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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Chemical Design of Spin Frustration to Realize Topological Spin Glasses

Patterning spins to generate collective behavior is at the core of condensed matter physics. Physicists develop techniques, including the fabrication of magnetic nanostructures and precision layering of materials specifically to engender frustrated lattices. As chemists, we can access such exotic materials through targeted chemical synthesis and create new lattice types by chemical design. Here, in this study, we introduce a new approach to induce magnetic frustration on a modified honeycomb lattice through a competition of alternating antiferromagnetic (AFM) and ferromagnetic (FM) nearest-neighbor interactions. By subtly modulating these two types of interactions through facile synthetic modifications, we created two systems: (1) a topological spin glass and (2) a frustrated spin-canted magnet with low-temperature exchange bias. To design this unconventional magnetic lattice, we used a metal–organic framework (MOF) platform, Ni 3 (pymca) 3 X 3 (NipymcaX where pymca = pyrimidine-2-carboxylato and X = Cl, Br). We isolated two MOFs, NipymcaCl and NipymcaBr, featuring canted Ni 2+ -based moments. Despite this similarity, differences in the single-ion anisotropies of the Ni 2+ spins result in distinct magnetic properties for each material. NipymcaCl is a topological spin glass, while NipymcaBr is a rare frustrated magnet with low-temperature exchange bias. Density functional theory calculations and Monte Carlo simulations on the NipymcaX lattice support the presence of magnetic frustration as a result of alternating AFM and FM interactions. Our calculations enabled us to determine the ground-state spin configuration and the distribution of spin–spin correlations relative to paradigmatic kagomé and triangular lattices. This modified honeycomb lattice is similar to the electronic Kekulé-O phase in graphene and provides a highly tunable platform to realize unconventional spin physics.

Exchange bias↗
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 OSTI2024

Toward understanding the dimensional crossover of canonical spin-glass thin films

Spin-glass thin films exhibit many features different from the bulk. The freezing temperatures of spin-glass films are suppressed for reduced thickness and follow the Kenning relation. The dynamics are altered near the vacuum interface. These phenomena are closely related to the lower critical dimension of spin glasses, the spin-glass correlation length, and the dimensional crossover from d = 3 to d = 2. In this article, we review the experimental facts and theoretical perspectives for spin-glass thin films. We focus on canonical spin-glass systems with the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction between magnetic impurities in a nonmagnetic host. Open questions to be addressed are emphasized.

interfacial effects↗
DOE OSTI2020

Confinement, reduced entanglement, and spin-glass order in a random quantum spin-ice model

In this work, we study an effective spin model derived perturbatively from a random transverse-field Ising model on the pyrochlore lattice. The model consists of spin configurations on the pyrochlore lattice, restricted to the spin-ice subspace, with spins interacting with random Ising exchange couplings as well as ring exchanges along the hexagons of the lattice. This model is studied by exact diagonalization up to N=64 site systems. Furthermore, we calculate spin-glass correlation functions and local entanglement entropy S T between spins in a single tetrahedron and the rest of the system. We find that the model undergoes two phase transitions. At weak randomness the model is in a quantum spin-ice phase where S T =ln 6. Increasing randomness, at low transverse fields, first leads to a frozen phase, with long-range spin-glass order and S T =ln 2 corresponding to the Cat states associated with Ising order. Further increase in randomness leads to a random resonating-hexagon phase with a frozen backbone of spins and a broad distribution of entanglement entropies. The implications of these studies for non-Kramers rare-earth pyrochlores are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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 OSTI2022

Spin liquid to spin glass crossover in the random quantum Heisenberg magnet

We study quantum SU($M$) spins with all-to-all and random Heisenberg exchange interactions of root-mean-square strength $J$. The $M \rightarrow \infty$ model has a spin liquid ground state with the spinons obeying the equations of the Sachdev-Ye-Kitaev (SYK) model. Numerical studies of the SU(2) model with $S=1/2$ spins show spin glass order in the ground state, but also display SYK spin liquid behavior in the intermediate frequency spin spectrum. We employ a $1/M$ expansion to describe the crossover from fractionalized fermionic spinons to a confining spin glass state with weak spin glass order $q_{EA}$. The SYK spin liquid behavior persists down to a frequency $\omega_\ast \sim J q_{EA}$, and for $\omega < \omega_\ast$, the spectral density is linear in $\omega$, thus quenching the extensive zero temperature entropy of the spin liquid. Furthermore, the linear $\omega$ spectrum is qualitatively similar to that obtained earlier using bosonic spinons for large $q_{EA}$. We argue that the extensive SYK spin liquid entropy is transformed as $T \rightarrow 0$ to an extensive complexity of the spin glass state.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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 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 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 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 OSTI2023

Neutron scattering study of fluctuating and static spin correlations in the anisotropic spin glass Fe 2 Ti O 5

The anisotropic spin-glass transition, in which spin freezing is observed only along the c axis in pseudobrookite Fe 2 TiO 5 , has long been perplexing because the Fe 3+ moments (d 5 ) are expected to be isotropic. Recently, neutron diffraction demonstrated that surfboard-shaped antiferromagnetic nanoregions coalesce above the glass transition temperature T g ≈55K, and a model was proposed in which the freezing of the surfboard magnetization fluctuations leads to the anisotropic spin-glass state. Given this model, we have carried out high-resolution inelastic neutron scattering measurements of the spin-spin correlations to understand the temperature dependence of the intrasurfboard spin dynamics on neutron (picosecond) timescales. Here, in this paper, we report on the temperature-dependence of the spin fluctuations measured from single-crystal Fe 2 TiO 5 . Strong quasi-elastic magnetic scattering, arising from intrasurfboard correlations, is observed well above T g . The spin fluctuations possess a steep energy–wave vector relation and are indicative of strong exchange interactions, consistent with the large Curie-Weiss temperature. As the temperature approaches T g from above, a shift in spectral weight from inelastic to elastic scattering is observed. At various temperatures between 4 and 300 K, a characteristic relaxation rate of the fluctuations is determined. Despite the freezing of most of the spin correlations, an inelastic contribution remains even at base temperature, signifying the presence of fluctuating intrasurfboard spin correlations to at least T/T g ≈0.1 , consistent with an energy landscape that is a hybrid between conventional and geometrically frustrated spin glasses.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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 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↗