Topological Spin Liquid on the Hyperkagome Lattice of Na4Ir3O8

Recent experiments on the “hyperkagome” lattice system Na₄Ir₃O₈ have demonstrated that it is a rare example of a three-dimensional spin-1/2 frustrated antiferromagnet. We investigate the role of quantum fluctuations as the primary mechanism lifting the macroscopic degeneracy inherited by classical spins on this lattice. In the semiclassical limit we predict, based on large-N calculations, that an unusual q→=0 coplanar magnetically ordered ground state is stabilized with no local zero modes that correspond to local deformations of the spin configurations. This phase melts in the quantum limit and a gapped topological Z₂ spin liquid phase emerges. In the vicinity of this quantum phase transition, we study the dynamic spin structure factor and comment on the relevance of our results for future neutron scattering experiments.