Spin relaxation close to the glass temperature of $\underline{\mathrm{Cu}}\mathrm{Mn}$ and $\underline{\mathrm{Au}}\mathrm{Fe}$ spin glasses is shown, by neutron spin echo, to follow a generalized exponential function which explicitly introduces hierarchically constrained dynamics and macroscopic interactions. The interaction parameter is directly related to the normalized Tsallis nonextensive entropy parameter $q$ and exhibits universal scaling with reduced temperature. At the glass temperature $q=5/3$ corresponding, within Tsallis’ $q$ statistics, to a mathematically defined critical value for the onset of strong disorder and nonlinear dynamics.

• Received 18 July 2008

DOI:https://doi.org/10.1103/PhysRevLett.102.097202