Spin Glass Systems Research Articles

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.

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.

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.

Hysteretic response to different modes of ramping an external field in sparse and dense Ising spin glasses

We consider the hysteretic behavior of Ising spin glasses at T=0 for various modes of driving. Previous studies mostly focused on an infinitely slow speed Ḣ by which the external field H was ramped to trigger avalanches of spin flips by starting with destabilizing a single spin while few have focused on the effect of different driving methods. First, we show that this conventional protocol imposes a system size dependence. Then, we numerically analyze the response of Ising spin glasses at rates Ḣ that are fixed as well, to elucidate the differences in the response. Specifically, we compare three different modes of ramping (Ḣ=c/N, Ḣ=c/N, and Ḣ=c for constant c) for two types of spin glass systems of size N, representing dense networks by the Sherrington–Kirkpatrick model and sparse networks by the lattice spin glass in d=3 dimensions known as the Edwards Anderson model. Depending on the mode of ramping, we find that the response of each system, in form of spin-flip avalanches and other observables, can vary considerably. In particular, in the N-independent mode applied to the lattice spin glass, which is closest to experimental reality, we observe a percolation transition with a broad avalanche distribution between phases of localized and system-spanning responses. We explore implications for combinatorial optimization problems pertaining to sparse systems.

Nematic phase of the n-component cubic-spin spin glass in d = 3: Liquid-crystal phase in a dirty magnet

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 components n≥3, in spatial dimension d=3, thus constituting a liquid-crystal phase in a dirty (quenched-disordered) magnet. This result is obtained from renormalization-group calculations that are exact on the hierarchical lattice and, equivalently, approximate on the cubic spatial lattice. The nematic phase completely intervenes between the spin-glass phase and the disordered phase. The Lyapunov exponents of the spin-glass chaos are calculated from n=1 up to n=12 and show odd-even oscillations with respect to n.

Exploring the critical behavior of the anomalous spin-glass transition in Ga1−xMnxS

Single-crystalline Ga1−xMnxS is a quasi-two-dimensional system that exhibits an anomalous spin-glass transition temperature compared with the other well-known spin-glass systems. In contrast to the other known spin-glasses that all have three-dimensional structures, our host chalcogenide GaS system is quasi-two-dimensional. Recent interest in utilizing spin-glass materials for applications in short-term, low-energy memory and processing power make this new 2-D system important for further exploration. We report on the critical behavior of the anomalous spin-glass transition in a single-crystalline Ga0.91Mn0.09S system. Using the scaling equation of state describing the spin-glass transition in Ga1−xMnxS, we obtained the relation χnl = C1H2/δ and extract the value δ = 5.5 ± 0.5 for this critical exponent as well as a value of ϕ = 4.8 for another critical exponent. We find this value of delta for the critical temperature Tc = 11.2 K, combined with the other critical exponents γ = 4.0 and β = 0.8 form a self-consistent description of the spin-glass transition in this unusual 2-D spin-glass system. Interestingly, these results represent convincing evidence that, despite Ga1−xMnxS having a quasi-two-dimensional structure, Ga1−xMnxS undergoes a true spin-glass transition and is related to the class of semiconducting spin-glass materials with short-range interactions. The spin-glass transition in Ga1−xMnxS is characterized by critical exponents similar to the three-dimensional spin-glass systems.

Proof of Avoidability of the Quantum First-Order Transition in Transverse Magnetization in Quantum Annealing of Finite-Dimensional Spin Glasses

It is rigorously shown that an appropriate quantum annealing for any finite-dimensional spin system has no quantum first-order transition in transverse magnetization. This result can be applied to finite-dimensional spin-glass systems, where the ground state search problem is known to be hard to solve. Consequently, it is strongly suggested that the quantum first-order transition in transverse magnetization is not fatal to the difficulty of combinatorial optimization problems in quantum annealing.

