We present an adaptive algorithm for the optimal phase space sampling in Monte Carlo simulations of 3D Heisenberg spin systems. Based on a golden rule of the Metropolis algorithm which states that an ...acceptance rate of is ideal to efficiently sample the phase space, the algorithm adaptively modifies a cone-based spin update method keeping the acceptance rate close to . We have assessed the efficiency of the adaptive algorithm through four different tests and contrasted its performance with that of other common spin update methods. In systems at low and high temperatures and anisotropies, the adaptive algorithm proved to be the most efficient for magnetization reversal and for the convergence to equilibrium of the thermal averages and the coercivity in hysteresis calculations. Thus, the adaptive algorithm can be used to significantly reduce the computational cost in Monte Carlo simulations of 3D Heisenberg spin systems.
Magnetic ordering in the two-dimensional (2D) limit has been one of the most important issues in condensed matter physics for the past few decades. The recent discovery of new magnetic van der Waals ...materials heralds a much-needed easy route for the studies of 2D magnetism: the thickness dependence of the magnetic ordering has been examined using Ising- and XXZ-type magnetic van der Waals materials. Here, we investigated the magnetic ordering of MnPS3, a 2D antiferromagnetic material of the Heisenberg-type, by Raman spectroscopy from bulk all the way down to the bilayer. The phonon modes that involve the vibrations of Mn ions exhibit characteristic changes as the temperature gets lowered through the Néel temperature. In bulk MnPS3, the Raman peak at ~155 cm−1 becomes considerably broadened near the Néel temperature, and upon further cooling is subsequently red-shifted. The measured peak positions and polarization dependences of the Raman spectra are in excellent agreement with our first-principles calculations. In few-layer MnPS3, the peak at ~155 cm−1 exhibits the characteristic red-shift at low temperatures down to the bilayer, indicating that the magnetic ordering is surprisingly stable at such a thin limit. Our work sheds light on the hitherto unexplored magnetic ordering in the Heisenberg-type antiferromagnetic systems in the atomic-layer limit.
We revisit the issue about the magnetization of the 120° order in the spin-1/2 triangular lattice Heisenberg model with density matrix renormalization group (DMRG). The accurate determination of the ...magnetization of this model is challenging for numerical methods and its value exhibits substantial disparities across various methods. We perform a large-scale DMRG calculation of this model by employing bond dimension as large asD=24000and by studying the system with width as large asLy=12. With careful extrapolation with truncation error and suitable finite size scaling, we give a conservative estimation of the magnetization asM0=0.208(8). The ground state energy per site we obtain isEg=-0.5503(8). Our results provide valuable benchmark values for the development of new methods in the future.
The spin-1 Heisenberg model with Dzyaloshinskii–Moriya interaction and in presence of a random magnetic field is studied by using the framework of the two-spin cluster approximation. The formalism is ...applied to the simple cubic lattice (q=6). At finite temperature, the phase diagrams of the system reveal the presence of tricritical points, implying the presence of second and first-order phase transitions. In addition, the occurrence of fourth-order critical points is also investigated.
Magnetism of transition metal (TM) oxides is usually described in terms of the Heisenberg model, with orientation-independent interactions between the spins. However, the applicability of such a ...model is not fully justified for TM oxides because spin polarization of oxygen is usually ignored. In the conventional model based on the Anderson principle, oxygen effects are considered as a property of the TM ion and only TM interactions are relevant. Here, we perform a systematic comparison between two approaches for spin polarization on oxygen in typical TM oxides. To this end, we calculate the exchange interactions in NiO, MnO and hematite (Fe2O3) for different magnetic configurations using the magnetic force theorem. We consider the full spin Hamiltonian including oxygen sites, and also derive an effective model where the spin polarization on oxygen renormalizes the exchange interactions between TM sites. Surprisingly, the exchange interactions in NiO depend on the magnetic state if spin polarization on oxygen is neglected, resulting in non-Heisenberg behavior. In contrast, the inclusion of spin polarization in NiO makes the Heisenberg model more applicable. Just the opposite, MnO behaves as a Heisenberg magnet when oxygen spin polarization is neglected, but shows strong non-Heisenberg effects when spin polarization on oxygen is included. In hematite, both models result in non-Heisenberg behavior. The general applicability of the magnetic force theorem as well as the Heisenberg model to TM oxides is discussed.
