We study the S>1 nearest-neighbor Heisenberg model with a ferromagnetic interaction J and a large non-collinear <111> easy-axis anisotropy D on a pyrochlore lattice. For a finite D>>|J|, the low-energy physics is described by a < 111 > Ising model with second- and third-neighbor exchange interactions. The extensive degeneracy of the ground state manifold in the infinite anisotropic limit is lifted by the transverse quantum fluctuations, and a q=0 ordered state is selected via the quantum order by disorder machanism, through a first-order phase transition at low temperature.
@article{arxiv.1005.4742,
title = {Quantum order by disorder in a semiclassical spin ice},
author = {Yang-Zhi Chou and Ying-Jer Kao},
journal= {arXiv preprint arXiv:1005.4742},
year = {2010}
}