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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Equilibrium Dynamics of Infinite-Range Quantum Spin Glasses in a Field

We determine the low-energy spectrum and Parisi replica-symmetry-breaking function for the spin-glass phase of the quantum Ising model with infinite-range random exchange interactions and transverse and longitudinal ( h ) fields. We show that, for all h , the spin-glass state has full replica symmetry breaking and the local spin spectrum is gapless, with a spectral density that vanishes linearly with frequency. These results are obtained using an action functional—argued to yield exact results at low frequencies—that expands in powers of a spin-glass order parameter, which is bilocal in time, and a matrix in replica space. We also present the exact solution of the infinite-range spherical quantum p -rotor model at nonzero h : here, the spin-glass state has one-step replica symmetry breaking and gaplessness only appears after imposition of an additional marginal stability condition. Possible connections to experiments on random arrays of trapped Rydberg atoms are noted. Published by the American Physical Society 2024

Tikhanovskaya, Maria↗
DOE OSTI2020

Collapse of the waiting time effect in a spin glass

Waiting time measurements are reported here for a bulk polycrystalline sample of the spin glass Cu 0.95 Mn 0.05 . We observe a suppression of aging as the glass temperature is approached from below. These results are interpreted in terms of a spin-glass correlation length approaching and reaching crystallite sizes. They provide a direct experimental connection between the correlation length scale and relaxation times in the spin-glass state. In particular, these measurements track the value of the dynamic critical exponent as the system transitions from the critical temperature regime to its low-temperature, quasistatic nonequilibrium phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Spectral form factor of a quantum spin glass

It is widely expected that systems which fully thermalize are chaotic in the sense of exhibiting random-matrix statistics of their energy level spacings, whereas integrable systems exhibit Poissonian statistics. In this paper, we investigate a third class: spin glasses. These systems are partially chaotic but do not achieve full thermalization due to large free energy barriers. We examine the level spacing statistics of a canonical infinite-range quantum spin glass, the quantum p-spherical model, using an analytic path integral approach. We find statistics consistent with a direct sum of independent random matrices, and show that the number of such matrices is equal to the number of distinct metastable configurations — the exponential of the spin glass “complexity” as obtained from the quantum Thouless-Anderson-Palmer equations. We also consider the statistical properties of the complexity itself and identify a set of contributions to the path integral which suggest a Poissonian distribution for the number of metastable configurations. Our results show that level spacing statistics can probe the ergodicity-breaking in quantum spin glasses and provide a way to generalize the notion of spin glass complexity beyond models with a semi-classical limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Excess-iron driven spin glass phase in Fe 1 + y Te 1 – x Se x

The iron-chalcogenide superconductor FeTe 1– x Se x displays a variety of exotic features distinct from iron pnictides. Although much effort has been devoted to understanding the interplay between magnetism and superconductivity near x = 0.5, the existence of a spin glass phase with short-range magnetic order in the doping range ( x ~ 0.1–0.3) has rarely been studied. Here, we use DC/AC magnetization and (quasi) elastic neutron scattering to confirm the spin-glass nature of the short-range magnetic order in a Fe 1.07 Te 0.8 Se 0.2 sample. The AC-frequency dependent spin-freezing temperature T f generates a frequency sensitivity Δ T f ( ω )/[ T f ( ω )Δlog 10 ω ] ≈ 0.028 and the description of the critical slowing down with τ = τ 0 ( T f / T SG – 1) - z v gives T SG ≈ 22 K and zv ≈ 10, comparable to that of a classical spin-glass system. We have also extended the frequency-dependent T f to the smaller time scale using energy-resolution-dependent neutron diffraction measurements, in which the T N of the short-range magnetic order increases systematically with increasing energy resolution. We find that by removing the excess iron through annealing in oxygen, the spin-freezing behavior disappears, and bulk superconductivity is realized. Thus, the excess Fe is the driving force for the formation of the spin-glass phase detrimental to bulk superconductivity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Cluster-Spin-Glass Magnetic Behavior and Morphology in the Coordination Polymer Alloys Fe y Co 1– y BTT

