Absence of magnetic order and unusual spin dynamics in the spin liquid candidate Na$_4$Ir$_3$O$_8$

Na$_4$Ir$_3$O$_8$ has spin-1/2 iridium ions on a hyperkagome lattice of corner sharing triangles and is a candidate three-dimensional spin liquid [1], which has led to active theoretical study [2,3,4]. Previously reported measurements have shown no evidence for magnetic ordering down to temperatures around three orders of magnitude below the Curie-Weiss constant of $\sim 650$K [1]. We have carried out muon-spin relaxation measurements which exclude magnetic ordering above 55mK. The field dependence of the muon spin relaxation rate provides further information on the spin dynamics with a temperature-dependent crossover between power laws at intermediate fields suggesting that more than one energy scale is relevant to the fluctuations in this system. $[1]$ Y.\ Okamoto {\em et al.}, Phys.\ Rev.\ Lett. {\bf 99}, 137207 (2007). $[2]$ M.\ J.\ Lawler {\em et al.}, Phys.\ Rev.\ Lett. {\bf 100}, 227201 (2008). $[3]$ Yi Zhou {\em et al.}, Phys.\ Rev.\ Lett. {\bf 101}, 197201 (2008). $[4]$ E.\ J.\ Bergholtz {\em et al.}, Phys.\ Rev.\ Lett. {\bf 105}, 237202 (2010).