Spin glass dynamics at the mesoscale

Abstract

The mesoscale allows a new probe of spin glass dynamics. Because of the spin glasses lower critical dimension d l > 2, the growth of the correlation length ξ(t, T ) can change the nature of the spin glass state at a crossover time tco when ξ(tco, T ) = ℓ, a minimum characteristic sample length (i.e. film thickness for thin films and crystallite size for bulk samples). For thin films, and times t < tco such that ξ(t, T ) < ℓ, conventional three dimensional dynamics are observed. When t > tco, a crossover to d = 2 behavior takes place. The parallel correlation length, associated with a Tg = 0 transition, increases in time from the saturated value of the perpendicular correlation length ℓ to an equilibrium value of the parallel correlation length proportional to T −ν . This results in a pancake-like correlated state, with a thickness ℓ and a temperature dependent in-plane radius that increases with decreasing temperature. Activated dynamics are associated with these states. Measurements on Cu:Mn thin films are analyzed quantitatively within this framework. We extract a temperature dependent activation energy from a fit to the frequency dependence of the dynamic susceptibility. The extrapolated temperature at which the activation energy would become large is close to the extrapolated glass transition temperature from ac susceptibility measurements. All known relevant experimental data are consistent with this approach. For polycrystalline materials, there is a distribution of length scales P(ℓ). For sufficiently broad distributions, a logarithmic time dependence is derived for the time decay of the thermoremanent magnetization MTRM(t, T ) using an approach originally derived by Ma. Properties dependent upon an effective waiting time t eff w are derived that are consistent with experiment, and further measurements are suggested.

End of aging as a probe of finite-size effects near the spin-glass transition temperature

“…The parallel correlation length, ξ (t, T ), is driven by a T = 0K transition temperature, 11 but renormalized by the correlations contained within the ξ ⊥ (t, T ) = L length scale. 12 The correlated volume is then "pancake-like" with thickness L and width ξ (T ), as confirmed by recent experiments. 13 Because the correlated volume is limited by these two length scales, there is no further growth of ξ in time for t > t co .…”

Mesoscopic real-space structures in spin-glass aging: The Edwards-Anderson model

“…Unlike the first assumption, the second is only supported a posteriori by the formula it produces, which empirically describes TRM decay data [17]. Importantly, the power-law terms vanish fairly rapidly and the remaining logarithmic decay, which formally arises by expanding a possibly large group of power-laws with small exponents, has a pre-factor which is T independent, as in the experimental data analysis of [17] but in contrast with the formula given in [4]. A similar behavior [6,56] is seen in the temperature independence of the magnetic creep rate of high T c superconductors.…”

“…a thermal quench. While spinglasses [1][2][3][4], colloidal suspensions [5], vortices in superconductors [6], magnetic nanoparticles in a ferrofluid [7] and ecosystems [8,9] may have little in common in terms of microscopic variables and interactions, strong similarities emerge in their aging phenomenology. For example, one point averages feature a logarithmic time dependence [10] which entails an asymptotically vanishing rate of change of the corresponding observables and clarifies why aging systems deceptively appear in equilibrium for observation times shorter than their age.…”

Universal critical behavior of the two-dimensional Ising spin glass

“…The system remains paramagnetic for any temperature T > 0, but the critical limit at T = 0 has puzzled theorists for many years . On the other hand, recent experiments in spin glasses are carried out in samples with a film geometry [37][38][39]. The analysis of these experiments will demand a strong theoretical command.…”