We report the synthesis of a series of pseudo-1D coordination polymer (CP) materials with the formula Fe y Co 1–y BTT (BTT = 1,3,5-benzenetrithiolate). These materials were structurally characterized by PXRD Rietveld, EXAFS, and PDF analyses, revealing that the CP superstructure enables a continuous and isomorphous alloy between the two homometallic compounds. Lower Fe loadings exhibit emergent spin glass magnetic behavior, such as memory effects and composition-dependent spin glass response time constants ranging from 6.9 × 10 –9 s to 1.8 × 10 –6 s. These data are consistent with the formation of spin clusters within the lattice. The magnetic behavior in these materials was modeled via replica exchange Monte Carlo simulation, which provides a good match for the experimentally measured spin glassing and magnetic phase transitions. Furthermore, these findings underscore how the rigid superstructure of CP and MOF scaffolds can enable the systematic tuning of physical properties, such as the spin glass behavior described here.

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

4 d element induced improvement of structural disorder and development of weakly reentrant spin-glass behavior in NiRuMnSn

The pursuit of efficient spin polarization in quaternary Heusler alloys with the general formula XX'YZ (where X, X', and Y are transition metals and Z is a p-block element) has been a subject of significant scientific interest. While previous studies showed that isoelectronic substitution of a 4d element in place of a 3d element in quaternary Heusler alloys improves the half-metallic ferromagnetic characteristics, our research here, on the quaternary Heusler alloy NiRuMnSn, reveals a strikingly different scenario. In this study, we present a detailed structural analysis of the material using x-ray absorption fine structure and neutron diffraction techniques which confirms the formation of a single-phase compound with 50:50 site disorder between Ni and Ru atoms at 4c and 4d sites. Contrary to expectations, our density functional theory calculations suggest a considerable decrease in spin polarization even in the ordered structure. Additionally, we report on the compound's exceptional behavior, displaying a rare reentrant spin-glass property below ~ 60 K, a unique and intriguing feature for quaternary Heusler-type compounds.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Exchange bias due to coupling between coexisting antiferromagnetic and spin-glass orders

Exchange bias is a property of widespread technological utility, but its underlying mechanism remains elusive, in part because it is rooted in the interaction of coexisting order parameters in the presence of complex magnetic disorder. In this study we show that a giant exchange bias housed within a spin-glass phase arises in a disordered antiferromagnet. The magnitude and robustness of the exchange bias emerges from a convolution of two energetic landscapes, namely the highly degenerate landscape of the spin glass biased by the sublattice spin configuration of the antiferromagnet. The former provides a source of uncompensated moment, whereas the latter provides a mechanism for its pinning, which leads to the exchange bias. Tuning the relative strengths of the spin-glass and antiferromagnetic order parameters reveals a principle for tailoring the exchange bias, with potential applications to spintronic technologies.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Extracting free-energy landscapes of AgMn spin glass thin films with 1/$f$ resistance fluctuations

The temperature-dependent 1/f noise is reported for AgMn (12 at. %) thin films with multiple thicknesses ranging from 15 to 80 nm. A significant increase in the noise magnitude occurs in the spin-glass state. Analysis of the temperature-dependent exponent provides information on the energy barrier distribution and height, which in turn are related to the spin-glass coherence length. Here, we compare our results with those obtained previously on CuMn (13.5 at. %) thin films with similar thicknesses. We observe a similar trend of the increase of the barrier height with respect to thickness, but with relatively lower values for the AgMn barriers as compared to CuMn.

