Topological spin liquid on the hyper-kagome lattice of Na_4Ir_3O_8

TL;DR

This paper explores the quantum effects in the hyper-kagome lattice of Na$_4$Ir$_3$O$_8$, predicting a transition from magnetic order to a gapped topological spin liquid phase, with implications for neutron scattering experiments.

Contribution

It introduces a theoretical model showing how quantum fluctuations induce a topological spin liquid in Na$_4$Ir$_3$O$_8$, advancing understanding of quantum spin liquids in three dimensions.

Findings

Prediction of a $f q=0$ coplanar magnetic order in the semi-classical limit.

Identification of a quantum phase transition to a gapped Z$_2$ spin liquid.

Analysis of dynamic spin structure factor relevant for neutron scattering.

Abstract

Recent experiments on the "hyper-kagome" lattice system Na$_4$Ir$_3$O$_8$ 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 semi-classical limit we predict, based on large-N calculations, that an unusual $\vec q=0$ coplaner magnetically ordered ground state is stabilized with no local "weather vane" modes. This phase melts in the quantum limit and a gapped topological Z$_2$ 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.