Dynamic scaling and aging phenomena in short-range Ising spin glass: Cu${}_{0.5}$Co${}_{0.5}$Cl${}_2$-FeCl${}_3$ graphite bi-intercalation compound

Static and dynamic behavior of short-range Ising-spin glass Cu${}_{0.5}$Co${}_{0.5}$Cl${}_2$-FeCl${}_3$ graphite bi-intercalation compounds (GBIC) has been studied with SQUID DC and AC magnetic susceptibility. The $T$ dependence of the zero-field relaxation time $\tau$ above a spin-freezing temperature $T_g$ (= 3.92 $\pm$ 0.11 K) is well described by critical slowing down. The absorption ${\chi }^{\mathrm{\prime }\mathrm{\prime }}$ below $T_g$ decreases with increasing angular frequency $\omega$, which is in contrast to the case of 3D Ising spin glass. The dynamic freezing temperature $T_f(H,\omega )$ at which d$M_{FC}(T,H)\mathrm{/}$d$H={\chi }^{\mathrm{\prime }}(T,H=0,\omega )$, is determined as a function of frequency (0.01 Hz $\le \omega \mathrm{/}2\pi \le$ 1 kHz) and magnetic field (0 $\leq H \leq$5kOe)\mathrm{.}Thedynamicscalinganalysisoftherelaxationtime$\tau(T,H)$definedas$\tau = 1/\omega$at$T = T_{f}(H,\omega)$ suggests the absence of SG phase in the presence of $H$ (at least above 100 Oe). Dynamic scaling analysis of ${\chi }^{\mathrm{\prime }\mathrm{\prime }}(T,\omega )$ and $\tau (T,H)$ near $T_g$ leads to the critical exponents ($\beta$ = 0.36 $\pm$ 0.03, $\gamma$ = 3.5 $\pm$ 0.4, $\nu$ = 1.4 $\pm$ 0.2, $z$ = 6.6 $\pm$ 1.2, $\psi$ = 0.24 $\pm$ 0.02, and $\theta$ = 0.13 $\pm$ 0.02). The aging phenomenon is studied through the absorption ${\chi }^{\mathrm{\prime }\mathrm{\prime }}(\omega ,t)$ below $T_g$. It obeys a $(\omega t{)}^{-b^{\mathrm{\prime }\mathrm{\prime }}}$ power-law decay with an exponent $b^{\prime \prime}\approx 0.15 - 0.2$. The rejuvenation effect is also observed under sufficiently large (temperature and magnetic-field) perturbations.