Magnetic boson peak in classical spin glasses

We revisited spin dynamics in archetypical classical spin-glass (SG) systems, such as Cu1−xMnx (x=0.017, 0.034, and 0.067) dilute alloys and iron aluminosilicate glass, using a modern neutron scattering spectrometer with high neutron flux. The former is crystalline, and the latter is amorphous, where their SG state is well separated from magnetically ordered phases. Bose-scaled localized magnetic excitations were observed in both compounds below the spin-freezing temperature (Tf). The spectrum exhibits a maximum at low energy and a broad tail on the high-energy side. The excitation energy tends to be higher for the material with higher Tf. Above Tf, the spectrum considerably changes with temperature, thereby indicating the emergence of the magnetic relaxation process. The magnetic excitation in the SG state has much in common with the boson peak in structural glasses. We consider that the Bose-scaled broad excitation peak is an elementary excitation inherent in disordered systems. Published by the American Physical Society 2024

High-Pressure Synthesis, Crystal Structure, and Physical Properties of a Spinel Compound Co0.7Al2S4.

In this paper, we report on the discovery of a spinel compound, Co0.7Al2S4, which was synthesized at high-pressure. The systematic characterizations were carried out by structural, magnetic, and heat capacity measurements. The compound crystallizes into a cubic structure with the space group Fd3̅m (no. 227) and the lattice constant a = 9.9580(1) Å. Magnetic susceptibility measurements suggest that Co0.7Al2S4 exhibits a spin glass ground state, freezing at Tf ∼ 7.2 K with a Weiss temperature Tθ ∼ -115.9 K, which is verified by ac magnetic susceptibility and heat capacity measurements. The frustration parameter f for Co0.7Al2S4 is calculated to be about 16.6, based on the formula f = | Tθ/Tf |, indicating that Co0.7Al2S4 is a high-frustration magnet. Specific heat data displays a T2 dependence below the freezing temperature, which is different from the linear dependence observed in a common spin glass system. Compared with the similar compound CoAl2O4, it is suggested that the vacancies in the Co sites should be responsible for the occurrence of the spin glass behavior of Co0.7Al2S4.

Optimized analysis of the AC magnetic susceptibility data in several spin-glass systems using the Vogel–Fulcher and Power laws

In spin-glasses (SG), the relaxation time τ (=1/2πf) vs Tf data at the peak position Tf in the temperature variation of the ac magnetic susceptibilities at different frequencies f is often fit to the Vogel–Fulcher Law (VFL): τ = τ0 exp[Ea/kB(Tf − T0)] and to the Power Law (PL): τ = τ0* [(Tf−TSG)/TSG]−zυ. Both of these laws have three fitting parameters each, leaving a degree of uncertainty since the magnitudes of the evaluated parameters τ0, Ea/kB, τ0*, and zυ depend strongly on the choice of T0 and TSG. Here, we report an optimized procedure for the analysis of τ vs Tf data on seventeen SG systems for which we could extract such data from published sources. In this optimized method, the data of τ vs Tf are fit by varying T0 in the linear plots of Ln τ vs 1/(Tf − T0) for the VFL and by varying TSG in the linear plot of Ln τ vs Ln (Tf − TSG)/TSG for the PL until optimum fits are obtained. The analysis of the associated magnitudes of τ0, Ea/kB,τ0*, and zυ for these optimum values of T0 and TSG shows that the magnitudes of τ0*, τ0, and zυ fail to provide a clear distinction between canonical and cluster SG. However, new results emerge showing Ea/(kBT0) < 1 in canonical SG, whereas Ea/(kBT0) >1 for cluster SG systems, and the optimized T0 < optimized TSG in all cases. Although some interpretation of these new results is presented, a more rigorous theoretical justification of the boundary near Ea/(kBT0) ∼ 1 is desired along with testing of these criteria in other SG systems.

