Ising System Research Articles

Optimizing hybrid ferromagnetic metal–ferrimagnetic insulator spin-Hall nano-oscillators: A micromagnetic study

Spin-Hall nano-oscillators (SHNOs) are nanoscale spintronic devices that generate high-frequency (GHz) microwave signals useful for various applications, such as neuromorphic computing and creating Ising systems. Recent research demonstrated that hybrid SHNOs consisting of a ferromagnetic metal (permalloy) and lithium ferrite-based (LAFO) insulating ferrimagnetic thin films have advantages in having lower auto-oscillation threshold currents (Ith) and generating larger microwave output power, making this hybrid structure an attractive candidate for spintronic applications. It is essential to understand how the tunable material properties of LAFO, e.g., its thickness, perpendicular magnetic anisotropy (Ku,LAFO), and saturation magnetization (Ms,LAFO), affect magnetic dynamics in hybrid SHNOs. We investigate the change in Ith and the output power of the device as the LAFO parameters vary. We find the Ith does not depend strongly on these parameters, but the output power has a highly nonlinear dependence on Ms,LAFO and Ku,LAFO. We further investigate the nature of the excited spin-wave modes as a function of Ku,LAFO and determine a critical value of Ku,LAFO above which propagating spin-waves are excited. Our simulation results provide a roadmap for designing hybrid SHNOs to achieve targeted spin excitation characteristics.

Antiferromagnetic Ising model in a triangular vortex lattice of quantum fluids of light.

Vortices are topologically distinctive objects appearing as phase twists in coherent fields of optical beams and Bose-Einstein condensates. Structured networks and artificial lattices of coupled vortices could offer a powerful platform to study and simulate interaction mechanisms between constituents of condensed matter systems, such as antiferromagnetic interactions, by replacement of spin angular momentum with orbital angular momentum. Here, we realize such a platform using a macroscopic quantum fluid of light based on exciton-polariton condensates. We imprint all-optical hexagonal lattice that results into a triangular vortex lattice, with each cell having a vortex of charge l = ±1. We reveal that pairs of coupled condensates spontaneously arrange their orbital angular momentum antiparallel, implying a form of artificial orbital "antiferromagnetism." We discover that correlation exists between the emergent vortex patterns in triangular condensate lattices and the low-energy solutions of the corresponding antiferromagnetic Ising system. Our study offers a path toward spontaneously ordered vortex arrays with nearly arbitrary configurations and controlled couplings.

LiHoF4 as a spin-half non-standard quantum Ising system

LiHoF_{4}4 is a magnetic material known for its Ising-type anisotropy, making it a model system for studying quantum magnetism. However, the theoretical description of LiHoF_{4}4 using the quantum Ising model has shown discrepancies in its phase diagram, particularly in the regime dominated by thermal fluctuations. In this study, we investigate the role of off-diagonal dipolar terms in LiHoF_{4}4, previously neglected, in determining its properties. We analytically derive the low-energy effective Hamiltonian of LiHoF_{4}4, including the off-diagonal dipolar terms perturbatively, both in the absence and presence of a transverse field. Our results encompass the full phase diagram, confirming the significance of the off-diagonal dipolar terms in reducing the zero-field critical temperature and determining the critical temperature’s dependence on the transverse field. We also highlight the sensitivity of this mechanism to the crystal structure by comparing our calculations with the Fe_{8}8 system.

Effect of Ferromagnetic Exchange Interaction and Crystalline Anisotropy on a Double-Cubic Spin-½ Spin-1 Ising System with a Free Surface

In this study, we employ Monte Carlo simulations to explore the magnetic characteristics of a double-cubic spin-½ and spin-1 ferromagnetic Ising superlattice system, focusing on the impact of surface exchange coupling, anisotropy, and layer thickness. We implemented free boundary conditions along the dimension with an exposed surface. Our findings illuminate the key role played by surface exchange coupling (JAS), which significantly influences the critical temperature (Tc), underscoring its ability to strengthen ferromagnetic interactions within the system. In contrast, the compensation temperature (Tcomp) exhibits relative stability. Furthermore, we unveil the crucial influence of crystalline anisotropy on Tcomp, with higher anisotropy values leading to its augmentation, while Tc remains unaffected. Moreover, when the number of layers is increased from 11 to 21, a marked rise in Tc is observed, accompanied by a minor increment in Tcomp, particularly evident under negative anisotropy conditions.

