Aging dynamics of ferromagnetic and reentrant spin glass phases in stage-2 Cu0.80_{0.80}C0.20_{0.20}Cl2_{2} graphite intercalation compound

Aging dynamics of a reentrant ferromagnet stage-2 Cu$_{0.8}$Co$_{0.2}$Cl$_{2}$ graphite intercalation compound has been studied using DC magnetic susceptibility. This compound undergoes successive transitions at the transition temperatures $T_{c}$ ($\approx 8.7$ K) and $T_{RSG}$ ($\approx 3.3$ K). The relaxation rate $S_{ZFC}(t)$ exhibits a characteristic peak at $t_{cr}$ below $T_{c}$. The peak time $t_{cr}$ as a function of temperature $T$ shows a local maximum around 5.5 K, reflecting a frustrated nature of the ferromagnetic phase. It drastically increases with decreasing temperature below $T_{RSG}$. The spin configuration imprinted at the stop and wait process at a stop temperature $T_{s}$ ($<T_{c}$) during the field-cooled aging protocol, becomes frozen on further cooling. On reheating, the memory of the aging at $T_{s}$ is retrieved as an anomaly of the thermoremnant magnetization at $T_{s}$. These results indicate the occurrence of the aging phenomena in the ferromagnetic phase ($T_{RSG}<T<T_{c}$) as well as in the reentrant spin glass phase ($T<T_{RSG}$).Comment: 9 pages, 9 figures; submitted to Physical Review

Nonequilibrium Dynamics and Aging in the Three--Dimensional Ising Spin Glass Model

The low temperature dynamics of the three dimensional Ising spin glass in zero field with a discrete bond distribution is investigated via MC simulations. The thermoremanent magnetization is found to decay algebraically and the temperature dependent exponents agree very well with the experimentally determined values. The nonequilibrium autocorrelation function $C(t,t_w)$ shows a crossover at the waiting (or {\em aging}) time $t_w$ from algebraic {\em quasi-equilibrium} decay for times $t$$\ll$$t_w$ to another, faster algebraic decay for $t$$\gg$$t_w$ with an exponent similar to one for the remanent magnetization.Comment: Revtex, 11 pages + 4 figures (included as Latex-files

Orchestrating learning activities using the CADMOS learning design tool

This paper gives an overview of CADMOS (CoursewAre Development Methodology for Open instructional Systems), a graphical IMS-LD Level A & B compliant learning design (LD) tool, which promotes the concept of &#x201C;separation of concerns&#x201D; during the design process, via the creation of two models: the conceptual model, which describes the learning activities and the corresponding learning resources, and the flow model, which describes the orchestration of these activities. According to the feedback from an evaluation case study with 36 participants, reported in this paper, CADMOS is a user-friendly tool that allows educational practitioners to design flows of learning activities using a layered approach

Aging dynamics in reentrant ferromagnet: Cu0.2_{0.2}Co0.8_{0.8}Cl2_{2}-FeCl3_{3} graphite bi-intercalation compound

Aging dynamics of a reentrant ferromagnet Cu$_{0.2}$Co$_{0.8}$Cl$_{2}$-FeCl$_{3}$ graphite bi-intercalation compound has been studied using AC and DC magnetic susceptibility. This compound undergoes successive transitions at the transition temperatures $T_{c}$ ($= 9.7$ K) and $T_{RSG}$ ($= 3.5$ K). The relaxation rate $S(t)$ exhibits a characteristic peak at $t_{cr}$ close to a wait time $t_{w}$ below $T_{c}$, indicating that the aging phenomena occur in both the reentrant spin glass (RSG) phase below $T_{RSG}$ and the ferromagnetic (FM) phase between $T_{RSG}$ and $T_{c}$. The relaxation rate $S(t)$ ($=\text{d}\chi_{ZFC}(t)/\text{d}\ln t$) in the FM phase exhibits two peaks around $t_{w}$ and a time much shorter than $t_{w}$ under the positive $T$-shift aging, indicating a partial rejuvenation of domains. The aging state in the FM phase is fragile against a weak magnetic-field perturbation. The time ($t$) dependence of $\chi_{ZFC}(t)$ around $t \approx t_{cr}$ is well approximated by a stretched exponential relaxation: $\chi_{ZFC}(t) \approx \exp[-(t/\tau)^{1-n}]$. The exponent $n$ depends on $t_{w}$, $T$, and $H$. The relaxation time $\tau$ ($\approx t_{cr}$) exhibits a local maximum around 5 K, reflecting a chaotic nature of the FM phase. It drastically increases with decreasing temperature below $T_{RSG}$.Comment: 16 pages,16 figures, submitted to Physical Review

