The Parisi solution of the mean-field spin glass has been widely accepted and celebrated. Its marginal stability in 3d and its complexity however raised the question of its relevance to real spin glasses. This paper gives a short overview of the important experimental results which could be understood within the mean-field solution. The existence of a true phase transition and the particular behaviour of the susceptibility below the freezing temperature, predicted by the theory, are clearly confirmed by the experimental results. The behaviour of the complex order parameter and of the Fluctuation Dissipation ratio are in good agreement with results of spontaneous noise measurements. The very particular ultrametric symmetry, the key feature of the theory, provided us with a simple description of the rejuvenation and memory effects observed in experiment. Finally, going a step beyond mean-field, the paper shortly discusses new analyses in terms of correlated domains characterized by their length scales, as well as new experiments on superspin glasses which compare well with recent theoretical simulations.

We present in this paper some new experimental results on the effect of temperature and field cyclings on the out-of-phase susceptibility of an insulating spin glass. The temperature-cycling experiments are consistent with a previously derived hierarchical scenario in which the probed metastable states continuously split into new substates as the temperature is lowered. The new results, however, suggest that the states of lowest free energy are not the same at different temperatures, supporting the idea of chaotic behaviour. Changing the magnetic field makes the system flow from one hierarchically organized set of states to another set of states with a different magnetization. An analysis of the field effect on the escape times of the states is proposed. It accounts for the observed behaviour of the a.c. susceptibility. It, moreover, predicts a scaling form for the time decay of the thermoremanent magnetization in terms of the probing field, which is nicely satisfied by the available experimental data.

In this paper, we review several important features of the out-of-equilibrium dynamics of spin glasses. Starting with the simplest experiments, we discuss the scaling laws used to describe the isothermal aging observed in spin glasses after a quench down to the low-temperature phase. We report in particular new results on the sub-aging behaviour of spin glasses. We then discuss the rejuvenation and memory effects observed when a spin glass is submitted to temperature variations during aging, from the point of view of both energy landscape pictures and real-space pictures. We highlight the fact that both approaches point out the necessity of hierarchical processes involved in aging. Finally, we report an investigation of the effect of small temperature variations on aging in spin glass samples with various anisotropies which indicates that this hierarchy depends on the spin anisotropy.

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.

The magnetization relaxations of three different types of geometrically frustrated magnetic systems have been studied with the same experimental procedures as previously used in spin glasses. The materials investigated are Y2Mo2O7 (pyrochlore system), SrCr8.6Ga3.4O19 (piled pairs of Kagomé layers) and (H3O)Fe3(SO4)2(OH)6 (jarosite compound). Despite a very small amount of disorder, all the samples exhibit many characteristic features of spin glass dynamics below a freezing temperature Tg, much smaller than their Curie–Weiss temperature θ. The ageing properties of their thermoremanent magnetization can be well accounted for by the same scaling law as in spin glasses, and the values of the scaling exponents are very close. The effects of temperature variations during ageing have been specifically investigated. In the pyrochlore and the bi-Kagomé compounds, a decrease of temperature after some waiting period at a certain temperature Tp reinitializes ageing, and the evolution at the new temperature is the same as if the system were just quenched from above Tg. However, as the temperature is raised back to Tp, the sample recovers the state it had previously reached at that temperature. These features are known in spin glasses as rejuvenation and memory effects. They are clear signatures of the spin glass dynamics. In the Kagomé compound, there is also some rejuvenation and memory, but much larger temperature changes are needed to observe the effects. In that sense, the behaviour of this compound is quantitatively different from that of spin glasses.

Experiments on spin glasses show that it is possible to store the memory of several aging stages performed successively at different temperatures while cooling from Tg. Here, we investigate how the sharpness of the memory effect in spin glass systems depends on the spin anisotropy. We find that the sharpness of the memory effect shows a systematic decrease with increasing anisotropy, which suggests that the temperature dependence of the free-energy barriers is, somewhat surprisingly, softer in the strong anisotropy (Ising) limit.

The effect of initial conditions on aging properties of the spin-glass state is studied for a single crystal Cu:Mn 1.5 at %. It is shown that the memory of the initial state, created by the cooling process, remains strong on all experimental time scales. The t/t(w) scaling properties of two relaxation functions, the thermoremanent magnetization (TRM) and the isothermal remanent magnetization (IRM) (with t(w1) = 0 and t(w2) = t(w)), are compared in detail. It is observed that the IRM relaxation as a function of t/t(w) demonstrates a superaging behavior. This result suggests that the subaging, exhibited by the TRM decay, arises from the influence of the cooling process, and cannot be considered a natural type of scaling in spin-glass dynamics.

The model 2d kagome system (H3O)Fe3(SO4)2(OH)6 and the 3d pyrochlore Y2Mo2O7 are two well characterized examples of low-disordered frustrated antiferromagnets which rather then condensing into spin liquid have been found to undergo a freezing transition with spin glass-like properties. We explore more deeply the comparison of their properties with those of spin glasses, by the study of characteristic rejuvenation and memory effects in the non-stationary susceptibility. While the pyrochlore shows clear evidence for these non-trivial effects, implying temperature selective aging, that is characteristic of a wide hierarchical distribution of equilibration processes, the kagome system does n not show clearly these effects. Rather, it seems to evolve towards the same final state independently of temperature.

We have studied the slow dynamics of the ferromagnetic phases of the re-entrant CdCr2xIn2-2xS4 system for 0.85 < x≤1 by means of low frequency ac susceptibility and magnetization measurements. Experimental procedures widely used in the investigation of the out-of-equilibrium dynamics of spin glasses (such as the x = 0.85 compound) have been applied to search for aging, rejuvenation and memory effects, and to test their dependence on the disorder introduced by dilution of the magnetic ions. Whereas the rejuvenation effect is found in all studied samples, the memory effect is clearly enhanced for increasing dilutions. The results support a description of aging in both ferromagnetic and re-entrant spin-glass phases in terms of hierarchical reconformations of domain walls pinned by the disorder.

