Aging dynamics across a dynamic Almeida-Thouless line in three dimensional Ising spin glass Cu$_{0.5}$Co$_{0.5}$Cl$_{2}$-FeCl$_{3}$ graphite bi-intercalation compound

Cu$_{0.5}$Co$_{0.5}$Cl$_{2}$-FeCl$_{3}$ graphite intercalation compound is a three-dimensional short-range Ising spin glass with a spin freezing temparature $T_{g}$ ($= 3.92 \pm 0.11$ K). The stability of the spin glass phase in the presence of a magnetic field $H$ has been studied from the time dependence of zero-field cooled (ZFC) susceptibility $\chi_{ZFC}$ after a ZFC aging protocol with a waittime $t_{w}$ ($= 1.0 \times 10^{4}$ and $3.0 \times 10^{4}$ sec). The relaxation rate $S(t)$ (= d$\chi_{ZFC}$/d$\ln t$) exhibits a local maximum at a characteristic time $t_{cr}$, The $t$ dependence of $\chi_{ZFC}$ is well described by a stretched exponential relaxation ($\approx \exp [-(t/\tau)^{1-n}$]) in the vicinity of $\tau \approx t_{w}$, where $t \approx t_{cr}$. The $H$ dependence of $t_{cr}$ and $\tau$ is measured at the fixed temperature $T$ (2.9 K $\leq T < T_{g}$): $\tau$ ($t_{cr}$) decreases with increasing $H$. Contour plots of $H$ and $T$ with constant $\tau$ form lines in the $H$-$T$ plane, depending on the value of $\tau$ chosen. We find that the line with $\tau \approx 2.0 \times 10^{3}$ sec coincides with an Almeida-Thouless (AT) line where the irreversible effect of succeptibility appears. This result indicates that the spin glass phase is unstable in the presence of $H$. There is no AT line for short-range Ising spin glass.