Spin Glass Research Articles

Probing marginal stability in the spherical p = 2 model

Abstract In this paper, we investigate the marginally stable nature of the low-temperature trivial spin-glass phase in spherical p = 2 spin glass by perturbing the system with three different kinds of non-linear interactions. In particular, we compare the effect of three additional dense four-body interactions, namely ferromagnetic couplings, purely disordered couplings and couplings with competing disordered and ferromagnetic interactions. Our study, characterized by the effort to present in a clear and pedagogical way the derivation of all the results, shows that the marginal stability property of the spherical spin glass depends in fact on which kind of perturbation is applied to the system. In general, a certain degree of frustration is needed in the additional terms in order to induce a transition from a trivial to a non-trivial spin-glass phase. On the other hand, the addition of generic non-frustrated interactions does not destabilize the trivial spin-glass phase.

Scaling whole-chip QAOA for higher-order ising spin glass models on heavy-hex graphs

We show that the quantum approximate optimization algorithm (QAOA) for higher-order, random coefficient, heavy-hex compatible spin glass Ising models has strong parameter concentration across problem sizes from 16 up to 127 qubits for p = 1 up to p = 5, which allows for computationally efficient parameter transfer of QAOA angles. Matrix product state (MPS) simulation is used to compute noise-free QAOA performance. Hardware-compatible short-depth QAOA circuits are executed on ensembles of 100 higher-order Ising models on noisy IBM quantum superconducting processors with 16, 27, and 127 qubits using QAOA angles learned from a single 16-qubit instance using the JuliQAOA tool. We show that the best quantum processors find lower energy solutions up to p = 2 or p = 3, and find mean energies that are about a factor of two off from the noise-free distribution. We show that p = 1 QAOA energy landscapes remain very similar as the problem size increases using NISQ hardware gridsearches with up to a 414 qubit processor.

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.

Covalent Stabilization of the Iridium-Containing Oxyhydrides Sr2Mn0.5Ir0.5O3.25H0.75 and Sr2Mn0.5Ir0.5O2.66H1.33.

Reaction between Sr2Mn0.5Ir0.5O4 and CaH2 or LiH yields the iridium-containing oxyhydride phases Sr2Mn0.5Ir0.5O3.25H0.75 or Sr2Mn0.5Ir0.5O2.66H1.33, respectively. Analysis of Mn K-edge XANES data indicate the presence of Ir3+ centers in these oxyhydride phases, whose low-spin d6 configuration is consistent with the "covalent stabilization" of the metastable oxyhydride phases, as seen previously in analogous ruthenium and rhodium containing materials. Neutron powder diffraction data indicate the hydride ions are located exclusively within the "equatorial" anion sites of Sr2Mn0.5Ir0.5O3.25H0.75. In contrast, hydride ions are observed on both the equatorial and axial anion sites of Sr2Mn0.5Ir0.5O2.66H1.33. This highly unusual anion distribution is attributed to a combination of the strong trans-influence of Ir-H σ-bonds and the stabilization of fac-IrO3H3 centers by spin-orbit coupling effects. Magnetization data indicate that Sr2Mn0.5Ir0.5O4 and Sr2Mn0.5Ir0.5O3.25H0.75 adopt spin glass states at low temperature, behavior which is attributable to the cation disorder in Sr2Mn0.5Ir0.5O4 and the cation and anion disorder in Sr2Mn0.5Ir0.5O3.25H0.75. In contrast, magnetization data collected from Sr2Mn0.5Ir0.5O2.66H1.33 show no evidence of any magnetic phase transition down to 5 K, consistent with the dilution of the magnetic network by the introduction of diamagnetic Ir3+ on the formation of the oxyhydride phase.

Cluster spin glass behaviour of Co2+−Al3+ layered double hydroxides

Frequency-dependent magnetic behaviour of cobalt-aluminium layered double hydroxides (LDH) with the Co/Al ratio of 2 and 3, was studied between 2 and 300 K. It was found from analysis of the temperature-dependent ac magnetic susceptibility that these LDH exhibit a magnetic cluster spin glass behaviour regardless of their basal spacing value and the Co/Al ratio as evidenced by EA/kBT0 > 1 relation obtained using Vogel-Fulcher law. The obtained values of Mydosh parameters in the range of 0.017–0.052 suggest that some of these materials are not far from the canonical spin glasses, implying a rather small size of the magnetic clusters.

