Investigation of fluctuating intra-unit cell magnetic order in cuprates by $\mu $SR

A mysterious intra-unit cell (IUC) magnetic order has been observed by spin polarized neutron scattering in the pseudogap phase of four different cuprate families. However, the origin of the IUC magnetic order is unclear, in particular because it has not been detected by the local magnetic probe methods nuclear magnetic resonance (NMR) and muon spin relaxation ($\mu $SR). One possible explanation is that the IUC magnetic order fluctuates at a rate slow enough to appear static on the time scale of neutron scattering, but too fast to cause relaxation of the $\mu $SR or NMR signal. I will discuss recent $\mu $SR measurements on Bi$_{\mathrm{2+x}}$Sr$_{\mathrm{2-x}}$CaCu$_{\mathrm{2}}$O$_{\mathrm{8+\delta }}$ and YBa$_{\mathrm{2}}$Cu$_{\mathrm{3}}$O$_{\mathrm{y}}$ that explore this possibility. The new results place narrow limits on the fluctuation rate of the unidentified IUC magnetic order, and raise new questions concerning the magnetism detected by $\mu $SR in high-$T_{\mathrm{c}}$ cuprates.