains the phase at 1/4 filling that is induced by an effective positive
biquadratic interaction. The reduction of the ordered magnetic moment by the
zero-point quantum fluctuation is considerably small, compared with those in
spin-only systems. The results suggest that the Chern insulator at 1/4 filling
remains robust under quantum fluctuations.
