  The ordering property of the classical pyrochlore Heisenberg antiferromagnet
with the ferromagnetic next-nearest-neighbor interaction is investigated by
means of a Monte Carlo simulation. The model is found to exhibit a first-order
transition at a finite temperature into a peculiar ordered state. While the
spin structure factor, i.e., the thermal average of the squared Fourier
amplitude of the spin, exhibits a finite long-range order characterized by the
commensurate spin order of the period four, the thermal average of the spin
itself almost vanishes. It means that, although the amplitude of the spin
Fourier component is long-range ordered, the associated phase degree of freedom
remains to be fluctuating.