Nuclear magnetic resonance studies in a model transverse field Ising system

The suppression of ferroquadrupolar order in TmVO4 in a magnetic field is well-described by the transverse field Ising model, enabling detailed studies of critical dynamics near the quantum phase transition. We describe nuclear magnetic resonance measurements in pure and Y-doped single crystals. The non-Kramers nature of the ground state doublet leads to a unique form of the hyperfine coupling that exclusively probes the transverse field susceptibility. Our results show that this quantity diverges at the critical field, in contrast to the mean-field prediction. Furthermore, we find evidence for quantum critical fluctuations present near Tm-rich regions in Y-doped crystals at levels beyond which long-range order is suppressed, suggesting the presence of quantum Griffiths phases.

Coupled parametric oscillators: From disorder-induced current to asymmetric Ising model

We study the effects of the interplay of weak disorder and weak coupling in a system of parametric micromechanical oscillators. Each oscillator is bistable, enabling the mapping of its stable states onto spin states. The coupling changes the rate of interstate switching of an oscillator depending on the state of other oscillators. We demonstrate that the change is exponentially strong and therefore manifests even for weak coupling. Difference in the oscillator eigenfrequencies translates into disorder in the system. The analysis and the experiment show that disorder leads to a nontrivial stationary state that displays current. The system provides a well-controlled and fully characterized implementation of the asymmetric Ising model, in which coupled spins affect each other differently. This model plays an important role in physics and biology. Our findings open the possibilities of constructing and exploring asymmetric Ising systems with controlled parameters and connectivity. Published by the American Physical Society 2024

Magnetic properties of a ferrimagnetic transverse Ising system on the multilayer kagome-like lattice

Based on the Trotter-Suzuki formula, the transverse Ising model is proposed to investigate the magnetic properties of a ferrimagnetic multilayer kagome-like lattice by Monte Carlo simulation. When different parameters are considered, the rich magnetization profiles and the multi-loop hysteresis behaviors are observed. It is found that there is a small peak in the transverse magnetization curve, which is related to the phase transition temperature.

Classical spin-liquid behavior in interactionally distorted antiferromagnetic spin systems on the kagome lattice

The influence of an interaction distortion of the antiferromagnetic system on the kagome lattice on its magnetic and thermodynamic properties is investigated in the framework of the antiferromagnetic J1−J2−J3 spin-1/2 Ising system with three different nearest-neighbor antiferromagnetic interactions on the star kagome-like recursive lattice. The exact solution of the model is found and the phase diagram is determined and analyzed. It is shown that, depending on the model parameters, three antiferromagnetic phases can be identified, which are separated from the paramagnetic phase by the second order phase transitions. The magnetic and entropy properties of all ground states of the model are determined. Three different ground states that arise from the paramagnetic phase in the zero-temperature limit are identified. Due to the frustration, each of these ground states is highly macroscopically degenerated with different values of the residual entropy. In addition, since the paramagnetic phase in the vicinity of these ground states also exhibits high degeneracy with the presence of strong correlations, related to the proximity of the second-order phase transitions, these ground states together with their immediate paramagnetic surroundings can be considered as regions with the classical spin-liquid behavior. It is also shown that the typical anomalous (Schottky-type) behavior of the specific heat with the existence of a two-peak (in general multi-peak) structure in its temperature dependence in the vicinity of the highly macroscopically degenerated ground states can be suppressed by the presence of the second-order phase transitions.

Effect of Cooling Rate on Dynamic Magnetic Hysteresis Loop Behaviors of Magnetic Materials by Using as a Model Mixed Spin (1, 3/2) Ising System Under an Oscillating Magnetic Field

Effect of Cooling Rate on Dynamic Magnetic Hysteresis Loop Behaviors of Magnetic Materials by Using as a Model Mixed Spin (1, 3/2) Ising System Under an Oscillating Magnetic Field

Magnetic properties and compensation temperatures of a graphene bilayer by Monte Carlo simulation

We used Monte Carlo simulation to study the magnetic properties and compensation behavior of a ferrimagnetic mixed-spin (3/2; 1/2) Ising system in a graphene bilayer. The effects of exchange interactions, crystal field, external magnetic field and temperature on the total magnetization, partial magnetizations, magnetic susceptibility, phase diagram and hysteresis behavior of the system were examined. Interesting results were obtained in this work, such as the compensation behavior and the multi-loop hysteresis phenomenon for specific values of the system’s physical parameters. Our results conform to those of other theoretical studies.