Nanostructure-induced functional combination of vanishing magnetostriction and magnetic softness in ferromagnetic (GaNi)xCoCrFe (x = 0.4–1.6) high-entropy alloys

Searching for high-entropy alloys with functional properties that emerge from their multi-scale structure, we have investigated the (GaNi)xCoCrFe (x = 0.4–1.6) system. We have characterized structure, microstructure, nanostructure and chemical composition of the individual phases in the multi-phase alloys and determined their magnetic, magnetostrictive and electrical properties. We found that the alloys are ferromagnetic and exhibit functional combination of magnetic softness and vanishing magnetostriction, classifying them as energy-efficient “supersilent” materials (inaudible to a human ear) for alternating-current (AC) electromagnetic applications in the audio-frequency range. The alloys develop a two-phase structure, a face-centered cubic (fcc) and a body-centered cubic (bcc), where the fcc phase fraction decreases, while the bcc fraction increases with the increasing (GaNi)x content. Ferromagnetism of the alloys originates from the highly nanostructured bcc phase, with the ferromagnetic Curie temperatures in the range TC = 750–700 K, depending on x. The fcc phase is not nanostructured and is paramagnetic at room temperature, but undergoes a spin glass transition at Tf≈6.4 K. The magnetic softness and vanishing magnetostriction of the alloys are both nanomagnetic phenomena. The magnetic-softness and magnetostriction parameters of the x = 1.3 and 1.6 alloys make them relevant for supersilent AC applications at low frequencies.

Superparamagnetic Relaxation in Ensembles of Ultrasmall Ferrihydrite Nanoparticles

The paper examines the impact of interparticle interactions on the superparamagnetic relaxation of ultrasmall nanoparticle ensembles, using Fe2O3∙nH2O iron oxyhydroxide (ferrihydrite) nanoparticles as an example. Two samples were analyzed: ferrihydrite of biogenic origin (with an average particle size of d ≈ 2.7 nm) with a natural organic shell, and a sample (with d ≈ 3.5 nm) that underwent low-temperature annealing, during which the organic shell was partially removed. The DC and AC magnetic susceptibilities (χ′(T), χ′′(T)) in a small magnetic field in the superparamagnetic (SPM) blocking region of the nanoparticles were measured. The results show that an increase in interparticle interactions leads to an increase in the SPM blocking temperature from 28 to 52 K according to DC magnetization data. It is shown that below the SPM blocking temperature, magnetic interactions of nanoparticles lead to the formation of a collective state similar to spin glass in bulk materials. The scaling approach reveals that the dynamics of correlated magnetic moments on the particle surface slow down with increasing interparticle interactions. Simulation of χ′′(T) dependence has shown that the dissipation of magnetic energy occurs in two stages. The first stage is directly related to the blocking of the magnetic moment of nanoparticles, while the second stage reflects the spin-glass behavior of surface spins and strongly depends on the strength of interparticle interactions.

Fragmented perspective of self-organized criticality and disorder in log gravity

We use a statistical model to discuss nonequilibrium fragmentation phenomena taking place in the stochastic dynamics of the log sector in log gravity. From the canonical Gibbs model, a combinatorial analysis reveals an important aspect of the n-particle evolution previously shown to generate a collection of random partitions according to the Ewens distribution realized in a disconnected double Hurwitz number in genus zero. By treating each possible partition as a member of an ensemble of fragmentations, and ensemble averaging over all partitions with the Hurwitz number as a special case of the Gibbs distribution, a resulting distribution of cluster sizes appears to fall as a power of the size of the cluster. Dynamical systems that exhibit a distribution of sizes giving rise to a scale-invariant power-law behavior at a critical point possess an important property called self-organized criticality. As a corollary, the log sector of log gravity is a self-organized critical system at the critical point μl = 1. A similarity between self-organized critical systems, spin glass models and the dynamics of the log sector which exhibits aging behavior reminiscent of glassy systems is pointed out by means of the Pòlya distribution, also known to classify various models of (randomly fragmented) disordered systems, and by presenting the cluster distribution in the log sector of log gravity as a distinguished member of this probability distribution. We bring arguments from a probabilistic perspective to discuss the disorder in log gravity, largely anticipated through the conjectured AdS3/LCFT2 correspondence.

Evidence for a Griffiths Phase to Cluster Spin Glass Transition in the La2/3Sr1/3(Mn1-3 xAl2 xTix)O3 System.

The presence of Griffiths phase to cluster spin glass transition has theoretically been predicted in both classical and quantum systems. However, its detection in a classical system has been lacking for decades, which hinders a complete understanding of the relationship between the Griffiths phase and cluster spin glass. Here, the experimental discovery of the Griffiths phase to cluster spin glass transition is reported in a classical magnetic system, diluted ferromagnets La2/3Sr1/3(Mn1-3 xAl2 xTix)O3 (0 ≤ x ≤ 0.12). The phase diagram of the system shows a transition from the Griffiths phase into a ferromagnetic state in the low disorder concentration range (0.01 < x ≤ 0.09). In the high disorder concentration range (0.09 < x ≤ 0.12), a Griffiths phase to cluster spin glass transition is identified, which nicely matches that of disordered quantum systems. Moreover, the Griffiths phase is essentially an unfrozen cluster spin glass with partially broken ergodicity is demonstrated experimentally. These findings serve as crucial experimental references for understanding the glassy phenomena in disordered magnets, facilitating future exploration of their unique properties and functionalities.

