Aging, rejuvenation and memory phenomena in spin glasses

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.     

Spin glass model based on the Onsager reaction field

Changes in the Onsager reaction field are used to account quantitatively for aging (the decrease in the magnetic susceptibility when cooling in zero field is halted below the glass temperature) and rejuvenation (the disappearance of aging phenomena on further cooling only to reappear at Tw on heating) that characterize spin glasses. These effects must be caused by interactions between the spins since, absent the interactions, the magnetic properties of N spins are just N times the magnetic property of a single spin that cannot display aging. A spin introduced at an empty site with a nonzero field becomes polarized, and the polarized spin in turn polarizes its neighbors, thereby changing the local field. This additional field is the Onsager reaction field. Ma's theory for the reaction field in spin glasses [PRB 22, 4484 (1980)10.1103/PhysRevB.22.4484] has been extended to provide a spin-glass model that can account for the experimental data.     

Aging and memory effects in a clathrate

The out-of-equilibrium low-frequency complex susceptibility of the orientational glass methanol(73%)-beta-hydroquinone-clathrate is studied using temperature-stop protocols in aging experiments. Although the material does not have a sharp glass transition aging effects including rejuvenation and memory similar to the effects in spin glasses are found at low temperatures.     

Temperature chaos, rejuvenation, and memory in Migdal-Kadanoff spin glasses

We use simulations within the Migdal-Kadanoff approach to probe the scales relevant for rejuvenation and memory in Ising spin glasses. First we investigate scaling laws for domain wall free energies and extract the chaos overlap length l(T,T'). Then we perform out of equilibrium simulations that follow experimental protocols. We find that (1) a rejuvenation signal arises at a length scale significantly smaller than l(T,T'), and (2) memory survives even if equilibration goes out to length scales larger than l(T,T'). Theoretical justifications of these phenomena are then considered.     

Aging phenomena in spin glasses and frustrated ferromagnets

An experimental protocol developed for spin glasses has been applied to a reentrant system. We compare the main features of the aging phenomena in both spin glass and ferromagnetic phases.     

Ferromagnetic modes in spin glasses and dilute ferromagnets

We generalize the theories for the dynamics of spin glasses of Halperin and Saslow, and Dzyaloshinskii and Volovik to include additional partial ferromagnetic order. We find that the sixfold degenerate antiferromagnetic spin wave modes obtained in both theories split into two longitudinal and 2×2 transverse modes with different dispersion. In a certain range of wave vectorsq one obtains antiferromagnetic, ferromagnetic, andq-independent modes. The damping of these modes is calculated for a phenomelogical hydrodynamic model and their implications for the specific heat and electrical resistivity are discussed.     

Structural evolution in deformation-induced rejuvenation in metallic glasses: A cavity perspective

Classical molecular dynamics simulations have been performed to investigate the structural evolution in deformationinduced rejuvenation in Cu_(80)Zr_(20) metallic glass. Metallic glasses obtained by different cooling rates can be rejuvenated into the glassy state with almost the same potential energy by compressive deformation. The aging effect in different metallic glasses in cooling process can be completely erased by the deformation-induced rejuvenation. The evolution of cavities has been analyzed to understand the structural evolution in rejuvenation. It is found that as metallic glasses are rejuvenated by mechanical deformation, a lot of cavities are created. The lower the potential energy is, the more the cavities are created. The cavities are mainly created in the regions without cavities or with small cavities populated, indicating that the irreversible rearrangements induced by deformation are accompanied by the creation of cavity. This finding elucidates the underlying structural basis for rejuvenation and aging in metallic glasses from the cavity perspective.     

Atomistic simulation of aging and rejuvenation in glasses

Slow structural relaxation ("aging") observed in many atomic, molecular, and polymeric glasses substantially alters their stress-strain relations and can produce a distinctive yield point. Using Monte Carlo simulation for a binary Lennard-Jones mixture, we have observed these phenomena and their cooling-rate dependences for the first time in an atomistic model system. We also observe that aging effects can be reversed by plastic deformation ("rejuvenation"), whereby the system is expelled from the vicinity of deep minima in its potential energy surface.     