Mean-field study of magnetic properties and hysteresis behavior in a bilayer graphene Ising system

Using the mean-field approximation based on the Gibbs-Bogoliubov inequality for the free energy, we conducted an investigation into the magnetic properties and hysteresis behavior of a graphene Ising bilayer, where the top and bottom layers are occupied by spins σ = 3/2 and S = 5/2, respectively. The effects of exchange interactions, crystal fields, external magnetic field and temperature on the total magnetization, partial magnetizations of each layer, total magnetic susceptibility, blocking temperature and hysteresis loops of the system were thoroughly analyzed. The variations of the blocking temperature as a function of various parameters in the system’s Hamiltonian were presented. Furthermore, we demonstrated the existence of multiple hysteresis loop behaviors under specific physical conditions.

Paradigm for approaching the forbidden spontaneous phase transition in the one-dimensional Ising model at a fixed finite temperature

The Ising model describes collective behaviors such as phase transitions and critical phenomena in various physical, biological, economical, and social systems. It is well known that spontaneous phase transition at finite temperature does not exist in the Ising model with short-range interactions in one dimension. Yet, little is known about whether this forbidden phase transition can be approached arbitrarily closely—at fixed finite temperature. Here I use symmetry analysis of the transfer matrix to reveal the existence of spontaneous ultranarrow phase crossover (UNPC) at finite temperature in one class of one-dimensional Ising models on decorated two-leg ladders, in which the crossover temperature T0 is determined solely by on-rung interactions and decorations, while the crossover width 2δT is independently, exponentially reduced (δT=0 means a genuine phase transition) by on-leg interactions and decorations. These findings establish a simple ideal paradigm for realizing an infinite number of one-dimensional Ising systems with spontaneous UNPC at desirable T0, which would be characterized in routine laboratory measurements as a genuine first-order phase transition with large latent heat thanks to the ultranarrow δT (say less than one nanokelvin), paving a way to push the limit in our understanding of phase transitions and the dynamical actions of frustration arbitrarily close to the forbidden regime. Published by the American Physical Society 2024

Dynamic Phase Transition in 2D Ising Systems: Effect of Anisotropy and Defects.

We investigate the dynamic phase transition in two-dimensional Ising models whose equilibrium characteristics are influenced by either anisotropic interactions or quenched defects. The presence of anisotropy reduces the dynamical critical temperature, leading to the expected result that the critical temperature approaches zero in the full-anisotropy limit. We show that a comprehensive understanding of the dynamic behavior of systems with quenched defects requires a generalized definition of the dynamic order parameter. By doing so, we demonstrate that the inclusion of quenched defects lowers the dynamic critical temperature as well, with a linear trend across the range of defect fractions considered. We also explore if and how it is possible to predict the dynamic behavior of specific magnetic systems with quenched randomness. Various geometric quantities, such as a defect potential index, the defect dipole moment, and the properties of the defect Delaunay triangulation, prove useful for this purpose.

Critical behavior of a mixed-spin Ising model on a square–octagon lattice

The magnetic behavior and phase diagrams of a mixed spin-5/2 and spin-3/2 Ising system on a two-dimensional square–octagon lattice were investigated using the mean-field approach based on the statistical Bogoliubov inequality. Two ground-state phase diagrams were plotted in two different planes. We also examined the effects of exchange interactions, crystal field, and external magnetic field on the magnetizations and phase diagrams of the system. First- and second-order phase transitions and isolated critical points were obtained for certain physical conditions. The influence of various physical system parameters on the blocking temperature was also clarified.

The Capabilities of Boltzmann Machines to Detect and Reconstruct Ising System's Configurations from a Given Temperature.

The restricted Boltzmann machine (RBM) is a generative neural network that can learn in an unsupervised way. This machine has been proven to help understand complex systems, using its ability to generate samples of the system with the same observed distribution. In this work, an Ising system is simulated, creating configurations via Monte Carlo sampling and then using them to train RBMs at different temperatures. Then, 1. the ability of the machine to reconstruct system configurations and 2. its ability to be used as a detector of configurations at specific temperatures are evaluated. The results indicate that the RBM reconstructs configurations following a distribution similar to the original one, but only when the system is in a disordered phase. In an ordered phase, the RBM faces levels of irreproducibility of the configurations in the presence of bimodality, even when the physical observables agree with the theoretical ones. On the other hand, independent of the phase of the system, the information embodied in the neural network weights is sufficient to discriminate whether the configurations come from a given temperature well. The learned representations of the RBM can discriminate system configurations at different temperatures, promising interesting applications in real systems that could help recognize crossover phenomena.

