Quantum order by disorder in a semiclassical spin ice

We study the effects of quantum fluctuations in spin ice by considering an S>1 quantum Heisenberg model with a nearest-neighbor ferromagnetic interaction J and a large noncollinear < 111 > easy-axis anisotropy D on a pyrochlore lattice. For a finite D >> vertical bar J vertical bar, the low-energy physics is described by a < 111 > Ising model with additional second-and third-neighbor exchange couplings of order O (J(2)/D), generated by the quantum fluctuations arising from the transverse components of the exchange coupling. The extensive degeneracy of ground states in the D -> infinity limit is lifted, and a q=0 ordered state is selected via the quantum order by disorder mechanism, through a first-order phase transition at low temperatures.