Spin-glass Dynamics Research Articles

Probing exotic spin correlations by muon spin depolarization measurements with applications to spin glass dynamics

We develop a new method to probe the local spin dynamic autocorrelation function, using magnetic field dependent muon depolarization measurements. We apply this method to muSR experiments in the dilute Heisenberg spin glass AgMn(p at. %) at T>T_g where the correlations of the Mn local magnetic moment are strongly non-exponential. Our results clearly indicate that the dynamics of this spin glass cannot be described by a distribution of correlation times. Therefore, we analyze the data assuming a local spin correlation function which is the product of a power law times a cutoff function. The concentration and temperature dependence of the parameters of this function are determined. Our major conclusion is that in the temperature region close to Tg the correlation function is dominated by an algebraic relaxation term.

Dynamic ultrametricity in spin glasses.

We investigate the dynamics of spin glasses from the "rheological" point of view, in which aging is suppressed by the action of small, nonconservative forces. The different features can be expressed in terms of the scaling of relaxation times with the magnitude of the driving force, which plays the role of the critical parameter. Stated in these terms, ultrametricity loses much of its mystery and can be checked rather easily. This approach also seems a natural starting point to investigate what would be the real-space structures underlying the hierarchy of time scales. We study in detail the appearance of this many-scale behavior in a mean-field model, in which dynamic ultrametricity is clearly present. A similar analysis is performed on numerical results obtained for a three-dimensional spin glass: In that case, our results are compatible with either that dynamic ultrametricity is absent or that it develops so slowly that even in experimental time-windows it is still hardly observable.

On the Re-Entrant State of the Pd11Co50Al39 Alloy

The re-entrant state in the Pd 11 Co 50 Al 39 alloy is investigated by dc and ac magnetization measurements. A dynamic scaling analysis of ac susceptibility data indicates a true spin-glass state below 5.6 K. Magnetic aging, characteristic of spin-glass dynamics, persists well into the re-entrant ferromagnetic phase of Pd 11 Co 50 Al 39 . Borders of the re-entrant spin-glass and ferromagnetic behaviour are established for this allov.

Dynamical studies of the response function in a spin glass

Experiments on the time dependence of the response function of a Ag(11 at% Mn) spin glass at a temperature below the zero-field spin glass temperature are used to explore the non-equilibrium nature of the spin glass phase. It is found that the response function is only governed by the thermal history in the very neighbourhood of the actual measurement temperature. The thermal history outside this narrow region is irrelevant to the measured response. This implies that the thermal history during cooling (cooling rate, wait times, etc.) is imprinted in the spin structure and that the fragment of this history surrounding any higher temperature can be recalled when this temperature is recovered. The observations are discussed in the light of a real-space droplet/domain phenomenology. The results also emphasise the importance of using controlled cooling procedures to acquire interpretable and reproducible experimental results on the non-equilibrium dynamics in spin glasses.

Off-equilibrium dynamics of a four-dimensional spin glass with asymmetric couplings

We study the off-equilibrium dynamics of the Edwards-Anderson spin glass in four dimensions under the influence of a non-Hamiltonian perturbation (i.e. with asymmetric couplings). We find that for small asymmetry the model behaves like the Hamiltonian model, while for large asymmetry the behaviour of the model can be well described by an interrupted ageing scenario. The autocorrelation function scales as , with a function of the asymmetry. For very long waiting times the previous regime crosses over to a time translational invariant regime with stretched exponential relaxation. The model does not show signs of reaching a time translational invariant regime for weak asymmetry, but in the ageing regime the exponent is always different from 1, showing a non-trivial ageing scenario also valid in the Hamiltonian model.

Dynamics of the four-dimensional spin glass in a magnetic field

We study the four dimensional Gaussian spin glass in presence of a magnetic field. Using off-equilibrium numerical simulations we have found that the probability distribution of the overlaps is built in the same way as that of the Mean Field approximation with replica symmetry breaking. Finally we have studied the violation of the fluctuation-dissipation theorem in presence of magnetic field.

Confinement effects in semimagnetic semiconductors

An overview is given of selected novel effects observed recently by various groups in modulated structures of Cd 1− x Mn x Te. Millikelvin studies of submicron wires doped with either indium or iodine have demonstrated the existence of a new mechanism, by which the universal conductance fluctuations can be generated in mesoscopic systems containing magnetic ions. Moreover, 1/ f conductance noise as well as thermal and magnetic irreversibilities have been observed, providing important information on spin-glass dynamics. Finite size effects in magnetic properties have been probed by direct static and dynamic SQUID measurements on superlattices consisting of few-monolayer spin-glass films separated by nonmagnetic barriers. The confined holes have been found to exert a strong influence upon the magnetic ions and to induce a ferromagnetic phase transition above 1 K in quantum wells modulation doped by nitrogen. Finally, it has been shown also that the giant spin-splitting of the bands offers a tool to tune the coupling between confined photon and exciton modes in photonic structures.

