Dynamic scaling and aging phenomena in a short-range Ising spin glass: ${\mathrm{Cu}}_{0.5}{\mathrm{Co}}_{0.5}{\mathrm{Cl}}_2{-\mathrm{F}\mathrm{e}\mathrm{C}\mathrm{l}}_3$ graphite bi-intercalation compound

Static and dynamic behavior of short-range Ising spin glass (SG) ${\mathrm{Cu}}_{0.5}{\mathrm{Co}}_{0.5}{\mathrm{Cl}}_2-{\mathrm{FeCl}}_3$ graphite bi-intercalation compounds has been studied with superconducting quantum interference device dc and ac magnetic susceptibility. The T dependence of the zero-field relaxation time $\tau$ above a spin-freezing temperature $T_g(=3.92\mathrm{}\pm 0.11\mathrm{K})$ is well described by critical slowing down. The absorption ${\chi }^{″}$ 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 ${\mathrm{dM}}_{\mathrm{FC}}\mathrm{}(T,H)/dH={\chi }^{\prime }(T,H=0,\omega )$ is determined as a function of frequency (0.01 Hz $<~\omega /2\mathrm{}\pi <~1\mathrm{kHz})$ and magnetic field $(0\mathrm{}<~H<~5\mathrm{kOe}).\mathrm{}$ The dynamic scaling analysis of the relaxation time $\tau \mathrm{}(T,H)\mathrm{}$ defined as $\tau =1/\omega$ 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 ${\chi }^{″}(T,\omega )$ and $\tau \mathrm{}(T,H)\mathrm{}$ near $T_g$ leads to the critical exponents $(\beta =0.36\mathrm{}\pm 0.03,$ $\gamma =3.5\mathrm{}\pm 0.4,$ $\nu =1.4\mathrm{}\pm 0.2,$ $z=6.6\mathrm{}\pm 1.2,$ $\psi =0.24\mathrm{}\pm 0.02,$ and $\theta =0.13\mathrm{}\pm 0.02).$ The aging phenomenon is studied through the absorption ${\chi }^{″}(\omega ,t)$ below $T_g.$ It obeys a $(\omega {t)}^{-b^{″}}$ power-law decay with an exponent $b^{″}\approx 0.15–\mathrm{0.2.}$ The rejuvenation effect is also observed under sufficiently large (temperature and magnetic-field) perturbations.