Free Energy Difference Fluctuations in Short-Range Spin Glasses

Free Energy Difference Fluctuations in Short-Range Spin Glasses

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, 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, Ni3(pymca)3X3 (NipymcaX where pymca = pyrimidine-2-carboxylato and X = Cl, Br). We isolated two MOFs, NipymcaCl and NipymcaBr, featuring canted Ni2+-based moments. Despite this similarity, differences in the single-ion anisotropies of the Ni2+ 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.

Intermediate-spin state of Co ions in magnetic and thermoelectric properties of double perovskite Ba2CoNbO6

Double perovskite Ba2CoNbO6, obtained by pyrolysis of nitrate-organic mixtures, was studied by XRD, XRF, DFT, AC/DC-magnetization, specific-heat, thermoelectric, and ESR methods. The sample has cubic symmetry space group Pm3m with a = b = c = 4.0074(11) Å. Deficiency in oxygen ions shows the presence of Co ions in both 3+ and 2+ valency. According to AC-magnetization and specific-heat data, Ba2CoNbO6 demonstrates spin-glass ordering at TSG = 30 K at external field value of 0.1 kOe. This temperature of spin glass transition drops with field power increase down to complete suppression at 10 kOe. The effective magnetic moment determined using the Curie-Weiss approximation is 4.29 μB, which is consistent with the theoretical estimation for Co ions in the intermediate-spin state. The peak at T = 90 K, observed in the temperature dependence of the specific heat and accompanied by a peak in the ESR linewidth, is possibly due to the structural transition at this temperature. The Seebeck coefficient of the compound is S = 4–6.5 μV/K and the band gap obtained within the small-polaron-jump conductivity model is ΔE = 0.284 eV in the temperature range of 350–550 K connected with DFT calculation. An intensity ESR line, related to Co2+ ions, was observed in ESR spectra.

Information scrambling and butterfly velocity in quantum spin glass chains

Information scrambling and butterfly velocity in quantum spin glass chains

Thermodynamic equilibrium of [formula omitted] Ising model on square lattice

We constructed a theoretical magnetic phase diagram in an external magnetic field T(P+), making it possible to determine the conditions for the existence of ferromagnets, antiferromagnets, and spin glass phases. The high-performance CUDA software package was used to the complete enumeration of all configurations of finite number spins in the ±J Ising model. We performed the rigorous numerical calculation of the partition function of N=8×8 systems of interacting spins with open boundary conditions. We used Monte Carlo methods like the Metropolis algorithm to calculate the critical temperatures for N=40×40 spins. The results of the Monte Carlo experiments are consistent with rigorous calculation data. The transition from the spin glass to the induced ferromagnetic state in an external field occurs without any critical change in the heat capacity. We used the ±J Ising model to calculate the instability line (AT—line) for the heat capacity of spin glass in the H−T diagram in an external magnetic field and the behavior of magnetic susceptibility in an external magnetic field. A rigorous calculation of the partition function allowed us to calculate all possible states and their thermodynamic probability. The calculation of the partition function meant that the model’s physics was obtained in an equilibrium state. The instability line was calculated for spin glass in the equilibrium state.

The magnetic characteristics of spinel-type MnCo2O4 at low temperatures

We report the magnetic properties of spinel oxide MnCo2O4 at low temperatures which is prepared through the sol-gel reaction process. The XPS results suggest that Mn3+ atoms exist in the octahedral sublattice originally occupied by Co3+ atoms. Afterwards, the AC susceptibility was measured at various frequencies, confirming a spin glass behavior at low temperatures. Additionally, analysis of the hysteresis loops revealed the presence of the exchange bias effect in our sample. The coexistence of spin glass behavior and the exchange bias effect in MnCo2O4 is attributed to the competition between ferromagnetic and antiferromagnetic interaction. The disorders of magnetic atoms in the lattice will also provide synergy for these magnetic behaviors.

Central limit theorem of overlap for the mean field Ghatak–Sherrington model

The Ghatak–Sherrington spin glass model is a random probability measure defined on the configuration space {0,±1,±2,…,±S}N with system size N and S⩾1 finite. This generalizes the classical Sherrington–Kirkpatrick (SK) model on the boolean cube {−1, +1}N to capture more complex behaviors, including the spontaneous inverse freezing phenomenon. We give a quantitative joint central limit theorem for the overlap and self-overlap array at sufficiently high temperature under arbitrary crystal and external fields. Our proof uses the moment method combined with the cavity approach. Compared to the SK model, the main challenge comes from the non-trivial self-overlap terms that correlate with the standard overlap terms.

