Extraction of the Spin Glass Correlation Length

The peak of the spin glass relaxation rate, $S\left(t\right)=d\left[{-M}_{\mathrm{TRM}}\right({t,t}_w\left)/H\right]/d\ln t$, is directly related to the typical value of the free energy barrier which can be explored over experimental time scales. A change in magnetic field $H$ generates an energy $E_z{=N}_s{\chi }_{\mathrm{fc}}{H}^2$ by which the barrier heights are reduced, where ${\chi }_{\mathrm{fc}}$ is the field cooled susceptibility per spin, and $N_s$ is the number of correlated spins. The shift of the peak of $S\left(t\right)$ gives $E_z$, generating the correlation length, $\xi (t,T)$ for $\mathrm{Cu}:\mathrm{Mn}6\mathrm{at}.\mathrm{}\%$ and ${\mathrm{CdCr}}_{1.7}{\mathrm{In}}_{0.3}{\mathrm{S}}_4$. Fits to power law dynamics, $\xi (t,T)\propto t^{\alpha \left(T\right)}$ and activated dynamics $\xi (t,T)\propto (\ln t{)}^{1/\psi }$ compare well with simulation fits but possess too small a prefactor for activated dynamics.