Rejuvenation in the Random Energy Model

We show that the Random Energy Model has interesting rejuvenation properties in its frozen phase. Different `susceptibilities' to temperature changes, for the free-energy and for other (`magnetic') observables, can be computed exactly. These susceptibilities diverge at the transition temperature, as (1-T/T_c)^-3 for the free-energy.Comment: 9 pages, 1 eps figur

Extraction of the Spin Glass Correlation Length

The peak of the spin glass relaxation rate, S(t)=d{-M_{TRM}(t,t_w)}/H/{d ln t}, is directly related to the typical value of the free energy barrier which can be explored over experimental time scales. A change in magnetic field H generates an energy E_z={N_s}{X_fc}{H^2} by which the barrier heights are reduced, where X_{fc} is the field cooled susceptibility per spin, and N_s is the number of correlated spins. The shift of the peak of S(t) gives E_z, generating the correlation length, Ksi(t,T), for Cu:Mn 6at.% and CdCr_{1.7}In_{0.3}S_4. Fits to power law dynamics, Ksi(t,T)\propto {t}^{\alpha(T)} and activated dynamics Ksi(t,T) \propto {ln t}^{1/psi} compare well with simulation fits, but possess too small a prefactor for activated dynamics.Comment: 4 pages, 4 figures. Department of Physics, University of California, Riverside, California, and Service de Physique de l'Etat Condense, CEA Saclay, Gif sur Yvette, France. To appear in Phys. Rev. Lett. January 4, 199

Scaling Law and Aging Phenomena in the Random Energy Model

We study the effect of temperature shift on aging phenomena in the Random Energy Model (REM). From calculation on the correlation function and simulation on the Zero-Field-Cooled magnetization, we find that the REM satisfies a scaling relation even if temperature is shifted. Furthermore, this scaling property naturally leads to results obtained in experiment and the droplet theory.Comment: 8 pages, 7 figures, to be submitted to J. Phys. Soc. Jp

Non-linear susceptibility in glassy systems: a probe for cooperative dynamical length scales

We argue that for generic systems close to a critical point, an extended Fluctuation-Dissipation relation connects the low frequency non-linear (cubic) susceptibility to the four-point correlation function. In glassy systems, the latter contains interesting information on the heterogeneity and cooperativity of the dynamics. Our result suggests that if the abrupt slowing down of glassy materials is indeed accompanied by the growth of a cooperative length ell, then the non-linear, 3 omega response to an oscillating field should substantially increase and give direct information on the temperature (or density) dependence of ell. The analysis of the non-linear compressibility or the dielectric susceptibility in supercooled liquids, or the non-linear magnetic susceptibility in spin-glasses, should give access to a cooperative length scale, that grows as the temperature is decreased or as the age of the system increases. Our theoretical analysis holds exactly within the Mode-Coupling Theory of glasses.Comment: 12 pages, 3 figures; a careful discussion of the spin-glass case in a field adde

On the Out of Equilibrium Relaxation of the Sherrington - Kirkpatrick model

We derive analytical results for the large-time relaxation of the Sherrington - Kirkpatrick model in the thermodynamic limit, starting from a random configuration. The system never achieves local equilibrium in any fixed sector of phase-space, but remains in an asymptotic out of equilibrium regime. We propose as a tool, both numerical and analytical, for the study of the out of equilibrium dynamics of spin-glass models the use of `triangle relations' which describe the geometry of the configurations at three (long) different times.Comment: 42 Pages + 3 Figures upon reques