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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

A brief review of spin glass magnetometry techniques

Spin glasses are inherently dynamical. Taken properly, measurements of these materials can capture their dynamics and provide a wealth of insight into the physics of the spin glass state. In this methods review, two magnetometry methods are directly compared–ac and dc. Because these measurements are taken differently, the resulting data of each method will contain different information about spin glass behavior. This review will specifically focus on how the out-of-equilibrium effects of aging, rejuvenation, and memory manifest in each of these techniques, and how to construct protocols to measure these effects. We then describe the physical significance of each type of measurement and how to interpret their results. Finally, we explicitly detail which applications are most appropriate for which method. This will help the reader select the most helpful technique to carry out their own future experiments.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Cluster spin glass correlations and dynamics in Zn 0.5⁢ Mn 0.5⁢ Te

Here, we present a combined magnetometry, muon spin-relaxation (𝜇⁢SR), and neutron-scattering study of the insulating spin glass Zn 0.5 ⁢Mn 0.5 ⁢Te, for which magnetic Mn 2+ and nonmagnetic Zn 2+ ions are randomly distributed on a face-centered cubic lattice. The magnetometry and 𝜇⁢SR results confirm a spin freezing transition around 𝑇 𝑓 ≈ 23 K, with the spin-fluctuation rate decreasing gradually and somewhat inhomogeneously through the sample volume as the temperature decreases toward 𝑇 𝑓 . Characteristic spin-correlation times well above 𝑇 𝑓 are on the order of 10 −10 s, much slower than typically observed in canonical spin glasses but in line with expectations for a cluster spin glass. Using magnetic pair distribution function (mPDF) analysis and reverse Monte Carlo (RMC) modeling of the magnetic diffuse neutron-scattering data, we show that the spin-glass ground state consists of clusters of spins exhibiting short-range-ordered type-III antiferromagnetic correlations with a locally ordered moment of 3.1⁢(1)⁢𝜇 B between nearest-neighbor spins. The type-III correlations decay exponentially as a function of spin separation distance with a correlation length of approximately 5 Å. The diffuse magnetic scattering and corresponding mPDF show no significant changes across 𝑇 𝑓 , indicating that the dynamically fluctuating short-range spin correlations in the paramagnetic state retain the same basic type-III configuration that characterizes the spin-glass state; the only change apparent from the neutron-scattering data is a gradual reduction of the correlation length and locally ordered moment with increasing temperature. Taken together, these results paint a unique and detailed picture of the local magnetic structure and dynamics in Zn 0.5 ⁢Mn 0.5⁢ Te and provide strong evidence that this material is best described as a cluster spin glass. In addition, this work showcases a statistical method for extracting diffuse scattering signals from neutron powder diffraction data, which we developed to facilitate the mPDF and RMC analysis of the neutron data. This method has the potential to be broadly useful for neutron powder diffraction experiments on a variety of materials with short-range atomic or magnetic order.

magnetism↗
DOE OSTI2025

Interplay between aging and rejuvenation in spin glasses

Aging in a single-crystal spin glass (Cu 0.92 ⁢Mn 0.08 ) has been measured using ac susceptibility techniques over a temperature range of 0.3–0.8𝑇 𝑔 . In these studies, traditional aging experiments (or “quench” aging protocols) are compared to aging curves constructed from finite-cooling-rate curves. By comparing the growth rates of spin glass order between the two types of aging curves, it is determined that quantitative comparisons between protocols that are taken by quenching and protocols using a finite cooling rate are not possible without a deeper understanding of the interplay between aging and rejuvenation. Finally, we then demonstrate that the data presented indicate that rejuvenation, rather than cumulative aging, is the cause of the discrepancies between the two growth rates.

dynamical phase transitions↗
DOE OSTI2025

Nature of temperature chaos in spin glasses

Temperature chaos (TC) in spin glasses has been claimed to exist no matter how small the temperature change, Δ⁢T. However, experimental studies have exhibited a finite value of Δ⁢T for a transition to TC. This paper explores the onset of TC with much higher resolution than before and over a larger temperature range. We find that TC is always present, though small at the smallest Δ⁢T that we can reliably measure. However, it grows rapidly as Δ⁢T increases, the region of rapid growth coinciding with the Δ⁢T predicted from renormalization group arguments and observed experimentally. Here, we are able to transcend the full range of TC, from the completely reversible state to one that is maximally decorrelated from the initially prepared state.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Investigation of experimental signatures of spin glass transition temperature

We present a series of temperature and field-dependent magnetization studies of large single-crystal spin glass samples, focusing on both field-cooled (FC) and zero-field-cooled (ZFC) magnetization studies, as well as ac susceptibility measurements. Using the above experimental techniques we aim to understand the nature of spin glass transition in presence of a field, a key factor in understanding the properties of these systems. Building on previous studies that have explored magnetic signatures indicative of spin glass transitions, our research employs a systematic approach to refine the identification of this transition temperature. Through static and dynamic measurements, we aim to shed light on the open issues regarding the key markers of spin glass transitions, enhancing our understanding of these complex systems.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Non-equilibrium dynamics in geometrically frustrated spin glass Bi 2 Fe 3 GaO 9 with a Cairo lattice