Spin-glass dynamics and the barrier model: Extraction of the Parisi physical order parameter

Abstract The fact that the model of barrier heights monotonically increases with increasing metastable state Hamming distance (the difference between the spin orientations of any two states) on a hierarchical (ultrametric) tree can account for the ageing phenomenon in spin glasses. We make use of this model to extract spin-glass dynamics, including the instantaneous value of the zero-field-cooled magnetization M ZFC, and the time dependences of the thermoremanent magnetization M TRM(t w, t) or, equivalently, of the zero-field magnetization M ZFC(t w, t), where t is the measurement time after waiting a time t w, below the spin-glass transition temperature T g. The pure states introduced by Parisi are thought to originate from metastable states because finite barriers diverge as the temperature is lowered. These infinite barriers encompass metastable states separated by a self-similar distribution of barrier heights, independent of temperature. The model for extraction of spin-glass dynamics which we have u...

Averaged and quenched propagation of chaos for spin glass dynamics

We study the asymptotic behaviour for both asymmetric and symmetric spin glass dynamics in a Sherrington-Kirkpatrick model as proposed by Sompolinsky-Zippelius. We prove, without any condition on time and temperature, averaged propagation of chaos results. Extending this result to replicated systems, we conclude that the law of a single spin converges to a non Markovian probability measure, in law with respect to the random interaction.

Symmetric Langevin spin glass dynamics

We study the asymptotic behavior of symmetric spin glass dynamics in the Sherrington–Kirkpatrick model as proposed by Sompolinsky–Zippelius. We prove that the averaged law of the empirical measure on the path space of these dynamics satisfies a large deviation upper bound in the high temperature regime. We study the rate function which governs this large deviation upper bound and prove that it achieves its minimum value at a unique probability measure $Q$ which is not Markovian. We deduce an averaged and a quenched law of large numbers. We then study the evolution of the Gibbs measure of a spin glass under Sompolinsky–Zippelius dynamics. We also prove a large deviation upper bound for the law of the empirical measure and describe the asymptotic behavior of a spin on path space under this dynamic in the high temperature regime.

Spin Glass Dynamics under a Change in Magnetic Field.

A barrier model is developed for spin glass dynamics. An ultrametric arrangement for spin glass states at magnetization $M$, with barrier heights increasing linearly with Hamming distance, is used to represent aging. Upon a change in magnetic field, with an associated change in Zeeman energy ${E}_{z}$, states with barrier heights $\ensuremath{\Delta}l{E}_{z}$ rapidly transition to the new ground state magnetization. Calculation of the time rate of change of the magnetization for finite hierarchies yields results in agreement with experiment. Forms for the most probable values of the Parisi physical order parameter for infinite hierarchies, $P(q)$, are extracted from experiment at representative temperatures.

Dynamics of heteropolymers in dilute solution: Effective equation of motion and relaxation spectrum.

The dynamics of a heteropolymer chain in solution is studied in the limit of long chain length. Using functional integral representation we derive an effective equation of motion, in which the heterogeneity of the chain manifests itself as a time-dependent excluded volume effect. At the mean field level, the heteropolymer chain is therefore dynamically equivalent to a homopolymer chain with both time-independent and time-dependent excluded volume effects. The perturbed relaxation spectrum is also calculated. We find that heterogeneity also renormalizes the relaxation spectrum. However, we find, to the lowest order in heterogeneity, that the relaxation spectrum does not exhibit any dynamic freezing, at the point when static (equilibrium) ``freezing'' transition occurs in heteropolymer. Namely, the breaking of fluctuation-dissipation theorem (FDT) proposed for spin glass dynamics does not have dynamic effect in heteropolymer, as far as relaxation spectrum is concerned. The implication of this result is discussed.

