  We study the pyrochlore Heisenberg antiferromagnet with additional positive
biquadratic interaction in the semiclassical limit. The classical ground state
manifold of the model contains an extensively large family of non-coplanar spin
states known as "color ice states". Starting from a color ice state, a subset
of spins may rotate collectively at no energy cost. Such excitation may be
viewed in this three-dimensional system as a "membrane-like" analog of the
well-known weathervane modes in the classical kagome Heisenberg
antiferromagnet. We investigate the weathervane modes in detail and elucidate
their physical properties. Furthermore, we study the order by disorder
phenomenon in this model, focusing on the role of harmonic fluctuations. Our
computationally-limited phase space search suggests that quantum fluctuations
select three different states as the magnitude of the biquadratic interaction
increases relative to the bilinear interaction, implying a sequence of phase
transitions solely driven by fluctuations.
