  Wrinkles commonly develop in a thin film deposited on a soft elastomer
substrate when the film is subject to compression. Motivated by recent
experiments [Agrawal et al., Soft Matter 8, 7138 (2012)] that show how wrinkle
morphology can be controlled by using a nematic elastomer substrate, we develop
the theory of small-amplitude wrinkles of an isotropic film atop a nematic
elastomer. The directors of the nematic elastomer are assumed to lie in a plane
parallel to the plane of the undeformed film. For uniaxial compression of the
film along the direction perpendicular to the elastomer directors, the system
behaves as a compressed film on an isotropic substrate. When the uniaxial
compression is along the direction of nematic order, we find that the soft
elasticity characteristic of liquid crystal elastomers leads to a critical
stress for wrinkling which is very small compared to the case of an isotropic
substrate. We also determine the wavelength of the wrinkles at the critical
stress, and show how the critical stress and wavelength depend on substrate
depth and the anisotropy of the polymer chains in the nematic elastomer.
