Memory and aging effect in hierarchical spin orderings of stage-2 CoCl$_{2}$ graphite intercalation compound

Stage-2 CoCl$_{2}$ graphite intercalation compound undergoes two magnetic phase transitions at $T_{cl}$ (= 7.0 K) and $T_{cu} $ (= 8.9 K). The aging dynamics of this compound is studied near $T_{cl}$ and $T_{cu}$. The intermediate state between $T_ {cl}$ and $T_{cu}$ is characterized by a spin glass phase extending over ferromagnetic islands. A genuine thermoremnant magnetization (TRM) measurement indicates that the memory of the specific spin configurations imprinted at temperatures between $T_{cl}$ and $T_{cu}$ during the field-cooled (FC) aging protocol can be recalled when the system is re-heated at a constant heating rate. The zero-field cooled (ZFC) and TRM magnetization is examined in a series of heating and reheating process. The magnetization shows both characteristic memory and rejuvenation effects. The time $(t)$ dependence of the relaxation rate $S_{ZFC}(t)=(1/H)$d$M_{ZFC}(t)$/d$\ln t$ after the ZFC aging protocol with a wait time $t_{w}$, exhibits two peaks at characteristic times $t_{cr1}$ and $t_{cr2}$ between $T_{cl}$ and $T_{cu}$. An aging process is revealed as the strong $t_{w}$ dependence of $t_{cr2}$. The observed aging and memory effect is discussed in terms of the droplet model.