Collective degrees of freedom and multiscale dynamics in spin glasses

Collective degrees of freedom and multiscale dynamics in spin glasses

Sanov results for Glauber spin-glass dynamics

In this paper we prove a Sanov result, i.e. a Large Deviation Principle (LDP) for the distribution of the empirical measure, for the annealed Glauber dynamics of the Sherrington-Kirkpatrick spin-glass. Without restrictions on time or temperature we prove a full LDP for the asymmetric dynamics and the crucial upper large deviations bound for the symmetric dynamics. In the symmetric model a new order-parameter arises corresponding to the response function in [SoZi83]. In the asymmetric case we show that the corresponding rate function has a unique minimum, given as the solution of a self-consistent equation. The key argument used in the proofs is a general result for mixing of what is known as Large Deviation Systems (LDS) with measures obeying an independent LDP.

Glassy dynamics of nanometric magnetic particles

When a system of small magnetic particles is not very much diluted, the susceptibility peak arises from a delicate combination of individual blocking behind anisotropy barriers and collective freezing due to dipolar interactions. We have studied a sample of 4 nm Permalloy particles in alumina (25% concentration), and measured the frequency dependence of the ac susceptibility. Our scaling analysis shows that cooperative freezing effects do indeed contribute significantly to the blocking temperature; accounting for the dipolar interactions, the value obtained for individual anisotropy barriers is 10 times lower than that crudely deduced from the blocking temperature. No clear evidence of infinite-range correlations is found, in contrast with the case of spin glasses. We have studied the relaxation of the zero-field-cooled magnetization with similar procedures as used to characterize the slow dynamics of spin glasses. We find that the relaxation is weakly sensitive to waiting time effects, and is more strongly influenced by the cooling time, as is usually quoted for structural glasses.

Phase space geometry and slow dynamics

We describe a non-Arrhenius mechanism for the slowing down of dynamics that is inherent to the high dimensionality of the phase space. We show that such a mechanism is at work both in a family of mean-field spin-glass models without any domain structure and in the case of ferromagnetic domain growth. The marginality of spin-glass dynamics, as well as the existence of a `quasi-equilibrium regime' can be understood within this scenario. We discuss the question of ergodicity in an out-of equilibrium situation.

Dynamic susceptibility of a reentrant ferromagnet.

The temperature, frequency, and magnetic-field dependence of the susceptibility of the standard reentrant ferromagnet (${\mathrm{Fe}}_{0.20}$${\mathrm{Ni}}_{0.80}$${)}_{75}$${\mathrm{P}}_{16}$${\mathrm{B}}_{6}$${\mathrm{Al}}_{3}$ has been investigated by ac-susceptibility measurements. In general the magnetic response is strongly nonlinear in the magnitude of the applied field h, but a distinct low-field region is found, h${\mathit{h}}_{0}$, where the dynamic susceptibility does not depend on the magnitude of the field. Thus, ac-susceptibility or zero-field-cooled magnetization measurements in low enough fields, h${\mathit{h}}_{0}$, allow studies of the inherent zero-field dynamics of reentrant ferromagnets. A dynamic scaling analysis of low-field dynamic susceptibility data near the ferromagnetic to reentrant spin-glass transition indicates a transition to a true spin-glass phase. Magnetic aging, another signature of spin-glass dynamics, is shown to exist in the reentrant spin-glass phase by low-field time-dependent zero-field-cooled magnetization measurements. \textcopyright{} 1996 The American Physical Society.

Order-parameter flow in the SK spin-glass: II. Inclusion of microscopic memory effects

We develop further a recent dynamical replica theory to describe the dynamics of the Sherrington-Kirkpatrick spin-glass in terms of closed evolution equations for macroscopic order parameters. We show how microscopic memory effects can be included in the formalism through the introduction of a dynamic order parameter function: the joint spin-field distribution. The resulting formalism describes very accurately the relaxation phenomena observed in numerical simulations, including the typical overall slowing down of the flow that was missed by the previous simple two-parameter theory. The advanced dynamical replica theory is either exact or a very good approximation.

Large deviations for Langevin spin glass dynamics

Large deviations for Langevin spin glass dynamics

Aging in a magnetic particle system.

The influence of dipolar interaction in a frozen ferrofluid has been experimentally studied. The ferrofluid consisted of particles of $\ensuremath{\gamma}$- ${\mathrm{Fe}}_{2}$${\mathrm{O}}_{3}$ with mean diameter 70 \AA{}. Four samples with volume concentration of magnetic particles ranging from 0.03% to 17% have been investigated. The magnetic relaxation of the most concentrated particle system shows typical spin glass dynamics at low temperature, e.g., the relaxation depends on the time spent at constant temperature before applying the magnetic field---the system ages. The most diluted sample shows isolated particle dynamics and no aging.