Generic model for the hyperkagome iridate Na4Ir3O8 in the local-moment regime

The hyperkagome iridate, Na4Ir3O8, has been regarded as a promising candidate material for a three-dimensional quantum spin liquid. Here the three-dimensional network of corner-sharing triangles forms the hyperkagome lattice of Ir4+ ions. Due to strong spin-orbit coupling, the local moments of Ir4+ ions are described by the pseudospin jeff=1/2 Kramers doublet. The Heisenberg model on this lattice is highly frustrated, and quantum/classical versions have been studied in earlier literature. In this work, we derive a generic local-moment model beyond the Heisenberg limit for the hyperkagome iridate by considering multiorbital interactions for all the t2g orbitals and spin-orbit coupling. The lifting of massive classical degeneracy in the Heisenberg model by various spin-anisotropy terms is investigated at the classical level, and the resulting phase diagram is presented. We find that different anisotropy terms prefer distinct classes of magnetically ordered phases, often with various discrete degeneracy. The implications of our results for recent μSR and NMR experiments on this material and possible quantum spin liquid phases are discussed.