Generic model for hyperkagome iridate in the local moment regime

TL;DR

This paper develops a comprehensive local-moment model for hyperkagome iridate, incorporating multi-orbital interactions and spin-orbit coupling, to better understand its magnetic phases and relevance to quantum spin liquids.

Contribution

It introduces a generic model beyond the Heisenberg limit for hyperkagome iridate, considering multi-orbital effects and spin anisotropy, advancing understanding of its magnetic behavior.

Findings

Different anisotropy terms favor distinct magnetic phases.

Classical degeneracy is lifted by spin-anisotropy terms.

Implications for experiments and quantum spin liquid phases are discussed.

Abstract

Hyperkagome iridate, Na$_4$Ir$_3$O$_8$, 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 Ir$^{4+}$ ions. Due to strong spin-orbit coupling, the local moments of Ir$^{4+}$ ions are described by the pseudospin $j_{\rm eff} = 1/2$ 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 multi-orbital interactions for all the $t_{2g}$ 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 $\mu$SR and NMR experiments on this material and possible quantum spin liquid phases are discussed.