Memory and Chaos Effects in Spin Glasses

Abstract

New low frequency ac susceptibility measurements on two different spin glasses show that cooling/heating the sample at a constant rate yields an essentially reversible (but rate dependent) χ(T ) curve; a downward relaxation of χ occurs during a temporary stop at constant temperature (ageing). Two main features of our results are: (i) when cooling is resumed after such a stop, χ goes back to the reversible curve (chaos) (ii) upon re-heating, χ perfectly traces the previous ageing history (memory). We discuss implications of our results for a real space (as opposed to phase space) picture of spin glasses.PACS numbers: 75.50.Lk 75.10.Nr to appear in Phys. Rev. Lett.The dynamic properties of the spin glass phase have been extensively studied by both experimentalists and theorists for almost two decades [1,2]. The observed properties reflect the out-of-equilibrium state of the system: the response to a field variation is logarithmically slow, and, in addition, depends on the time spent at low temperature ("ageing"). Ageing is fully reinitialized by heating the sample above the glass temperature T g . It corresponds to the slow evolution of the system towards equilibrium, starting at the time of the quench below T g . Many aspects of ageing are similar to the"physical ageing" phenomena that have been characterized in the mechanical properties of glassy polymers [3]. In the last few years, some interesting progress in the theoretical understanding of ageing in disordered systems has been achieved [4].From the studies of the critical behaviour at T g [5], it appears that the approach of T g is associated to the divergence of a spin-spin correlation length, as is the case in the phase transition of classical ordered systems. In the spin glass phase, the system is out of equilibrium: as in simple ferromagnets, it is tempting to associate ageing with the progressive growth of a typical domain size towards an equilibrium infinite value. However, this simple picture cannot account for all the experimental observations. In particular, the effect of small temperature cycles (within the spin-glass phase) is rather remarkable [6,7]:• on the one hand, ageing at a higher temperature barely contributes to ageing at a lower temperature. Said differently (as will be discussed again below), the thermal history at sufficiently higher temperatures is irrelevant. This is at variance with a simple scenario of thermal activation over barriers, where the time spent at higher temperature would obviously help the system to find its equilibrium state. Everything happens as if there were strong changes of the free-energy landscape with temperature. This point is suggestive of the "chaotic" aspect of the spin glass phase that has been predicted from mean field theory [8] and from scaling arguments in [9,10].• on the other hand, interesting memory effects concomitantly appear: the state reached by the system at a given temperature can be retrieved after a negative temperature cycle.In the present letter, we describe some new experiments which rev...

Memory effect and spin-glass-like behavior in Co-Ag granular films

“…30 The reduction of T p is consistent with the results reported by De Toro et al 30 in Co 29 Ag 71 and Co 25 Ag 75 ͑atomic fractions͒ granular films with almost the same annealing temperature ͑298°C͒. However, as we mentioned previously, if the annealing temperature increases up to 400°C, the ZFC and FC curves ͑not shown here͒ will no longer coalesce within the measuring temperature range.…”

“…We focused on the study of memory effect because it is usually considered as typical characteristics of the spinglass dynamics and has been clearly observed in different ͑canonical͒ spin-glass systems. [25][26][27] Although the spin-glass state was found in Fe-Cu ͑Ref. 28͒ and Co-Cu ͑Ref.…”

Rejuvenation and memory in model spin glasses in three and four dimensions

“…Memory and rejuvenation 7,8 are sophisticated manifestations of aging in experiments where the temperature is not kept constant. Rejuvenation arises when changing temperature from T 1 to T 2 ͑T 1 and T 2 smaller than the critical temperature T c ͒ a system that has spent some time at T 1 , so that ͑ , t w ͒ barely depends on t w .…”

“…10͒, although rejuvenation is very diminished as compared with the imaginary part. With the sophisticated dip-experiment temperature-change protocol, 7 memory and rejuvenation are truly spectacular.…”

Glassy dynamics in CuMn thin-film multilayers

“…Some attempts are given in Refs. [15][16][17][18]. The experiments detailed in our paper distinguish between these two approaches by direct measurement of a microscopic parameter, the system's maximum barrier height, ∆ max (L), when ξ(t > t co , T ) is fixed at L. Before going into more detail, it is important to outline the analysis utilized in this paper.…”