Driven and non-driven surface chaos in spin-glass sponges

A spin-glass system with a smooth or fractal outer surface is studied by renormalization-group theory, in bulk spatial dimension d=3. Independently varying the surface and bulk random-interaction strengths, phase diagrams are calculated. The smooth surface does not have spin-glass ordering in the absence of bulk spin-glass ordering and always has spin-glass ordering when the bulk is spin-glass ordered. With fractal (d>2) surfaces, a sponge is obtained and has surface spin-glass ordering also in the absence of bulk spin-glass ordering. The phase diagram has the only-surface-spin-glass ordered phase, the bulk and surface spin-glass ordered phase, and the disordered phase, and a special multicritical point where these three phases meet. All spin-glass phases have distinct chaotic renormalization-group trajectories, with distinct Lyapunov and runaway exponents which we have calculated.

Enhancement of the magnetocaloric effect in geometrically frustrated cluster spin glass systems

In this work, we theoretically demonstrate that a strong enhancement of the magnetocaloric effect is achieved in geometrically frustrated cluster spin-glass systems just above the freezing temperature. We consider a network of clusters interacting randomly which have triangular structure composed of Ising spins interacting antiferromagnetically. The intercluster disorder problem is treated using a cluster spin glass mean-field theory, which allows exact solution of the disordered problem. The intracluster part can be solved using exact enumeration. The coupling between the inter and intracluster problem incorporates the interplay between effects coming from geometric frustration and disorder. As a result, it is shown that there is the onset of cluster spin glass phase even with very weak disorder. Remarkably, it is exactly within a range of very weak disorder and small magnetic field that is observed the strongest isothermal release of entropy.

Magnetic proximity in a coupled ferromagnet–spin glass system

We study the competition between ferromagnetic and spin glass phases using a system of coupled infinite-range Ising and Sherrington-Kirkpatrick models. We obtain the replica-symmetric solution for the free energy of this system in terms of magnetization and Edwards-Anderson order parameters in both subsystems. Using these order parameters we are able to identify different phases in the system and determine which phase is dominant for different strengths of the coupling between two subsystems. We observe that both subsystems are in the same phase although with different order parameters. The phase boundary between paramagnetic-ferromagnetic and paramagnetic--spin glass phases is more or less similar to that in the Sherrington-Kirkpatrick phase diagram. But the boundary between ferromagnetic--spin glass phases becomes qualitatively different as the coupling between the two subsystems changes. Remarkably, for intermediate values of the coupling, this phase boundary is such that there could be a reentrant transition between spin glass and ferromagnetic phases by increasing the temperature. We found that for some range of the coupling, the second-order transition between these phases turns into first order at a tricritical point. Further, we carry out the stability analysis by considering deviations from the replica-symmetric solution.

Nematic ordering in the Heisenberg spin-glass system in three dimensions.

Nematic ordering, where the spins globally align along a spontaneously chosen axis irrespective of direction, occurs in spin-glass systems of classical Heisenberg spins in d=3. In this system where the nearest-neighbor interactions are quenched randomly ferromagnetic or antiferromagnetic, instead of the locally randomly ordered spin-glass phase, the system orders globally as a nematic phase. This nematic ordering of the Heisenberg spin-glass system is dramatically different from the spin-glass ordering of the Ising spin-glass system. The system is solved exactly on a hierarchical lattice and, equivalently, Migdal-Kadanoff approximately on a cubic lattice. The global phase diagram is calculated, exhibiting this nematic phase, and ferromagnetic, antiferromagnetic, disordered phases. The nematic phase of the classical Heisenberg spin-glass system is also found in other dimensions d>2: We calculate nematic transition temperatures in 24 different dimensions in 2<d≤4.

The Restricted Boltzmann Machine Ansatz through Adiabiatic Routes

We discuss the expressive power of the quantum restricted Boltzmann machine Ansatz in order to represent faithfully the operation process of a quantum spin-glass system undergoing an adiabatic quantum computation process. We address both the representability and the trainability problems associated to the restricted Boltzmann machine Ansatz when we try to describe the ground state of a quantum Ising spin-glass in a transverse field. In our approach, we obtain the ground state of the system using exact diagonalization and find the optimal restricted Boltzman machine. Our preliminary results show that due to the complex spin-glass landscape, for some topologies of the restricted Bolztmann machine, the parameters of the representation are hard to be found.