Geometric Landscape Annealing as an Optimization Principle Underlying the Coherent Ising Machine

Given the fundamental importance of combinatorial optimization across many diverse domains, there has been widespread interest in the development of unconventional physical computing architectures that can deliver better solutions with lower resource costs. However, a theoretical understanding of their performance remains elusive. We develop such understanding for the case of the coherent Ising machine (CIM), a network of optical parametric oscillators that can be applied to any quadratic unconstrained binary optimization problem. We focus on how the CIM finds low-energy solutions of the Sherrington-Kirkpatrick spin glass. As the laser gain of this system is annealed, the CIM interpolates between gradient descent on coupled soft spins to descent on coupled binary spins. By combining the Kac-Rice formula, the replica method, and supersymmetry breaking, we develop a detailed understanding of the evolving geometry of the high-dimensional energy landscape of the CIM as the laser gain increases, finding several phase transitions in the landscape, from flat to rough to rigid. Additionally, we develop a novel cavity method that provides a geometric interpretation of supersymmetry breaking in terms of the reactivity of a rough landscape to specific external perturbations. Our energy landscape theory successfully matches numerical experiments, provides geometric insights into the principles of CIM operation, and yields optimal annealing schedules. Published by the American Physical Society 2024

Planar XY magnetic glass state in the Gd2ScNbO7 pyrochlore

Here a spin glass system with emergent planar ordered spin clusters is investigated. The mixed B-site pyrochlore Gd2ScNbO7has been synthesized and characterized through a variety of techniques, including x-ray diffraction, magnetic susceptibility, muon spin relaxation, heat capacity and neutron scattering. Despite a Curie-Weiss temperature of -3.93(3) K, indicating net antiferromagnetic interactions, no signs of long ranged magnetic ordering are found down toT= 0.3 K. Instead, a disordered magnetic state emerges with a small correlation length of 2.1(1) Å of single tetrahedra. A Reverse Monte Carlo analysis of the polarized neutron scattering data reveals short-range antiferromagnetic order with emergent XY spin ordering similar to the parent pyrochlore compounds. Muon spin relaxation, and AC susceptibility measurements confirm that the magnetization condenses into a glass, with 10 % of the potential entropy missing in the specific heat. This magnetic ground state is similar to what is observed in Gd2Sn2O7just above the ordering temperature, without the eventual long-range ordering at low temperature.

Small field chaos in spin glasses: Universal predictions from the ultrametric tree and comparison with numerical simulations

Replica symmetry breaking (RSB) for spin glasses predicts that the equilibrium configuration at two different magnetic fields are maximally decorrelated. We show that this theory presents quantitative predictions for this chaotic behavior under the application of a vanishing external magnetic field, in the crossover region where the field intensity scales proportionally to [Formula: see text], being N the system size. We show that RSB theory provides universal predictions for chaotic behavior: They depend only on the zero-field overlap probability function [Formula: see text] and are independent of other system features. In the infinite volume limit, each spin-glass sample is characterized by an infinite number of states that have a tree-like structure. We generate the corresponding probability distribution through efficient sampling using a representation based on the Bolthausen-Sznitman coalescent. Using solely [Formula: see text] as input we can analytically compute the statistics of the states in the region of vanishing magnetic field. In this way, we can compute the overlap probability distribution in the presence of a small vanishing field and the increase of chaoticity when increasing the field. To test our computations, we have simulated the Bethe lattice spin glass and the 4D Edwards-Anderson model, finding in both cases excellent agreement with the universal predictions.

Axial, planar-diagonal, body-diagonal fields on the cubic-spin spin glass in d=3: A plethora of ordered phases under finite fields.

A nematic phase, previously seen in the d=3 classical Heisenberg spin-glass system, occurs in the n-component cubic-spin spin-glass system, between the low-temperature spin-glass phase and the high-temperature disordered phase, for number of spin components n≥3, in spatial dimension d=3, thus constituting a liquid-crystal phase in a dirty (quenched-disordered) magnet. Furthermore, under application of a variety of uniform magnetic fields, a veritable plethora of phases is found. Under uniform magnetic fields, 17 different phases and two spin-glass phase diagram topologies (meaning the occurrences and relative positions of the many phases), qualitatively different from the conventional spin-glass phase diagram topology, are seen. The chaotic rescaling behaviors and their Lyapunov exponents are calculated in each of these spin-glass phase diagram topologies. These results are obtained from renormalization-group calculations that are exact on the d=3 hierarchical lattice and, equivalently, approximate on the cubic spatial lattice. Axial, planar-diagonal, or body-diagonal finite-strength uniform fields are applied to n=2 and 3 component cubic-spin spin-glass systems in d=3.