We summarize the different puzzles raised by aging experiments of spin glasses and their various interpretations. We try to reconcile the ``real space,'' dropletlike 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 abruptly 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 free-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 the ``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. Experiments are presented to test some recent predictions of the strong chaos scenario, with negative results.

Specific heat measurements have been performed on single-crystalline Ce(Ru1−xRhx)2Si2 (x=0.15,0.35) in various magnetic fields parallel to the c-axis. For x=0.15, the magnetic specific heat Cmag shows a jump due to the spin density wave for B6T. For x=0.35, Cmag/T shows the NFL behavior for B<6T and the FL behavior for B>6T.

We have compared aging phenomena in the ${\mathrm{Fe}}_{0.5}{\mathrm{Mn}}_{0.5}{\mathrm{TiO}}_{3}$ Ising spin glass and in the ${\mathrm{CdCr}}_{1.7}{\mathrm{In}}_{0.3}{\mathrm{S}}_{4}$ Heisenberg-like spin glass by means of low-frequency ac susceptibility measurements. At constant temperature, aging obeys the same $``\ensuremath{\omega}t$ 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 \ensuremath{\psi} introduced in the scaling theories.

Electrical resistivity measurements have been performed on the dilute uranium compound UxLa1−xRu2Si2 (x=0.07) with the current along the a and the c axes between 300K and 28mK. The electrical resistivity, ρ, along the a and the c axes decreases as temperature is lowered below 300K. In the low-temperature region between 7K and 28mK, the magnetic contribution of the 5f electron to the resistivity, ρm, exhibits the Fermi-liquid behavior with a clear T2 dependence. The Kadowaki–Woods ratio A5f/γ5f2 is estimated from ρm and the specific heat data previously reported, and is found to be the same order as that of URu2Si2. This indicates that the enhanced density of states at the Fermi level causes the T2 dependence of ρm in the dilute uranium compound UxLa1−xRu2Si2.

We have measured the resistivity of single-crystalline Ce(Ru0.5Rh0.5)2Si2 as a function of an external magnetic field. While this compound is known to show non-Fermi-liquid (NFL) behavior at zero field, we discovered recovery of the conventional Fermi-liquid (FL) behavior above 1 T. It can be considered as the effect of suppression of the spin fluctuations caused by applying a magnetic field. On the other hand, the large positive magnetoresistance is observed at 40 mK which shows rather strong field dependence at low field region (H<1 T), which may be connected with the effect of the disorder due to the Rh-doping.

Aging phenomena have been studied in very different materials like polymers, supercooled liquids or disordered orientational crystals. We recall here the main features of aging in spin glasses, and use this example of magnetic systems as a guideline for the description of the others. A particular attention is put on the sensitivity of aging to the cooling rate and to temperature variations. This allows us to point out differences between temperature specific processes, yielding ``rejuvenation and memory effects'' as known in spin glasses, and domain growth processes, giving cumulative contributions at different temperatures. The relevance of wall depinning processes to rejuvenation and memory effects is discussed at the light of recent results on disordered ferromagnets.

The low temperature properties of Ce(Ru1-xRhx)(2)Si-2 (0 less than or equal to x less than or equal to 1), U(Ru1-xRhx)(2)Si-2 (0 less than or equal to x less than or equal to 1) and UxLa1-xRu2Si2 (0 less than or equal to x less than or equal to 0.15) are reviewed with emphasis on experiments of susceptibility, non-linear susceptibility, specific heat, resistivity, thermal expansion, neutron scattering and mu SR. New experimental data has led to new insights to the physical understanding of these heavy fermions. In Rh rich side, antiferromagnetic order associated with the localized character of the f-electrons sets in for both Ce(Ru1-xRhx)(2)Si-2 (0 less than or equal to x less than or equal to 1) and U(Ru1-xRhx)(2)Si-2 (0 less than or equal to x less than or equal to 1) compounds. For Ce(Ru1-xRhx)(2)Si-2 compound, x-dependence of the material is investigated in detail. In Ru rich side, the ground state is a Fermi liquid for x < 0.03; an anisotropic spin density wave (SDW) appears for 0.03 < x < 0.4 with a maximum T-N = 5.5 K at x = 0.15. The nature of the anisotropic SDW is characterized by the anisotropic anomaly in the resistivity below T-N The anisotropy of the SDW is discussed from the view point of nesting of the Fermi surfaces of itinerant heavy fermion quasi-particle bands. Another interesting feature is the non-Fermi liquid behavior observed for x = 0.4 and 0.5. Appearance of quantum Griffiths's like phase is indicated for x = 0.5 from the measurements of mu SR, low field ac-susceptibilty and nonlinear susceptibiltiy. The temperature dependence of the susceptibility and the magnetoresistance with 0.1 T de-field are well explained in terms of the mean field theory based on spin fluctuations. The phase transition of URu2Si2 at 17.5 K(= T-o) is considered to be due to quadrupolar ordering from the behaviors of a sharp anomaly in nonlinear susceptibility at T-o and very large consumption of entropy below T-o compared to a small staggered ordered moment, 0.02 mu(B) We recently found that the phase transition is not due to magnetic origin by neutron scattering experiment under pressure. The susceptibility and magnetization in dilute alloys of UxLa1-xRu2Si2 are well explained by assuming a non-Kramers doublet ground state of the J = 4 crystalline field level. From these experiments, the phase transition of URu2Si2 at T-o is understood by the model of quadrupolar ordering of the non-Kramers doublet which coexists with antiferromagntic short range order.