Nonreciprocal Directional Dichroism in Magnetoelectric Spin Glass.

Optical absorption spectra in the visible and near-infrared light were measured for magnetoelectric spin glass Ni_{0.4}Mn_{0.6}TiO_{3} under various field-cooled conditions. Despite the absence of long-range magnetic-dipole order, this spin-glass system exhibits nonreciprocal directional dichroism (NDD) at zero external field after a magnetoelectric field-cooled procedure. This result is distinct from previous studies on NDD in systems with magnetic toroidal moments induced either by long-range magnetic-dipole order or by applying crossed electric and magnetic fields. The present Letter conclusively demonstrates that the observed NDD originates from magnetoelectrically induced ferroic order of magnetic toroidal moments without conventional magnetic-dipole order.

Nonlinear PDEs approach to statistical mechanics of dense associative memories

Dense associative memories (DAMs) are widely used models in artificial intelligence for pattern recognition tasks; computationally, they have been proven to be robust against adversarial inputs and, theoretically, leveraging their analogy with spin-glass systems, they are usually treated by means of statistical-mechanics tools. Here, we develop analytical methods, based on nonlinear partial differential equations, to investigate their functioning. In particular, we prove differential identities involving DAM’s partition function and macroscopic observables useful for a qualitative and quantitative analysis of the system. These results allow for a deeper comprehension of the mechanisms underlying DAMs and provide interdisciplinary tools for their study.

Phase relations, structure, properties and DFT study of compounds in the Sc-rich part of the systems Sc-{Mn,Fe,Co,Ni}-Ga

Phase relations, structure, properties and DFT study of compounds in the Sc-rich part of the systems Sc-{Mn,Fe,Co,Ni}-Ga

Stochastic fluctuations promote ordered pattern formation of cells in the Notch-Delta signaling pathway.

The Notch-Delta signaling pathway mediates cell differentiation implicated in many regulatory processes including spatiotemporal patterning in tissues by promoting alternate cell fates between neighboring cells. At the multicellular level, this "lateral inhibition” principle leads to checkerboard patterns with alternation of Sender and Receiver cells. While it is well known that stochasticity modulates cell fate specification, little is known about how stochastic fluctuations at the cellular level propagate during multicell pattern formation. Here, we model stochastic fluctuations in the Notch-Delta pathway in the presence of two different noise types–shot and white–for a multicell system. Our results show that intermediate fluctuations reduce disorder and guide the multicell lattice toward checkerboard-like patterns. By further analyzing cell fate transition events, we demonstrate that intermediate noise amplitudes provide enough perturbation to facilitate “proofreading” of disordered patterns and cause cells to switch to the correct ordered state (Sender surrounded by Receivers, and vice versa). Conversely, high noise can override environmental signals coming from neighboring cells and lead to switching between ordered and disordered patterns. Therefore, in analogy with spin glass systems, intermediate noise levels allow the multicell Notch system to escape frustrated patterns and relax towards the lower energy checkerboard pattern while at large noise levels the system is unable to find this ordered base of attraction.

Spin-Glass-Like Behavior in Mn3Ga0.3Sn0.7N Compound

The magnetic transition, thermal property, and the distance of Mn–Mn of Mn3Ga0.3Sn0.7N compound with the Sn element substitution of Ga in Mn3GaN compounds were investigated. Magnetic measurements indicate that the existence of spin glass system at high temperature (502 K) in Mn3Ga0.3Sn0.7N compound may be attributed to competing antiferromagnetic (AFM) and ferromagnetic (FM) interactions due to the doped Sn inducing ferromagnetic orders in Mn3GaN and the partially random Sn substitute Ga at a corner site of the lattice. It is not clear how much role the pure Sn power, which is not doped into Ga site completely, played in inducing the magnetic characteristic. This finding will be helpful to reveal the mechanism of the antiperovskites’ intriguing physics properties and to develop more smart materials.