36 MATERIALS SCIENCE↗
DOE OSTI2021

The quantum p -spin glass model: a user manual for holographers

We study a large-N bosonic quantum mechanical sigma-model with a spherical target space subject to disordered interactions, more colloquially known as the p-spin spherical model. Replica symmetry is broken at low temperatures and for sufficiently weak quantum fluctuations, which drives the system into a spin glass (SG) phase. The first half of this paper is dedicated to a discussion of this model's thermodynamics, with particular emphasis on the marginally stable SG. This phase exhibits an emergent conformal symmetry in the strong coupling regime, which dictates its thermodynamic properties. It is associated with an extensive number of nearby states in the free energy landscape. We discuss in detail an elegant approximate solution to the SG equations, which interpolates between the conformal regime and an ultraviolet-complete short distance solution. In the second half of this paper we explore the real-time dynamics of the model and uncover quantum chaos as measured by out-of-time-order four-point functions, both numerically and analytically. We find exponential Lyapunov growth, which intricately depends on the model's couplings and becomes strongest in the quantum critical regime. We emphasize that the SG phase also exhibits quantum chaos, albeit with parametrically smaller Lyapunov exponent than in the replica symmetric phase. An analytical calculation in the marginal SG phase suggests that this Lyapunov exponent vanishes in a particular infinite coupling limit. Finally, we comment on the potential meaning of these observations from the perspective of holography.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Scaling Law Describes the Spin-Glass Response in Theory, Experiments, and Simulations

The correlation length ξ, a key quantity in glassy dynamics, can now be precisely measured for spin glasses both in experiments and in simulations. However, known analysis methods lead to discrepancies either for large external fields or close to the glass temperature. We solve this problem by introducing a scaling law that takes into account both the magnetic field and the time-dependent spin-glass correlation length. Here, the scaling law is successfully tested against experimental measurements in a CuMn single crystal and against large-scale simulations on the Janus II dedicated computer.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Replica symmetry breaking in spin glasses in the replica-free Keldysh formalism

We show that the algebra of Parisi ultrametric matrices is recovered by the real-time, replica-free, Dyson-Keldysh equations of infinite-range quantum spin glasses in the late time glassy limit. This connects to earlier results on classical and quantum systems showing how ultrametricity emerges from the persistent slow aging dynamics of the glass phase. The stationary spin glass state thereby spontaneously breaks thermal symmetry, or the Kubo-Martin-Schwinger relation of a state in global thermal equilibrium. We describe the Keldysh path integral of the infinite-range Ising model in transverse and longitudinal fields, and in the context of the Landau expansion of the action functional, show how the long-time limit connects to the full replica symmetry breaking obtained in the equilibrium formalism. We also illustrate our formalism by applying it to the spherical quantum p p -spin model, which only exhibits one-step replica symmetry breaking.

Lang, Johannes (ORCID:0000000283533392)↗
DOE OSTI2024

Observation of critical scaling in spin glasses below T c using thermoremanent magnetization

Time-dependent thermoremanent magnetization (TRM) studies have been instrumental in probing energy dynamics within the spin glass phase. In this paper, we review the evolution of the TRM experiment over the last half century and discuss some aspects related to how it has been used in the understanding of spin glasses. We also report on recent experiments using high-resolution DC SQUID magnetometry to probe the TRM at temperatures less than but near to the transition temperature T c . These experiments have been performed as a function of waiting time, temperature, and five different magnetic fields. We find that as the transition temperature is approached from below, the characteristic time scale of TRM is suppressed up to several orders of magnitude in time. In the highest-temperature region, we find that the waiting time effect subsides, and a waiting time-independent crossover line is reached. We also find that increasing the magnetic field further suppresses the crossover line. Using a first-principles energy argument across the crossover line, we derive an equation that is an excellent fit to the crossover lines for all magnetic fields probed. The data show strong evidence for critical slowing down and an H = 0 Oe phase transition.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Evidence for temperature chaos in spin glasses

We study the field cooled magnetization of a CuMn spin glass (SG) under temperature perturbations. The T-cycling curves are compared with the reference curve without temperature cycling. There is a crossover from the cumulative aging region to noncumulative aging region as the temperature change is increased. The cumulative aging range scales with the chaos length, ℓ c , becoming comparable to the correlation length, ξ, at the crossover boundary. The extracted chaos exponent, ζ=1.1, is in agreement with theoretical predictions. Furthermore, our results strongly suggest temperature chaos exists in real SG systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Quantifying Memory in Spin Glasses

