Abundance of spin liquids in the $S=1$ bilinear-biquadratic model on the pyrochlore lattice, and its application to NaCaNi₂F₇

Long considered the ''poor cousins'' of spin-1/2 systems, magnets built of spin-1 moments have recently come to fore as a rich source of novel phases of matter. Here we explore the phases which arise in a spin-1 magnet on the pyrochlore lattice, once biquadratic interactions are taken into account. Using a combination of variational and Monte Carlo techniques, built around the exact treatment of spin-1 at the level of a single site, we uncover seven distinct spin liquid phases. Dynamical calculations for one of these spin liquids are shown to be in good agreement with inelastic neutron scattering on the spin-1 pyrochlore NaCaNi₂F₇. These results suggest that the range of spin liquid phases found in spin-1 pyrochlores may be even richer than in materials with (pseudo-)spin-1/2 moments.