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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Spin glass dynamics through the lens of the coherence length

Spin glass coherence lengths can be extracted from experiment and from numerical simulations. They encompasses the correlated region, and their growth in time makes them a useful tool for exploration of spin glass dynamics. Because they play the role of a fundamental length scale, they control the transition from the reversible to the chaotic state. This review explores their use for spin glass properties, ranging from scaling laws to rejuvenation and memory.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Spin-glass dynamics in the presence of a magnetic field: exploration of microscopic properties

The synergy between experiment, theory, and simulations enables a microscopic analysis of spin-glass dynamics in a magnetic field in the vicinity of and below the spin-glass transition temperature T g . The spin-glass correlation length, ξ(t, t w ; T), is analysed both in experiments and in simulations in terms of the waiting time t w after the spin glass has been cooled down to a stabilised measuring temperature T < T g and of the time t after the magnetic field is changed. This correlation length is extracted experimentally for a CuMn 6 at. % single crystal, as well as for simulations on the Janus II special-purpose supercomputer, the latter with time and length scales comparable to experiment. The non-linear magnetic susceptibility is reported from experiment and simulations, using ξ(t, t w ; T) as the scaling variable. Previous experiments are reanalysed, and disagreements about the nature of the Zeeman energy are resolved. The growth of the spin-glass magnetisation in zero-field magnetisation experiments, M ZFC (t, t w ; T), is measured from simulations, verifying the scaling relationships in the dynamical or non-equilibrium regime. Lastly, our preliminary search for the de Almeida–Thouless line in D = 3 is discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Electronic 1/f noise as a probe of dimensional effects on spin-glass dynamics

Over the past decade, spin-glass simulations have improved to the point that they now access time- and length-scales comparable to experiments at the mesoscale. A recent series of thin-film field-cooled/zero-field-cooled magnetization (FC/ZFC) experiments demonstrated activated spin dynamics, with a temperature-independent activation energy proportional to the logarithm of the film thickness and with coefficients in remarkable agreement with the simulation. These measurements require the application of small magnetic fields, which has been shown to affect the spin-glass energy landscape. Measurements of the 1/f noise in metallic spin-glasses have been previously shown to be a sensitive probe of the spin dynamics, and the measurements can be made without applying a magnetic field. In this mini-review, we review these techniques and discuss how transport measurements can fit into the current landscape of spin-glass measurements. We compare previous measurements to more recent measurements on similar films, made with ostensibly different cooling protocols, and compare both the previous and recent measurements to the magnetometry. The transport measurements—taken over a wider range of temperature than magnetometry—suggest that the maximum spin-glass energy barrier height is temperature-dependent, not fixed, possibly due to two-dimensional dynamics. We discuss this possibility, along with future measurements, which may be able to resolve this mystery.

1/f noise↗
DOE OSTI2025

Spin-glass dynamics: Experiment, theory, and simulation

This review updates the field of spin glasses with broad application to a large variety of physical systems. In particular, this review tracks the progress of experiment, theory, and large scale simulations. It highlights the importance of their synergy, from the inception of the field to the present day, and includes future opportunities for research.

Dahlberg, E. D. [Univ. of Minnesota, Minneapolis, ↗
DOE OSTI2022

Direct observation of a dynamical glass transition in a nanomagnetic artificial Hopfield network

Spin glasses, generally defined as disordered systems with randomized competing interactions, are a widely investigated complex system. Theoretical models describing spin glasses are broadly used in other complex systems, such as those describing brain function, error-correcting codes5 or stock-market dynamics. This wide interest in spin glasses provides strong motivation to generate an artificial spin glass within the framework of artificial spin ice systems. Here we present the experimental realization of an artificial spin glass consisting of dipolar coupled single-domain Ising-type nanomagnets arranged onto an interaction network that replicates the aspects of a Hopfield neural network. Using cryogenic X-ray photoemission electron microscopy (XPEEM), we performed temperature-dependent imaging of thermally driven moment fluctuations within these networks and observed characteristic features of a two-dimensional Ising spin glass. Specifically, the temperature dependence of the spin glass correlation function follows a power-law trend predicted from theoretical models on two-dimensional spin glasses. As a result, we observe clear signatures of the hard-to-observe rugged spin glass free energy in the form of sub-aging, out-of-equilibrium autocorrelations and a transition from stable to unstable dynamics.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Activated penetrant dynamics in glass forming liquids: size effects, decoupling, slaving, collective elasticity and correlation with matrix compressibility

