Competing orders in the spin-one pyrochlore lattice antiferromagnet

We study the physics of the spin-one local moments with a generic interacting spin model on a pyrochlore lattice. We develop a flavor wave theory and combine with a mean-field approach to study the global phase diagram of this model and establish the relation between different phases in the phase diagram. We find the regime of the quantum paramagnetic phase where a degenerate line of the magnetic excitations emerges in the momentum space. We further predict the critical properties of the transition out of the quantum paramagnet to the proximate orders. The presence of quantum order by disorder in the part of the ordered phases is then suggested. We discuss the potential relevance to the fluoride pyrochlore NaCaNi₂F₇ and comment on the role of the spin-orbit coupling in the Ru-based pyrochlore A₂Ru₂O₇, and the Mo-based pyrochlore A₂Mo₂O₇.