Aging dynamics in a reentrant ferromagnet: ${\mathrm{Cu}}_{0.2}{\mathrm{Co}}_{0.8}{\mathrm{Cl}}_2-\mathrm{Fe}{\mathrm{Cl}}_3$ graphite bi-intercalation compound

The aging dynamics of a reentrant ferromagnet ${\mathrm{Cu}}_{0.2}{\mathrm{Co}}_{0.8}{\mathrm{Cl}}_2-\mathrm{Fe}{\mathrm{Cl}}_3$ graphite bi-intercalation compound has been studied using ac and dc magnetic susceptibility. This compound undergoes successive transitions at the transition temperatures $T_c$ $(=9.7\mathrm{K})$ and $T_{\mathit{RSG}}$ $(=3.5\mathrm{K})$. The relaxation rate $S\left(t\right)$ $[=\mathrm{d}{\chi }_{\mathit{ZFC}}\left(t\right)∕\mathrm{d}\ln t]$ exhibits a characteristic peak at $t_{\mathit{cr}}$ close to a wait time $t_W$ below $T_c$, indicating that the aging phenomena occur in both the reentrant spin glass phase below $T_{\mathit{RSG}}$ and the ferromagnetic (FM) phase between $T_{\mathit{RSG}}$ and $T_c$. The aging state in the FM phase is fragile against a weak magnetic-field perturbation. The time $\left(t\right)$ dependence of ${\chi }_{\mathit{ZFC}}\left(t\right)$ around $t\approx t_{\mathit{cr}}$ is well approximated by a stretched exponential relaxation, ${\chi }_{\mathit{ZFC}}\left(t\right)\approx \exp [-{(t∕\tau )}^{1-n}]$, around $t=t_W$. The exponent $n$ depends on $t_W$, $T$, and $H$. The relaxation time $\tau$ $(\approx t_{\mathit{cr}})$ exhibits a local maximum around $5\mathrm{K}$, reflecting a frustrated nature of the FM phase. It drastically increases with decreasing temperature below $T_{\mathit{RSG}}$.

Figure 1

(Color online) (a) ${\chi }^{″}(\omega ,T)$ vs $T$ at various $f$ $(0.01⩽f⩽1000\mathrm{Hz})$. $h=50\mathrm{mOe}$. (b) $T$ dependence of ${\chi }_{\mathit{ZFC}}$ (●) and ${\chi }_{\mathit{FC}}$ (엯) at $H=1\mathrm{Oe}$ for ${\mathrm{Cu}}_{0.2}{\mathrm{Co}}_{0.8}{\mathrm{Cl}}_2-\mathrm{Fe}{\mathrm{Cl}}_3$ GBIC. The measurement was carried out after the ZFC aging protocol: annealing of the system at $50\mathrm{K}$ for $1.2\times {10}^3\sec$ at $H=0$ and quenching from $50\text{to}1.9\mathrm{K}$. During the ZFC measurement with increasing $T$ from $1.9\text{to}20\mathrm{K}$, the system was aging at $T_1=7.0\mathrm{K}$ (ZFC-1 measurement) and $T_2=3.5\mathrm{K}$ (ZFC-2 measurement) for wait time $t_{W1}=t_{W2}=1.5\times {10}^4\sec$ in the presence of $H=1\mathrm{Oe}$. After the ZFC measurement, the system was annealed at $T=50\mathrm{K}$ for $1.2\times {10}^3\sec$ in the presence of $H$ $(=1\mathrm{Oe})$. The FC measurement (denoted as FC-1 and FC-2 ) was carried out with decreasing $T$ from $20\text{to}1.9\mathrm{K}$. The $T$ dependence of FC-1 susceptibility is the same as that of FC-2 susceptibility.

Figure 2

(Color online) (a)–(c) Relaxation rate $S$ $[=\mathrm{d}{\chi }_{\mathit{ZFC}}∕\mathrm{d}\ln t]$ vs $t$ at various $T$. $H=1\mathrm{Oe}$. $t_W=1.5\times {10}^4\sec$. $H$ is applied along a direction perpendicular to the $c$ axis. The ZFC aging protocol: annealing of the system at $50\mathrm{K}$ for $1.2\times {10}^3\sec$ at $H=0$, quenching from $50\mathrm{K}$ to $T$, and then isothermal aging at $T$ and $H=0$ for a wait time $t_W$. The measurement was started at $t=0$ when the field $H$ was turned on.

Figure 3

(Color online) (a) and (b) $S$ vs $t$ at various $T$. $H=1\mathrm{Oe}$. $t_W=3.0\times {10}^4\sec$.

