Time-dependent correlations of the Edwards-Anderson order parameter above the spin-glass transition

In 1975 Edwards and Anderson introduced a new paradigm that interacting quenched systems, such as a spin-glass, have a phase transition in which long time memory of spatial patterns is realized without spatial correlations. We show here that the information about the time-dependent correlations above the spin-glass transition are embedded in the four spin correlations of the intensity of speckle pattern. This encodes the spin-orientation memory and can be measured by the technique of resonant magnetic x-ray photon correlation spectroscopy (RM- XPCS). We have implemented this method to observe and accurately characterize the critical slowing down of the spin orientation fluctuations in the classic metallic spin glass alloy $Cu_{1-x}{Mn}_x$ over time scales of ${2}$ sec. to $2 \times 10^{\mathbf{4}}$ secs. Remarkably the divergence of the correlation time as a function of temperature is consistent with the Vogel-Vulcher law, universally used to characterize the viscous relaxation time in structural glasses. Our method also opens the way for studying phase transitions in systems such as spin ices, quantum spin liquids, the structural glass transition, as well as possibly provide new perspectives on the multifarious problems in which spin-glass concepts have found applications.