Quantum spin liquids are elusive states of matter that are characterized by a lack of long-range magnetic order, which renders their excitation spectra the key to identifying them. Studying the magnetic response of a class of spin-liquid states with fermionic spinons and broken time reversal symmetry (TRS) on the three-dimensional hyperkagome lattice of Na${}_4$Ir${}_3$O${}_8$, we demonstrate that the spinon Fermi surface has a topological transition as a function of the flux intensity generated by the spinons moving along loops within the unit cell. The spin dynamical structure factor reveals small pockets of gapped regions in energy and momentum existing below the topological transition and nondispersive high-intensity peaks which broaden when the TRS gets broken. These dynamical fingerprints closely track the nature of the spin-liquid ground state of Na${}_4$Ir${}_3$O${}_8$.

• Received 20 August 2013

DOI:https://doi.org/10.1103/PhysRevB.88.144422