Dynamic scaling and aging phenomena in short-range Ising spin glass: Cu$_{0.5}$Co$_{0.5}$Cl$_{2}$-FeCl$_{3}$ graphite bi-intercalation compound

Abstract

Static and dynamic behavior of short-range Ising-spin glass Cu$_{0.5}$Co$_{0.5}$Cl$_{2}$-FeCl$_{3}$ graphite bi-intercalation compounds (GBIC) has been studied with SQUID DC and AC magnetic susceptibility. The $T$ dependence of the zero-field relaxation time $τ$ above a spin-freezing temperature $T_{g}$ (= 3.92 $\pm$ 0.11 K) is well described by critical slowing down. The absorption $χ^{\prime\prime}$ below $T_{g}$ decreases with increasing angular frequency $ω$, which is in contrast to the case of 3D Ising spin glass. The dynamic freezing temperature $T_{f}(H,ω)$ at which d$M_{FC}(T,H)/$d$H=χ^{\prime}(T,H=0,ω)$, is determined as a function of frequency (0.01 Hz $\leq ω/2π\leq$ 1 kHz) and magnetic field (0 $\leq H \leq$ 5 kOe). The dynamic scaling analysis of the relaxation time $τ(T,H)$ defined as $τ= 1/ω$ at $T = T_{f}(H,ω)$ suggests the absence of SG phase in the presence of $H$ (at least above 100 Oe). Dynamic scaling analysis of $χ^{\prime \prime}(T, ω)$ and $τ(T,H)$ near $T_{g}$ leads to the critical exponents ($β$ = 0.36 $\pm$ 0.03, $γ$ = 3.5 $\pm$ 0.4, $ν$ = 1.4 $\pm$ 0.2, $z$ = 6.6 $\pm$ 1.2, $ψ$ = 0.24 $\pm$ 0.02, and $θ$ = 0.13 $\pm$ 0.02). The aging phenomenon is studied through the absorption $χ^{\prime \prime}(ω, t)$ below $T_{g}$. It obeys a $(ωt)^{-b^{\prime \prime}}$ power-law decay with an exponent $b^{\prime \prime}\approx 0.15 - 0.2$. The rejuvenation effect is also observed under sufficiently large (temperature and magnetic-field) perturbations.