Competing phases and topological excitations of spin-1 pyrochlore antiferromagnets

Abstract

Most works on pyrochlore magnets deal with the interacting spin-1/2 local moments. We here study the spin-one local moments on the pyrochlore lattice, and propose a generic interacting spin model on a pyrochlore lattice. Our spin model includes the antiferromagnetic Heisenberg interaction, the Dzyaloshinskii-Moriya interaction and the single-ion spin anisotropy. 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 parts of the ordered phases is then suggested. We point out the existence of degenerate and topological excitations in various phases. We discuss the relevance with fluoride pyrochlore material NaCaNi$_2$F$_7$ and explain the role of the spin-orbit coupling and the magnetic structures of the Ru-based pyrochlore A$_2$Ru$_2$O$_7$ and the Mo-based pyrochlore A$_2$Mo$_2$O$_7$.