Aging in spin glasses as a random walk: Effect of a magnetic field

Scaling Law Describes the Spin-Glass Response in Theory, Experiments, and Simulations

The correlation length ξ, a key quantity in glassy dynamics, can now be precisely measured for spin glasses both in experiments and in simulations. However, known analysis methods lead to discrepancies either for large external fields or close to the glass temperature. We solve this problem by introducing a scaling law that takes into account both the magnetic field and the time-dependent spin-glass correlation length. The scaling law is successfully tested against experimental measurements in a CuMn single crystal and against large-scale simulations on the Janus II dedicated computer.

Aging is a log-Poisson process, not a renewal process

Aging is a ubiquitous relaxation dynamic in disordered materials. It ensues after a rapid quench from an equilibrium "fluid" state into a nonequilibrium, history-dependent jammed state. We propose a physically motivated description that contrasts sharply with a continuous-time random walk (CTRW) with broadly distributed trapping times commonly used to fit aging data. A renewal process such as CTRW proves irreconcilable with the log-Poisson statistic exhibited, for example, by jammed colloids as well as by disordered magnets. A log-Poisson process is characteristic of the intermittent and decelerating dynamics of jammed matter usually activated by record-breaking fluctuations ("quakes"). We show that such a record dynamics provides a universal model for aging, physically grounded in generic features of free-energy landscapes of disordered systems.

Magnetic Field Dependence of Spin Glass Free Energy Barriers

We measure the field dependence of spin glass free energy barriers in a thin amorphous Ge:Mn film through the time dependence of the magnetization. After the correlation length ξ(t,T) has reached the film thickness L=155  Å so that the dynamics are activated, we change the initial magnetic field by δH. In agreement with the scaling behavior exhibited in a companion Letter [M. Baity-Jesi et al., Phys. Rev. Lett. 118, 157202 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.157202], we find that the activation energy is increased when δH<0. The change is proportional to (δH)^{2} with the addition of a small (δH)^{4} term. The magnitude of the change of the spin glass free energy barriers is in near quantitative agreement with the prediction of a barrier model.

Direct dynamical evidence for the spin glass lower critical dimension 2<d(ℓ)<3

A dynamical method is introduced to study the effect of dimensionality on phase transitions. Direct experimental measurements for the lower critical dimension for spin glasses is provided as an example. The method makes use of the spin glass correlation length ξ(t,T). Once nucleated, it can become comparable to sample dimensions in convenient time and temperature ranges. Thin films of amorphous Ge:Mn alloys were prepared with thickness L≈15.5  nm. Conventional behavior is observed as long as ξ(t,T)<L. At the measurement time tco, when ξ(tco,T)≈L, the time dependence is observed to cross over to exponential. These results are interpreted using spin glass dynamics, and are consistent with a lower critical dimension for spin glasses, dℓ, between 2<dℓ<3.

Replenish and relax: explaining logarithmic annealing in ion-implanted c-Si

We study ion-damaged crystalline silicon by combining nanocalorimetric experiments with an off-lattice kinetic Monte Carlo simulation to identify the atomistic mechanisms responsible for the structural relaxation over long time scales. We relate the logarithmic relaxation, observed in a number of disordered systems, with heat-release measurements. The microscopic mechanism associated with this logarithmic relaxation can be described as a two-step replenish and relax process. As the system relaxes, it reaches deeper energy states with logarithmically growing barriers that need to be unlocked to replenish the heat-releasing events leading to lower-energy configurations.

Aging of a colloidal glass under a periodic shear

The aging dynamics under a periodic shear of a concentrated suspension of saponite particles is measured. It is observed that the dynamics is fastened by the application of a moderate shear amplitude. Nevertheless, this acceleration does not affect the dynamics of the suspension when the shear is ceased. By applying a succession of shear of various amplitudes, we conclude that the dynamics of the suspension at a time t(w) after complete rejuvenation is independent of the shear history between times 0 and t(w) , as soon as the amplitude of the applied shear is smaller than the characteristic shear gamma(c) necessary to completely rejuvenate the suspension.

Spin anisotropy and slow dynamics in spin glasses

We report on an extensive study of the influence of spin anisotropy on spin glass aging dynamics. New temperature cycle experiments allow us to compare quantitatively the memory effect in four Heisenberg spin glasses with various degrees of random anisotropy and one Ising spin glass. The sharpness of the memory effect appears to decrease continuously with the spin anisotropy. Besides, the spin glass coherence length is determined by magnetic field change experiments for the first time in the Ising sample. For three representative samples, from Heisenberg to Ising spin glasses, we can consistently account for both sets of experiments (temperature cycle and magnetic field change) using a single expression for the growth of the coherence length with time.

Linear and nonlinear response in the aging regime of the one-dimensional trap model

We investigate the behavior of the response function in the one-dimensional trap model using scaling arguments that we confirm by numerical simulations. We study the average position of the random walk at time t(w)+t, given that a small bias h is applied at time t(w). Several scaling regimes are found, depending on the relative values of t, t(w), and h. Comparison with the diffusive motion in the absence of bias allows us to show that the fluctuation-dissipation relation is valid even in the aging regime, at least for times such that linear response is obeyed. However, for sufficiently long times, the response always becomes nonlinear in h.

Metastable states in spin glasses and disordered ferromagnets

We study analytically M-spin-flip stable states in disordered short-ranged Ising models (spin glasses and ferromagnets) in all dimensions and for all M. Our approach is primarily dynamical, and is based on the convergence of sigma(t), a zero-temperature dynamical process with flips of lattice animals up to size M and starting from a deep quench, to a metastable limit sigma(infinity). The results (rigorous and nonrigorous, in infinite and finite volumes) concern many aspects of metastable states: their numbers, basins of attraction, energy densities, overlaps, remanent magnetizations, and relations to thermodynamic states. For example, we show that their overlap distribution is a delta function at zero. We also define a dynamics for M=infinity, which provides a potential tool for investigating ground state structure.