In this work, we employ the microscopic self-consistent cooperative hopping theory of penetrant activated dynamics in glass forming viscous liquids and colloidal suspensions to address new questions over a wide range of high matrix packing fractions and penetrant-to-matrix particle size ratios. The focus is on the mean activated relaxation time of smaller tracers in a hard sphere fluid of larger particle matrices. This quantity also determines the penetrant diffusion constant and connects directly with the structural relaxation time probed in an incoherent dynamic structure factor measurement. The timescale of the non-activated fast dissipative process is also studied and is predicted to follow power laws with the contact value of the penetrant–matrix pair correlation function and the penetrant–matrix size ratio. For long time penetrant relaxation, in the relatively lower packing fraction metastable regime the local cage barriers are dominant and matrix collective elasticity effects unimportant. As packing fraction and/or penetrant size grows, much higher barriers emerge and the collective elasticity associated with the correlated matrix dynamic displacement that facilitates penetrant hopping becomes important. This results in a non-monotonic variation with packing fraction of the degree of decoupling between the matrix and penetrant alpha relaxation times. The conditions required for penetrant hopping to become slaved to the matrix alpha process are determined, which depend mainly on the penetrant to matrix particle size ratio. By analyzing the absolute and relative importance of the cage and elastic barriers we establish a mechanistic understanding of the origin of the predicted exponential growth of the penetrant hopping time with size ratio predicted at very high packing fractions. A dynamics-thermodynamics power law connection between the penetrant activation barrier and the matrix dimensionless compressibility is established as a prediction of theory, with different scaling exponents depending on whether matrix collective elasticity effects are important. Quantitative comparisons with simulations of the penetrant relaxation time, diffusion constant, and transient localization length of tracers in dense colloidal suspensions and cold viscous liquids reveal good agreements. Multiple new predictions are made that are testable via future experiments and simulations. Extension of the theoretical approach to more complex systems of high experimental interest (nonspherical molecules, semiflexible polymers, crosslinked networks) interacting via variable hard or soft repulsions and/or short range attractions is possible, including under external deformation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Pressure-induced nonmonotonic cross-over of steady relaxation dynamics in a metallic glass

Relaxation dynamics, as a key to understand glass formation and glassy properties, remains an elusive and challenging issue in condensed matter physics. In this work, in situ high-pressure synchrotron high-energy X-ray photon correlation spectroscopy has been developed to probe the atomic-scale relaxation dynamics of a cerium-based metallic glass during compression. Although the sample density continuously increases, the collective atomic motion initially slows down as generally expected and then counterintuitively accelerates with further compression (density increase), showing an unusual nonmonotonic pressure-induced steady relaxation dynamics cross-over at ~3 GPa. Furthermore, by combining in situ high-pressure synchrotron X-ray diffraction, the relaxation dynamics anomaly is evidenced to closely correlate with the dramatic changes in local atomic structures during compression, rather than monotonically scaling with either sample density or overall stress level. In conclusion, these findings could provide insight into relaxation dynamics and their relationship with local atomic structures of glasses.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Effects of Composition and Oxidation States on the Structures of Chromium-Containing Sodium Silicate Glasses: Molecular Dynamics Simulations using Machine Learning Interatomic Potentials