Investigation of the magnetic properties of the fullerene C30 with mixed spins: A Monte Carlo study

In this study, we employed Monte Carlo simulations to investigate the magnetic properties of C30 fullerene with mixed spins, where S = 2 and σ = 1 Ising system. We explored the ground-state phase diagrams to establish a foundational understanding of its magnetic behaviors. Magnetization and magnetic susceptibility were studied as functions of reduced temperature, highlighting the impact of mixing S and σ spins. Furthermore, we determined the evolution of the reduced transition temperature concerning the exchange interaction between S and S. Additionally, we investigated the influence of parameters such as reduced exchange interactions, temperature, and crystal field on the total magnetization. Finally, we analyzed magnetic hysteresis cycles to observe how loop surfaces change with variations in parameters, including exchange interaction, temperature, and crystal field.

Phase diagrams of semi-infinite systems by renormalization group theory and Monte Carlo simulation

In this work, we used the Migdal–Kadanoff renormalization group method to investigate two three-dimensional semi-infinite Ising systems. In the first one, the surface and bulk sites are occupied by spin-3/2 and spin-1/2 respectively, whereas those of the second one are occupied by spin-1/2 on the surface and spin-3/2 in the bulk. Based on the ratio of bulk and surface exchange interactions, we explored different topologies of phase diagrams showing various second order phase transitions, namely ordinary, extraordinary, surface and special transitions. We also found that both systems exhibited first order phase transitions, multicritical points and critical end-points. The existence of a first order phase transition at low temperatures was confirmed by plotting the derivative of the free energy. The Monte Carlo simulation was also used to verify and compare the results obtained by the renormalization group for the two semi-infinite systems.

Critical Ising system testing of high-quality random number generators

Specialized hardware implemented on field programmable gate array (FPGA) is used to simulate critical 2D Ising lattices up to 40962. Four mainstream, high-quality pseudorandom number generators (PRNGs) including Xorshift, Mersenne Twister, Xorwow, and ALFG are tested on this system, and three of them are found to misbehave with different degree of confidence levels. It is observed that PRNGs with quality issues tend to misbehave in critical Ising systems and the ones with bigger issues start to misbehave in smaller critical Ising systems and vice versa. The size at which a PRNG misbehaves is proposed as a measure of a PRNG’s quality.

Phase transitions of a mixed spin ferrimagnet in high temperatures

In this research paper molecular mean field theory (MMFT) has been investigated based on Gibbs-Bogoliubov free energy function of a ferromagnetic mixed spin-3 and spin-5/2 Blume-Capel model with different magnetic crystal fields. The free energy of the proposed ferrimagnet has been evaluated depending on the trial Hamiltonian operator. Minimizing the free energy, one may induce characteristic features of the longitudinal magnetizations, phase transitions and spin compensation temperatures, in the ranges of low temperatures, respectively. In particular, we study the effect of crystal field domains on the critical phenomena for the proposed model. The sublattice magnetization dependence of freerenergy function has been discussed as well. Our results predict the existence of multiple spin compensation sites in the disordered Blume-Capel Ising system for a simple cubic lattice.

Confinement of Fractional Excitations in a Triangular Lattice Antiferromagnet.

High-resolution neutron and THz spectroscopies are used to study the magnetic excitation spectrum of Cs_{2}CoBr_{4}, a distorted-triangular-lattice antiferromagnet with nearly XY-type anisotropy. What was previously thought of as a broad excitation continuum [L. Facheris etal., Phys. Rev. Lett. 129, 087201 (2022)PRLTAO0031-900710.1103/PhysRevLett.129.087201] is shown to be a series of dispersive bound states reminiscent of "Zeeman ladders" in quasi-one-dimensional Ising systems. At wave vectors where interchain interactions cancel at the mean field level, they can indeed be interpreted as bound finite-width kinks in individual chains. Elsewhere in the Brillouin zone their true two-dimensional structure and propagation are revealed.