Figure 4

(Color online) $t_{\mathit{cr}}$ vs $T$ and $\tau$ vs $T$. $t_{\mathit{cr}}$ is a characteristic time at which $S\left(t\right)$ has a maximum $S_{\mathit{max}}$. $\tau$ is the relaxation time for the stretched exponential relaxation. $H=1\mathrm{Oe}$. (a) $t_W=1.5\times {10}^4\sec$. (b) $t_W=3.0\times {10}^4\sec$. The solid lines are a guide to the eye. The inset of (a) shows the plot of $1∕\tau$ vs $1∕T$ $(T<T_{\mathit{RSG}})$, where the solid line is a least-squares fit to Eq. (5). The fitting parameters are given in the text.

Figure 5

(Color online) $S_{\mathit{max}}$ vs $T$ for the three cases: (i) $H=1\mathrm{Oe}$ and $t_W=3.0\times {10}^4\sec$ (●), (ii) $H=1\mathrm{Oe}$ and $t_W=1.5\times {10}^4\sec$ (엯), and (iii) $H=10\mathrm{Oe}$ and $t_W=2.0\times {10}^3\sec$ (▴). The solid lines are a guide to the eye.

Figure 6

(Color online) (a) $n$ vs $T$ and (b) $A$ vs $T$, where $t_W=3.0\times {10}^4\sec$ (●) and $1.5\times {10}^4\sec$ (엯). $H=1\mathrm{Oe}$. The solid lines are a guide to the eye.

Figure 7

(Color online) $S$ vs $t$ at various $H$. (a) $T=3.3\mathrm{K}$ and $t_W=1.5\times {10}^4\sec$. (b) $T=7.0\mathrm{K}$ and $t_W=1.5\times {10}^4\sec$.

Figure 8

(Color online) (a) $t_{\mathit{cr}}$ vs $H$ and $\tau$ vs $H$ at $T=3.3$ and $7.0\mathrm{K}$. (b) $t_{\mathit{cr}}$ vs $H$ at $T=3.3$ and $7.0\mathrm{K}$. The solid lines are least-squares fits to Eq. (7) for data at low $H$. The fitting parameters are given in the text.

Figure 9

(Color online) (a) $S_{\mathit{max}}$ vs $H$ and (b) $n$ vs $H$ at $T=3.3$ and $7.0\mathrm{K}$. $t_W=1.5\times {10}^4\sec$. The solid lines are a guide to the eye.

Figure 10

(Color online) $S$ vs $t$ at various $t_W$ $(2\times {10}^3⩽t_W⩽2.0\times {10}^4\sec )$. $H=1\mathrm{Oe}$. (a) $T=3.5\mathrm{K}$. (b) $T=7.0\mathrm{K}$.

Figure 11

(Color online) (a) $t_{\mathit{cr}}$ vs $t_W$ and $\tau$ vs $t_W$. The solid line is a least-squares fit to $\tau ={\tau }_0\exp (t_W∕t_0)$ for $\tau$ at $3.5\mathrm{K}$ $(t_W⩾1.0\times {10}^4\sec )$. The fitting parameters are given in the text. (b) $n$ vs $t_W$ at $T=3.5$ and $7.0\mathrm{K}$. $H=1\mathrm{Oe}$. The solid lines are a guide to the eye.

Figure 12

(Color online) (a) $t$ dependence of $S$ at $T=T_f=7.0\mathrm{K}$ under the $T$ shift from $T_i$ to $T_f$, where $T_i=4.9$, 5.6, and $6.3\mathrm{K}$. $H=1\mathrm{Oe}$. The ZFC aging protocol is as follows: quenching of the system from $50\mathrm{K}$ to $T_i$ and isothermal aging at $T=T_i$ and $H=0$ for $t_W=3.0\times {10}^4\sec$. The measurement was started at $t=0$, just after $T$ was shifted from $T_i$ to $T_f$ and subsequently $H$ $(=1\mathrm{Oe})$ was turned on. (b) $t_{\mathit{cr}}$ vs $\Delta T$. The solid line is a fitting curve to Eq. (9). The fitting parameters are given in the text.

Figure 13

(Color online) $t$ dependence of ${\chi }^{″}(\omega ,t)$ at (a) $T=3.75\mathrm{K}$, (b) $T=7.0\mathrm{K}$, and (c) $T=8.5\mathrm{K}$. $f=0.05$, 0.1, 0.5, and $1\mathrm{Hz}$. The time $t$ is the time taken after the sample is quenched from $50\mathrm{K}$ to $T$. $H=0$. The solid lines are the least-squares fits to Eq. (10). The fitting parameters are listed in Table .