Chromium represents a significant challenge for the vitrification of high-level nuclear waste into silicate and borosilicate glasses due to its low solubility and variable oxidation states, which can limit the waste loading due to promotion of crystallization or phase separation during processing. In this study, we modeled chromium containing silicate glasses using molecular dynamics simulations with three machine learning interatomic potentials (MLIPs), MACE, CHGNet, and PFP were employed, to gain insights on glass composition and oxidation states on the structures of these glasses. One of the goals is to evaluate their ability of these MLIPs to accurately represent the general structure of silicate glasses and chromium local environments as a function of chromium oxidation states. Density Functional Theory (DFT) based calculations and experimental data such as neutron structure factors were used to validate the structural models. It was found that the foundation models of all three MLIPs are able to reproduce general structural features of the sodium silicate glass structure consistent with experimental and DFT data, but only CHGNet and PFP can accurately capture the oxidation states and local environment of chromium: tetrahedral for Cr6+ and octahedral for Cr3+. Furthermore, we studied the effect of varying Cr3+/ Cr6+ (Cr3+/Crtotal) ratio and total chromium content using PFP. Our results show that Cr6+ enhances network polymerization by reducing non-bridging oxygens through Na? charge compensation required due to the formation of chromate (CrO42-) species, while Cr³? acts as a network modifier that disrupts connectivity. System size effects on the structural characteristics and chromium environments were also tested using the PFP potential. This work highlights the importance of careful validation on the precision, transferability, and potential of MLIPs for modeling glasses containing transition metal elements that can exist in multiple oxidation states. It is also encouraging to see the foundational models are all three MLFFs are able to reproduce the basic sodium silicate glass structures, while suggesting additional training or refining is needed to improve the description of more complex systems containing transition metals.

Puga, Christina L.↗
DOE OSTI2021

Nature of dynamic gradients, glass formation, and collective effects in ultrathin freestanding films

Significance The origin of spatially heterogeneous alterations in the dynamics of nanoconfined liquids has been a major question in physics, chemistry, and materials science for over 30 y. We combine simulation and theory to establish a unified predictive microscopic understanding in freestanding films at low to medium molecular weight, spanning from thick to ultrathin films. The simulation-based phenomenology of altered dynamics is theoretically predicted and understood based on a combination of coupled near-interface gradients of local caging constraints and interfacial and finite size-induced changes in a collective elastic barrier to motion. No invocation of any realized or incipient critical-like phenomenon is necessary, which may have broad implications for other confined systems and the mechanism of the bulk glass transition.

nanoconfinement↗
DOE OSTI2025

Molecular Dynamics Simulation and Theoretical Analysis of Structural Relaxation, Bond Exchange Dynamics, and Glass Transition in Vitrimers

Vitrimers are a class of polymer networks featuring dynamic covalent cross-links that can undergo associative bond exchange. There has been recent interest in these materials due to their promise as recyclable thermosets or self-healing polymers because of the ability of vitrimer networks to rearrange at the molecular level and undergo macroscopic flow. However, the practical use of these materials often occurs in the supercooled regime or glassy state, where the implications of dynamic bonds are complicated by the interplay between slow activated segmental dynamics, cross-link (i.e., bond-exchange) kinetics, and ultimately material properties. Here, in this paper, we combine coarse-grained molecular dynamics simulation and microscopic statistical mechanical theory to understand how cross-linking kinetics affect material dynamics and how this couples to segmental relaxation of the polymeric network strands across a spectrum of length and time scales, especially in the supercooled regime. We characterize the Kuhn segmental alpha relaxation time and bond exchange time for vitrimer systems across various cross-link densities, temperatures, and bond exchange rates. Simulation and theory both exhibit a bending-up behavior for bond exchange time upon cooling, suggesting a coupling between bond exchange dynamics and segmental relaxation that intensifies with faster bond exchange kinetics. We also found bond exchange dynamics have an impact on Kuhn segment alpha relaxation time, which is most significant at higher cross-link densities. Both these effects are most prominent when the bond exchange time is similar to the Kuhn segment alpha relaxation time, and the resulting coupling of these two relaxation processes is tied to both the probability of a free end to find a bonded pair and the time scale of the constraints imposed by the dynamic cross-links. This relationship is reflected by a cross-link dependence of a theoretical parameter which represents the quantitative degree of coupling between bond exchange and segmental dynamics. Overall, the combination of simulation and theory clarifies the intricate interaction between bond kinetics and segmental relaxation and demonstrates the ability to provide molecular-level insights into vitrimer dynamics over a wide temperature range.

