Aging, rejuvenation, and memory effects in short-range Ising spin glass: Cu $\mathsf{_{0.5}}$ Co $\mathsf{_{0.5}}$ Cl $\mathsf{_{2}}$ -FeCl $\mathsf{_{3}}$ graphite bi-intercalation compound

Abstract

Non-equilibrium aging dynamics in 3D Ising spin glass Cu$_{0.5}$Co$_{0.5}$Cl$_{2}$-FeCl$_{3}$ GBIC has been studied by zero-field cooled (ZFC) magnetization and low frequency AC magnetic susceptibility ($f = 0.05$ Hz), where $T_{g} = 3.92 \pm 0.11$ K. The time dependence of the relaxation rate $S(t) = (1/H)$d$M_{ZFC}/$d$\ln t$ for the ZFC magnetization after the ZFC aging protocol, shows a peak at a characteristic time $t_{cr}$ near a wait time $t_{w}$ (aging behavior), corresponding to a crossover from quasi equilibrium dynamics to non-equilibrium. The time $t_{cr}$ strongly depends on $t_{w}$, temperature ($T$), magnetic field ($H$), and the temperature shift ($\Delta T$). The rejuvenation effect is observed in both $\chi^{\prime}$ and $\chi^{\prime\prime}$ under the $T$-shift and $H$-shift procedures. The memory of the specific spin configurations imprinted during the ZFC aging protocol can be recalled when the system is re-heated at a constant heating rate. The aging, rejuvenation, and memory effects observed in the present system are discussed in terms of the scaling concepts derived from numerical studies on 3D Edwards-Anderson spin glass model.