Rejuvenation and memory, long considered the distinguishing features of spin glasses, have recently been proven to result from the growth of multiple length scales. This insight, enabled by simulations on the Janus II supercomputer, has opened the door to a quantitative analysis. We combine numerical simulations with comparable experiments to introduce two coefficients that quantify memory. A third coefficient has been recently presented by Freedberg et al. Here, we show that these coefficients are physically equivalent by studying their temperature and waiting-time dependence.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Collapse of the effective response time near the spin glass transition temperature

Kenning et al. discovered the collapse of the effective response time, 𝑡$^{eff}_{𝐻}$⁡(𝑡 w ;𝑇), independent of aging time, 𝑡 w , as one approached the spin glass transition temperature 𝑇 g from below. Nordblad and Lundgren observed the same effect by reducing the temperature from 𝑇 g ⁡(𝐻). We analyze the behavior of ln⁡ 𝑡$^{eff}_{𝐻}$⁡(𝑡 w ;𝑇) in the temperature range near and below 𝑇 g using a scaling law that takes into account both the magnetic field 𝐻 and the time-dependent spin-glass coherence length 𝜉⁡(𝑡,𝑡 w ;𝑇). As a result, an overdetermined predictive fit to the experimental data accounts for a quasioscillatory structure of ln ⁡𝑡$^{eff}_{𝐻}$⁡ (𝑡 w ;𝑇) as a function of magnetic field 𝐻 2 for reduced temperatures as large as 𝑇/𝑇 g = 0.98.

Frustrated magnetism↗
DOE OSTI2020

Experimental determination of the critical spin-glass correlation length in single-crystal CuMn

Using high resolution SQUID magnetometry we have made detailed measurements of the waiting time effect of the Thermoremanent Magnetization (TRM) decays on a single crystal CuMn(6%) spin glass sample near T g . In this study, we have systematically mapped the rapid decrease of the characteristic timescale tw eff , approaching T g from below, for waiting times ranging from 100 s to 100000 s. Using tw eff to determine the length scale of the growth of correlations during the waiting time, ξ TRM , (observed in both numerical studies and experiment), we observe both growth of ξ TRM in the spin glass phase and then a rapid reduction very close to T g . We interpret this reduction in ξ TRM , for all waiting times, as being governed by the critical correlation length scale ξ crit = a(T - T c ) -v .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Experimental observation of spin glass state in the highly disordered quaternary Heusler alloy FeRuMnGa

The realization of the spin-glass (SG) state in Heusler alloys is very rare despite the presence of inherent structural and elemental disorder in those compounds. Although a few half- and full-Heusler alloys are known to exhibit the SG state, there is hardly any manifestation of the same in cases of quaternary Heusler compounds. Here we report the observation of a SG state in a highly disordered equiatomic quaternary Heusler compound: FeRuMnGa where the SG state is in between the canonical SG and the cluster glass. Different intricate features of the SG state including nonequilibrium magnetic dynamics at low temperatures in the compound are unveiled through our comprehensive magnetic, heat capacity, and neutron-diffraction studies. Further the structural disorder in the sample is neither conventional A2 - nor B2 -type whereas those two types are commonly observed for Heusler compounds. The presence of disorder also plays a significant role in electron transport properties of the alloy, which is reflected in its exhibition of semimetallic behavior and anomalous Hall effect at low temperatures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Fluctuation-induced interactions and the spin-glass transition in Fe 2 TiO 5

In this work, we investigate the spin-glass transition in the strongly frustrated well-known compound Fe 2 TiO 5 . A remarkable feature of this transition, widely discussed in the literature, is its anisotropic properties: The transition manifests itself in the magnetic susceptibly only along one axis, despite Fe 3 + d 5 spins having no orbital component. We demonstrate, using neutron scattering, that below the transition temperature T g = 55 K, Fe 2 TiO 5 develops nanoscale surfboard-shaped antiferromagnetic regions in which the Fe 3 + spins are aligned perpendicular to the axis which exhibits freezing. We show that the glass transition may result from the freezing of transverse fluctuations of the magnetization of these regions and we develop a mean-field replica theory of such a transition, revealing a type of magnetic van der Waals effect.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