dynamic relaxation↗
DOE OSTI2024

Insights on the structure and properties of sodium iron phosphate glasses from molecular dynamics simulations

Iron phosphate glasses are promising nuclear waste forms while more detailed understanding of their structures and structure-property relations are still needed to better design waste glass compositions. In this work we report studies of three series of sodium iron phosphate (NFP) glasses: 60P 2 O 5 -(40-x)Fe 2 O 3 -xNa 2 O (x = 0→40), (100–2x)P 2 O 5 -xFe 2 O 3 -xNa 2 O (x = 5→17.5) and one with different iron redox ratio, to understand the composition as well as the iron redox effects on the structure and properties of these glasses using molecular dynamics simulations with effective two-body and three-body potentials. Structural analyses, including pair distribution function, bond angle distribution, Q n distribution, and polyhedral connectivity, were performed to obtain in-depth information on short-range and medium-range structural features. The P-O pair distributions showed a first peak splitting with phosphorus-bridging and non-bridging oxygen contributions. This and the average P-O and other cation-oxygen bond distances are in excellent agreement with experiments. The coordination number of P 5+ remained four while that of Fe 3+ increased from 4.30 to 4.72 with decreasing Fe/Na ratio. Polyhedral linkage analysis showed [PO 4 ] units linked with [PO 4 ] and [FeO x ] through corner-sharing while the [PO 4 ]-[FeO x ] linkages become dominant for compositions with Fe 2 O 3 larger than 15 mol%. The effect of iron redox ratio on the structure of NFP glasses was also studied and it was found that bond lengths and coordination numbers were not strongly affected, while the reduction of iron introduced higher network distortions, as evident by O-P-O bond angle and Q n distribution. The glass transition temperature (T g ) showed a monotonic increase with Fe 2 O 3 in the first series, in good agreement with experiments, while those of the second series showed a maximum at P 2 O 5 = 82 mol%. Here, calculated elastic moduli were found to increase with Fe 2 O 3 in the first glass series, which was be explained by the increase of network connectivity, while those of the second series decrease with Fe 2 O 3 due to decrease of P 2 O 5 .

36 MATERIALS SCIENCE↗
DOE OSTI2022

Structural magnetic glassiness in the spin ice Dy 2 Ti 2 O 7

The origin and nature of glassy dynamics presents one of the central enigmas of condensed-matter physics across a broad range of systems ranging from window glass to spin glasses. The spin-ice compound Dy 2 Ti 2 O 7 , which is perhaps best known as hosting a three-dimensional Coulomb spin liquid with magnetically charged monopole excitations, also falls out of equilibrium at low temperature. How and why it does so remains an open question. Based on an analysis of low-temperature diffuse neutron-scattering experiments employing different cooling protocols alongside recent magnetic noise studies, combined with extensive numerical modeling, we argue that upon cooling, the spins freeze into what may be termed a “structural magnetic glass,” without an a priori need for chemical or structural disorder. Specifically, our model indicates the presence of frustration on two levels, first producing a near-degenerate constrained manifold inside which phase ordering kinetics is in turn frustrated. A remarkable feature is that monopoles act as sole annealers of the spin network and their pathways and history encode the development of glass dynamics, allowing the glass formation to be visualized. Our results suggest that spin ice Dy 2 Ti 2 O 7 provides one prototype of magnetic glass formation specifically and a setting for the study of kinetically constrained systems more generally.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Superposition principle and nonlinear response in spin glasses