We have explored the magnetic relaxation of the spin glass phase in Bi 2 Fe 3 GaO 9 , a geometrically frustrated magnet with a unique Cairo lattice made of pentagonal building blocks. Using dc magnetization measurements, we find the relaxation behavior in single crystals follows the Arrhenius law as a function of temperature but remains relatively constant under different magnetic fields. Through a carefully designed protocol, we observe significant rejuvenation and memory effects, reminiscent of classical dilute spin glasses rather than spin jamming systems. Our finding suggests that Bi 2 Fe 3 GaO 9 is probably located in the crossover between conventional spin glass and perfect spin jam and thus provides an excellent platform for investigating the evolution of underlying magnetic structure, paving the way for further neutron scattering research.

aging↗
DOE OSTI2026

Temporal and spatial separations between spin glass and short-range order

Broken-symmetry-induced order parameters account for many phenomena in physics. For spin glasses, this framework dictates the theoretical construction, whereas experiments have only established dynamical behaviors but not the physical entity. Experimental techniques have limitations when the spin glass is probed as an isolated state. Here, we create an evolution from a long-range order using well-controlled non-magnetic substitution on a sublattice. Neutron magnetic diffuse scattering of pico-second timescale reveals that the dynamics of short- and long-range order formation are not affected by disorder, but their spatial ranges are. Across all specimens, the inflection point of spin correlation length’s temperature dependence fully matches with the peak in heat capacity, while spin glass can freeze at millisecond timescale either above or below this characteristic temperature of spin-order formation. Our results identify the spin glass as single, uncorrelated spins at domain walls between spin clusters, and an uncorrelated coexistence of the two.

Dronova, Margarita G [Okinawa Institute of 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 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

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 OSTI2025

Manipulating Cu vacancy in Yb triangular lattice Materials: Investigating the quantum disordered compound CuYbSe 2 and spin glass Cu 2.73 ⁢YbP 2

Yb-based triangular lattice materials have attracted significant attention due to their potential for hosting exotic magnetic quantum states. In this paper, we report the structural, magnetic, and thermodynamic properties of two Yb triangular lattice compounds with vacancy disorder at nonmagnetic Cu sites: CuYbSe 2 and Cu 2.73 ⁢YbP 2 . Single-crystal x-ray diffraction determines notable Cu-site vacancies in both materials. Unlike a single Cu site with 0.5 occupancy in CuYbSe 2 , Cu 2.73 ⁢YbP 2 only presents 27% vacancies on one of three Cu sites. Magnetic susceptibility measurements indicate dominant antiferromagnetic interactions between Yb 3+ ions. The effective magnetic moment is consistent with an effective spin-1/2 state of Yb 3+ . CuYbSe 2 exhibits strong magnetic anisotropy between in-plane and out-of-plane directions with the estimated exchange interactions 𝐽 𝑎 /𝑘 B = 6.48 K and 𝐽 𝑐 /𝑘 B = 2.55 K. No magnetic ordering is observed down to 0.4 K, supporting its quantum disordered ground state and candidacy as a quantum spin liquid. In contrast, Cu 2.73 ⁢YbP 2 shows clear evidence of spin freezing at 4.5 K in both magnetization and heat capacity data, indicating a spin glass state. The field-induced magnetic orders are found in CuYbSe 2 . These results highlight the critical role of structural vacancies in perturbing Yb-based triangular lattices. In conclusion, we demonstrate that while the intrinsic Yb triangular lattices are comparable, the presence of Cu vacancies can fundamentally alter the magnetic ground state—tuning the system between quantum disordered and spin glass behavior.

Frustrated magnetism↗
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 OSTI2025

Disorder-induced spin excitation continuum and spin-glass ground state in the inverse spinel CuGa 2 O 4

Spinel-structured compounds serve as prototypical examples of highly frustrated systems and are promising candidates for realizing the long-sought quantum spin liquid (QSL) state. However, structural disorder is inevitable in many real QSL candidates and its impact remains a topic of intense debate. In this work, we conduct comprehensive investigations on CuGa 2 ⁢ O 4 , a spinel compound with significant structural disorder, focusing on its thermodynamic properties and spectroscopic behaviors. No long-range magnetic order is observed down to ∼80 mK, as evidenced by magnetic susceptibility, specific-heat, and elastic neutron scattering measurements. More intriguingly, inelastic neutron scattering experiments reveal a broad gapless continuum of magnetic excitations around the Brillouin zone boundary, resembling the magnetic excitation spectra expected for a QSL. Nevertheless, a spin-freezing transition at 𝑇 f ≈ 0.88 K is identified from the cusp in the dc susceptibility curves, where a bifurcation between zero-field-cooling and field-cooling curves occurs. Furthermore, ac susceptibility measurements show a peak close to 𝑇 f at low frequency, which shifts to higher temperature with increasing frequency. These results show that CuGa 2 ⁢ O 4 has a spin-glass ground state, consistent with the establishment of short-range order inferred from the specific-heat measurements. Collectively, these results illustrate the crucial role of disorder in defining the excitation spectrum out of the disordered ground state. Furthermore, our findings shed light onto the broader class of 𝐴⁢𝐵 2 ⁢O 4 spinels and advance our understanding of the spin dynamics in magnetically disordered systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Iterative quantum optimization of spin glass problems with rapidly oscillating transverse fields

