Extraction of the Spin Glass Correlation Length

Abstract

The peak of the spin glass relaxation rate, $S(t)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}d[{\ensuremath{-}M}_{\mathrm{TRM}}({t,t}_{w})/H]/d\mathrm{ln}t$, 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 ${E}_{z}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}N}_{s}{\ensuremath{\chi}}_{\mathrm{fc}}{H}^{2}$ by which the barrier heights are reduced, where ${\ensuremath{\chi}}_{\mathrm{fc}}$ is the field cooled susceptibility per spin, and ${N}_{s}$ is the number of correlated spins. The shift of the peak of $S(t)$ gives ${E}_{z}$, generating the correlation length, $\ensuremath{\xi}(t,T)$ for $\mathrm{Cu}:\mathrm{Mn}6\mathrm{at}.%$ and ${\mathrm{CdCr}}_{1.7}{\mathrm{In}}_{0.3}{\mathrm{S}}_{4}$. Fits to power law dynamics, $\ensuremath{\xi}(t,T)\ensuremath{\propto}{t}^{\ensuremath{\alpha}(T)}$ and activated dynamics $\ensuremath{\xi}(t,T)\ensuremath{\propto}(\mathrm{ln}t{)}^{1/\ensuremath{\psi}}$ compare well with simulation fits but possess too small a prefactor for activated dynamics.