Discovery of slow magnetic fluctuations and critical slowing down in the pseudogap phase of YBa$_2$Cu$_3$O$_y$

Evidence for intra-unit-cell (IUC) magnetic order in the pseudogap region of high-$T_c$ cuprates below a temperature $T^ast$ is found in several studies, but NMR and $mu$SR experiments do not observe the expected static local magnetic fields. It has been noted, however, that such fields could be averaged by fluctuations. Our measurements of muon spin relaxation rates in single crystals of YBa$_2$Cu$_3$O$_y$ reveal magnetic fluctuations of the expected order of magnitude that exhibit critical slowing down at $T^ast$. These results are strong evidence for fluctuating IUC magnetic order in the pseudogap phase.