In this work, we introduce a new iterative quantum algorithm, called Iterative Symphonic Tunneling for Satisfiability problems (IST-SAT), which solves quantum spin glass optimization problems using high-frequency oscillating transverse fields. IST-SAT operates as a sequence of iterations, in which bitstrings returned from one iteration are used to set spin-dependent phases in oscillating transverse fields in the next iteration. Over several iterations, the novel mechanism of the algorithm steers the system toward the problem ground state. We benchmark IST-SAT on sets of hard MAX-3-XORSAT problem instances with exact state vector simulation, and report polynomial speedups over Trotterized adiabatic quantum computation and the best known semi-greedy classical algorithm. When IST-SAT is seeded with a sufficiently good initial approximation, the algorithm converges to exact solution(s) in a polynomial number of iterations. Our numerical results identify a critical Hamming radius, or quality of initial approximation, where the time-to-solution crosses from exponential to polynomial scaling in problem size. This work proposes IST-SAT a new quantum algorithm, which improves upon solutions obtained from initial classical or quantum optimization algorithms. The steering mechanism we introduce through IST-SAT presents a new path toward achieving quantum advantage in optimization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Spin-glass state in nickelate superconductors

Magneto-optical measurements in La 0.8 Sr 0.2 NiO 2 and Nd 0.825 Sr 0.175 NiO 2 reveal an intriguing new facet of infinite-layer nickelate superconductors: the onset of spin-glass behavior at a temperature far exceeding the superconducting critical temperature T c . This discovery sharply contrasts with copper oxide superconductors, where magnetism and superconductivity remain largely exclusive. Moreover, the magnitude and onset temperature of the polar Kerr effect in Nd 0.825 Sr 0.175 NiO 2 fabricated on SrTiO 3 and (LaAlO 3 ) 0.3 (Sr 2 TaAlO 6 ) 0.7 substrates differ dramatically, while T c does not.

FOS: Physical sciences↗
DOE OSTI2025

Spin Glass Behavior and Giant Magnetoresistance via Aliovalent Fe/Ni Alloying in Amorphous Tetrathiafulvalene-Tetrathiolate Coordination Polymers

The discovery of materials with programmable combinations of charge transport and magnetic properties is a major goal in synthetic chemistry. Molecular materials, such as coordination polymers (CPs), are emerging candidates in this field due to their synthetic modularity. While there are many conductive or magnetic CPs, single-component examples with both properties are still emerging. Here, in this work, we demonstrate how alloying paramagnetic Fe(III) centers into a highly conductive Ni-based CP results in novel amorphous materials with high conductivity and giant magnetoresistance. Aliovalent doping with paramagnetic Fe centers engenders spin-glass transitions, while Ni and the strong π-stacking interactions of tetrathiafulvalene-2,3,6,7-tetrathiolate (TTFtt) ligands support conductivity. Ni 0.69 Fe 0.31 TTFtt has σ ≈ 200 S/cm and a 1.8 K magnetoresistance of −52% at 5 T, among the largest for any coordination solid. This work demonstrates not only how magnetic properties can be rationally incorporated into conductive CPs, but also an unexpected potential for amorphous materials in spintronic applications.

amorphous materials↗
DOE OSTI2025

Scattering neutrinos, spin models, and permutations

We consider a class of Heisenberg all-to-all coupled spin models inspired by neutrino interactions in a supernova with N degrees of freedom. These models are characterized by a coupling matrix that is relatively simple in the sense that there are only a few, relative to N , nontrivial eigenvalues, in distinction to the classic Heisenberg spin-glass models, leading to distinct behavior in both the high-temperature and low-temperature regimes. When the momenta of the neutrinos are uniform and random in directions, we can calculate the large- N partition function for the quantum Heisenberg model. In particular, the high-temperature partition function predicts a non-Gaussian density of states, providing interesting counterexamples showing the limits of general theorems on the density of states for quantum spin models. We can repeat the same argument for classical Heisenberg models, also known as rotor models, and we find the high-temperature expansion is completely controlled by the eigenvalues of the coupling matrix, and again predicts non-Gaussian behavior for the density of states as long as the number of eigenvalues does not scale linearly with N . Indeed, we derive the amusing fact that these partition functions are essentially the generating function for counting permutations in the high-temperature regime. Finally, for the case relevant to neutrinos in a supernova, we identify the low-temperature phase as a unique state with the direction of the momenta of the neutrino dictating its coherent state in flavor-space, a state we dub the “flavor-momentum-locked” state. Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