Aging,rejuvenation, and memory phenomena in a lead-based relaxor ferroelectric

Isothermal aging and temperature cycle experiments were done on the relaxor ferroelectric lead magnesium niobate mixed with 10% lead titanate (PMN-10PT) around and below the diffuse maximum of the dielectric loss. With increasing aging time t_w the isothermal evolution of the linear susceptibility follows a power law and does not show frequency scaling. The non-linear susceptibility, however, obeys nearly perfect ωt _w-scaling. After aging the sample at a single temperature we observed both rejuvenation and memory effects in temperature cycle experiments. This observation indicates symmetric behavior in the sense that it shows up irrespective of whether cooling with subsequent re-heating or heating with subsequent re-cooling was performed. The memory effect is absent if subsequent to aging the temperature is increased significantly above that corresponding to the maximum in the dielectric loss. The symmetric behavior within negative and positive temperature cycles under these conditions can be rationalized by the notion of movable domain walls. These become fixed in their configuration on a large spatial scale while more flexible wall segments still show re-conformation processes when cooling or heating the sample after aging. Received 18 December 2001 and Received in final form 28 January 2002     

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.     

Memory of multiple aging stages above the freezing temperature in the Relaxor ferroelectric PLZT

The dynamic dielectric susceptibility and the elastic compliance of the relaxor ferroelectric lanthanum lead zirconate titanate (PLZT) 9/65/35 have been measured under different cooling and heating protocols in order to study aging and memory. The memory of multiple aging stages at different temperatures has been found (several dips in the susceptibility curves on heating), as in spin glass systems below the glass transition. Remarkably, in PLZT the memory of several aging stages is retained also above the freezing temperature deduced from the dynamic susceptibilities. The results are discussed in light of the existing models of aging and memory in spin and dipolar glasses.     

Absence of an equilibrium ferromagnetic spin-glass phase in three dimensions

Using ground state computations, we study the transition from a spin glass to a ferromagnet in 3D spin glasses when changing the mean value of the spin-spin interaction. We find good evidence for replica symmetry breaking up until the critical value where ferromagnetic ordering sets in, and no ferromagnetic spin glass phase. This phase diagram is in conflict with the droplet/scaling and mean field theories of spin glasses. We also find that the exponents of the second order ferromagnetic transition do not depend on the microscopic Hamiltonian, suggesting universality of this transition.     

Signatures of structural recovery in colloidal glasses

Colloids near the glass concentration are often taken as models for molecular glasses. Yet, an important aspect of the dynamics of molecular glasses, structural recovery, has not been elucidated in colloids. We take advantage of a thermosensitive colloidal suspension to study the structural recovery after concentration jumps by using diffusing wave spectroscopy. The three classical aging signatures observed in molecular glasses are studied and the results are compared with those typical of molecular glasses. For the intrinsic isotherms, unlike molecular glasses, the colloid shows huge changes in relaxation time at equilibrium while the times required to reach the equilibrium state are nearly constant. For asymmetry of approach, we find a similar nonlinearity to that observed in the molecular glasses. For the memory experiment, while a memory effect is seen, the response is qualitatively different from that in molecular glasses.     

Biaxial magnetic structures in rare-earth compounds: GdMg and HoP

The flopside spin structure, where the magnetic moments form two sublattices which at low temperatures are mutually perpendicular was first found in HoP and then in other rare-earth pnictides. There are large orbital contributions to the magnetic moments of these compounds and it had been thought that they play an important role in stabilizing the flopside spin structure. However, recently this spin structure has been found in GdMg. As Gd³⁺ is an S-state ion, there are negligible orbital effects. We have developed a model Hamiltonian which is able to explain both the occurence of initially a ferromagnetic phase and then at low temperature the flopside spin structure in two very dissimilar compounds GdMg and HoP. For GdMg we find that the competition between the near neighbor ferromagnetic and antiferromagnetic bilinear exchange interactions is such that while they produce a transition to a ferromagnetic phase at 110 K, an unusually small amount of biquadratic (quadrupolar) coupling is able to stabilize a flopside phase at low temperature which is able to resist collapse in a field as large as 150 kOe. For HoP we find that although anisotropic bilinear pair interactions - as for example pseudo-dipole - exist, they cannot be the primary origin of the flopside phase; quadrupole pair interactions are essential to explain the appearance of first the ferromagnetic and then the flopside phases found in HoP. On the basis of our model calculations we are able to explain the data extant on these compounds and we make some predictions which are open to experimental verification.     

Tapping spin glasses and ferromagnets on random graphs.

We consider a tapping dynamics, analogous to that in experiments on granular media, on spin glasses and ferromagnets on random thin graphs. Between taps, zero temperature single spin flip dynamics takes the system to a metastable state. Tapping corresponds to flipping simultaneously any spin with probability p. This dynamics leads to a stationary regime with a steady state energy E(p). We analytically solve this dynamics for the one-dimensional ferromagnet and +/-J spin glass. Numerical simulations for spin glasses and ferromagnets of higher connectivity are carried out; in particular, we find a novel first order transition for the ferromagnetic systems.