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 $\tau$ above a spin-freezing temperature $T_g$ (= 3.92 $\pm$ 0.11 K) is well described by critical slowing down. The absorption ${\chi }^{\prime \prime }$ below $T_g$ decreases with increasing angular frequency $\omega$, which is in contrast to the case of 3D Ising spin glass. The dynamic freezing temperature $T_f(H,\omega )$ at which d$M_{FC}(T,H)/$d$H={\chi }^{\prime }(T,H=0,\omega )$, is determined as a function of frequency (0.01 Hz $\le \omega /2\pi \le$ 1 kHz) and magnetic field (0 $\le H\le$ 5 kOe). The dynamic scaling analysis of the relaxation time $\tau (T,H)$ defined as $\tau =1/\omega$ at $T=T_f(H,\omega )$ suggests the absence of SG phase in the presence of $H$ (at least above 100 Oe). Dynamic scaling analysis of ${\chi }^{\prime \prime }(T,\omega )$ and $\tau (T,H)$ near $T_g$ leads to the critical exponents ($\beta$ = 0.36 $\pm$ 0.03, $\gamma$ = 3.5 $\pm$ 0.4, $\nu$ = 1.4 $\pm$ 0.2, $z$ = 6.6 $\pm$ 1.2, $\psi$ = 0.24 $\pm$ 0.02, and $\theta$ = 0.13 $\pm$ 0.02). The aging phenomenon is studied through the absorption ${\chi }^{\prime \prime }(\omega ,t)$ below $T_g$. It obeys a $(\omega t{)}^{-b^{\prime \prime }}$ 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.

14 pages, 19 figures; to be published in Phys. Rev. B (September 1, 2003)

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• Domain growth by isothermal aging in 3d Ising and Heisenberg spin glasses
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• Aging, rejuvenation, and memory effects in short-range Ising spin glass: Cu${}_{0.5}$Co${}_{0.5}$Cl${}_2$-FeCl${}_3$ graphite bi-intercalation compound
• Nonlinear magnetic susceptibility and aging phenomena in reentrant ferromagnet: Cu${}_{0.2}$Co${}_{0.8}$Cl${}_2$-FeCl${}_3$ graphite bi-intercalation compound
• Aging dynamics across a dynamic Almeida-Thouless line in three dimensional short-range Issuing spin glass Cu${}_{0.5}$Co${}_{0.5}$Cl${}_2$-FeCl${}_3$ graphite bi-intercalation compound