The extended principle of superposition has been a touchstone of spin-glass dynamics for almost 30 years. Here the Uppsala group has demonstrated its validity for the metallic spin glass, CuMn, for magnetic fields H up to 10 Oe at the reduced temperature T r = T/T g = 0.95, where T g is the spin-glass condensation temperature. For H > 10 Oe, they observe a departure from linear response which they ascribe to the development of nonlinear dynamics. The thrust of this paper is to develop a microscopic origin for this behavior by focusing on the time development of the spin-glass correlation length, ξ(t, t w ; H). Here, t is the time after H changes, and t w is the time from the quench for T > T g to the working temperature T until H changes. We connect the growth of ξ(t, t w ; H) to the barrier heights Δ(t w ) that set the dynamics. The effect of H on the magnitude of Δ (t w ) is responsible for affecting differently the two dynamical protocols associated with turning H off (TRM, or thermoremanent magnetization) or on (ZFC, or zero-field-cooled magnetization). This difference is a consequence of nonlinearity based on the effect of H on Δ (t w ). Superposition is preserved if Δ(t w ) is linear in the Hamming distance Hd (proportional to the difference between the self-overlap q EA and the overlap q[Δ(t w )]). However, superposition is violated if Δ(t w ) increases faster than linear in Hd. We have previously shown, through experiment and simulation, that the barriers Δ(t w ) do increase more rapidly than linearly with Hd through the observation that the growth of ξ(t,t w ;H) slows down as ξ(t,t w ; H) increases. In this paper, we display the difference between the zero-field-cooled ξ ZFC (t, t w ; H) and the thermoremanent magnetization ξ TRM (t, t w ; H) correlation lengths as H increases, both experimentally and through numerical simulations, corresponding to the violation of the extended principle of superposition in line with the finding of the Uppsala Group.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Deep glassy state dynamic data challenge glass models: Elastic models

The idea of an “ideal” glass transition temperature has persisted at least since the work from Kauzmann when it was observed that the entropy of glass-forming liquids extrapolated to below that of the crystal, thus suggesting the need for a phase transition at a finite or non-zero absolute temperature. This thermodynamic paradox was also found to be related to the observations of a diverging of the extrapolated viscosity or relaxation times at a temperature near to this ideal glass transition. Recently, however, we have carried out experiments using both an ancient amber material and an ultra-stable amorphous fluoropolymer that challenge the ideas of the divergence of the viscosity or relaxation times at this ideal glass transition. In the present manuscript we have evaluated two theories of the glass transition that are based on ideas related to elasticity of the amorphous glass-forming material. We find that the models from both J. Dyre and his group and of K.S. Schweizer and his group not only show non-diverging behavior but are also in some agreement with the new data, though still showing somewhat slower dynamics than those observed in the experiments. The work shows that the data are good enough to distinguish between theories and it is suggested that other mechanisms may be needed to fully describe the non-diverging responses of the ultra-stable glasses.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Effects of Surface Orientation and Termination Plane on Glass‐to‐Crystal Transformation of Lithium Disilicate by Molecular Dynamics Simulations

Glass‐to‐crystal transformation of lithium disilicate is studied using molecular dynamics simulations using an effective partial charge potential. The structural evolution of the interface between glassy and crystalline lithium disilicate is analyzed to simulate crystallization of glass on pre‐existing crystal seeds. Besides previously used atomic number density, the distribution of Q n species (Si tetrahedra with n bridging oxygen) is shown to be an effective parameter for following this transformation quantitatively. The early stages of crystal growth are significantly affected by the orientation and termination of the surface of adjacent crystal, as indicated by calculated atomic density, partial ordering, atomic segregation, and an increase in Q 3 concentration. In particular, under‐coordinated Si within the outer crystal layer is found to be most effective in transforming the amorphous structure toward crystallinity. The increase in Q 3 in the glass close to interface region most clearly shows the initial stage of lithium disilicate crystal growth.

Sun, Wei↗