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...

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The peak of the spin glass relaxation rate, S(t) = d[ − MT RM (t, tw)/H]/dℓnt, 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 Ez = Nsχ f c H 2 by which the barrier heights are reduced, where χ f c is the field cooled susceptibility per spin, and Ns is the number of correlated spins. The shift of the peak of S(t) gives Ez, generating the correlation length, ξ(t, T ), for Cu : M n 6at.% and CdCr1.7In0.3S4. Fits to power law dynamics, ξ(t, T ) ∝ t α(T ) and activated dynamics ξ(t, T ) ∝ (ℓnt) 1/ψ compare well with simulation fits, but possess too small a prefactor for activated dynamics.PACS numbers: 75.50. Lk, 75.10.Nr, 75.40.Gb The study of the irreversible behavior of the spin glass magnetization under a change of magnetic field allows exploration of the available states of a random frustrated system. [1,2] There are various representations for the long time evolution and the dynamics of spin glasses, [3-5] but a coherent, overall accepted real space description remains lacking.[6] The purpose of this paper is to extract a time and temperature dependent spin glass correlation length from a specially structured set of experiments, and to compare our results with available theoretical predictions.The definition of a correlation length for a spin glass is difficult to express in measurable terms. Marinari et al. [7] and Kisker et al. [8] introduced the time dependent equal time correlation function at time t. In the notation of Ref. 7,where the average is done at time t, and σ i (σ i+x ) and τ i (τ i+x ) represent the z component of Ising spins at sites i (i + x) in two thermalized configurations in a box of volume V . To avoid accidental contributions to G(x, t), the two configurations are chosen to have zero overlap, q = V −1 i σ i τ i . Refs. 7 and 8 both observed, through their simulation studies, that for large times t the correlation function G(x, t) differs from zero for distances not too much larger than a dynamic correlation length ξ(t, T ). Simulations of Marinari et al. [7] obtain satisfactory fits for ξ(t, T ) ∝ (t/τ 0 ) αT /Tg , appropriate to power law dynamics, [4] while Kisker et al. [8] fit satisfactorily both this proportionality and equally well ξ(t, T ) ∝ [(T /T g )ℓn(t/τ 0 )] 1/ψ , appropriate to activated dynamics. [5] Our measurements consist of cooling a sample in a magnetic field through the glass temperature T g to the measuring temperature T , waiting a time t w , then cutting the field to zero and measuring the decay of the magnetization. This generates the response function,where M T RM (t, t w ) is the thermoremanent magnetization at time t after cutting the magnetic field to zero. Our approach, justified previously through magnetic field cycling [9] and used to determine the Parisi physical order parameter P (q), [1] makes use of the scaling relationship introduced by Vincent et al. [2]. They show that barrier heights surmounted during aging are reduced upon a...

We summarize the different puzzles raised by aging experiments of spin-glasses and their various interpretations. We try to reconcile the 'real space', droplet like pictures with the hierarchical pictures that have been proposed in the past. The basic ingredient is a strong separation of the time scales that govern the dynamics of the system on different length scales. Changing the temperature changes the length scale at which the system is observed, thereby allowing rejuvenation (that concerns short length scales) and memory (stored in long length scales) to coexist. We show that previous experiments can be reanalyzed in terms of vanishing energy barriers at the spin-glass transition, an important ingredient to obtain a fast separation of time scales. We propose to distinguish between 'fixed landscape rejuvenation', which is already present in simple two (or multi) level systems, from the 'strong' chaos effect on scales larger than an 'overlap length' conjectured in the context of the droplet model. We argue that most experiments can be accounted for without invoking the existence of an overlap length. New experiments are presented to test some recent predictions of the strong chaos scenario, with negative results.

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.

We performed low-frequency (f= 0.1 Hz) ax. susceptibility measurements on the CdCr,.,InOsS4 insulating spin glass. The experiments were selected in an attempt to discriminate between the droplet model and a hierarchical picture characterized by a continuous splitting of the metastable states with decreasing temperatures. We studied the effect of small temperature changes on the aging of the out-of-phase susceptibility X" below the freezing temperature Tg . We find that the predictions of the droplet model do not agree with some aspects of the results which appear as direct consequences of a hierarchical organization in phase space.

We have compared aging phenomena in the Fe 0.5 Mn 0.5 TiO 3 Ising spin glass and in the CdCr 1.7 In 0.3 S 4 Heisenberg-like spin glass by means of low-frequency ac susceptibility measurements. At constant temperature, aging obeys the same ''t scaling'' in both samples as in other systems. Investigating the effect of temperature variations, we find that the Ising sample exhibits rejuvenation and memory effects which are qualitatively similar to those found in other spin glasses, indicating that the existence of these phenomena does not depend on the dimensionality of the spins. However, systematic temperature cycling experiments on both samples show important quantitative differences. In the Ising sample, the contribution of aging at low temperature to aging at a slightly higher temperature is much larger than expected from thermal slowing down. This is at variance with the behavior observed until now in other spin glasses, which show the opposite trend of a free-energy barrier growth as the temperature is decreased. We discuss these results in terms of a strongly renormalized microscopic attempt time for thermal activation and estimate the corresponding values of the barrier exponent introduced in the scaling theories.