Exploring magnetic configurations of magnets often involves utilizing the four-state method to obtain the magnetic interaction matrix, and Monte Carlo method to simulate spin textures and phase ...transition processes. However, computing the interaction matrix between magnetic atoms using the four-state method requires plenty of individual calculations. Despite manual simplifying the number of individual calculations based on material's symmetry is possible, there remains a necessity for an automated approach to streamline the process for high-throughput screening of magnetic materials. Meanwhile, the traditional sequential Monte Carlo simulation encounters challenges of low efficiency and long time consuming in dealing with large systems. Furthermore, the prior parallelism in the Heisenberg model was limited to parallel computation of the system's energy or run several replicas in parallel. Hence, in our pursuit of comprehensive parallelization for the Heisenberg model, we have introduced a novel adaptation of the checkerboard algorithm, enabling a fully parallelizable simulation of the Heisenberg model. To address these problems, we have developed Sym4state.jl, a program specifically designed to simplify the computation of magnetic interaction matrix and simulate spin textures under various environmental conditions. This program, available as a Julia package, can be freely accessed at https://github.com/A-LOST-WAPITI/Sym4state.jl.
Program title: Sym4state.jl
CPC Library link to program files:https://doi.org/10.17632/s6dkmgrjfw.1
Developer's repository link:https://github.com/A-LOST-WAPITI/Sym4state.jl
Licensing provisions: MIT
Programming language: Julia
Nature of problem: Employing the four-state method to calculate magnetic interaction matrix for magnetic materials can be simplified based on material symmetry, however, there is a lack of automated approach to streamline the simplification. Additionally, the commonly used Metropolis method for simulating magnetic texture can only make parallel computation of the system's energy or run several replicas in parallel, which could hardly boost the performance when simulating the large-scale magnetic textures.
Solution method: We simplify the four-state method calculations by utilizing the principles of energy invariance under symmetry operations and time reversal operations. To enhance the efficiency of the Metropolis algorithm, we have designed a strategy to divide the entire 2D lattice into multiple domains. We then execute the Metropolis algorithm in parallel for each individual domain, thereby improving the overall computational efficiency.
Additional comments including restrictions and unusual features: While the methods aimed at simplifying the four-state method and parallelizing the Metropolis algorithm are applicable to both 2D and 3D systems, the current program is specifically designed for the calculation and simulation of magnetism in 2D materials. As a result, compatibility with 3D systems has not yet been implemented.
Efficient numerical methods are promising tools for delivering unique insights into the fascinating properties of physics, such as the highly frustrated quantum many-body systems. However, the ...computational complexity of obtaining the wave functions for accurately describing the quantum states increases exponentially with respect to particle number. Here we present a novel convolutional neural network (CNN) for simulating the two-dimensional highly frustrated spin-<inline-formula><tex-math notation="LaTeX">1/2</tex-math> <mml:math> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> <inline-graphic xlink:href="li-ieq1-3145163.gif"/> </inline-formula> <inline-formula><tex-math notation="LaTeX">J_1-J_2</tex-math> <mml:math> <mml:mrow> <mml:msub> <mml:mi>J</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>-</mml:mo> <mml:msub> <mml:mi>J</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> <inline-graphic xlink:href="li-ieq2-3145163.gif"/> </inline-formula> Heisenberg model, meanwhile the simulation is performed at an extreme scale system with low cost and high scalability. By ingenious employment of transfer learning and CNN's translational invariance, we successfully investigate the quantum system with the lattice size up to <inline-formula><tex-math notation="LaTeX">24\times 24</tex-math> <mml:math> <mml:mrow> <mml:mn>24</mml:mn> <mml:mo>×</mml:mo> <mml:mn>24</mml:mn> </mml:mrow> </mml:math> <inline-graphic xlink:href="li-ieq3-3145163.gif"/> </inline-formula>, within 30 million cores of the new generation of sunway supercomputer. The final achievement demonstrates the effectiveness of CNN-based representation of quantum-state and brings the state-of-the-art record up to a brand-new level from both aspects of remarkable accuracy and unprecedented scales.
We present TB2J, a Python package for the automatic computation of magnetic interactions, including exchange and Dzyaloshinskii–Moriya, between atoms of magnetic crystals from the results of density ...functional calculations. The program is based on the Green’s function method with the local rigid spin rotation treated as a perturbation. As input, the package uses the output of either Wannier90, which is interfaced with many density functional theory packages, or of codes based on localized orbitals. One of the main interests of the code is that it requires only one first-principles electronic structure calculation in the non-relativistic case (or three in the relativistic case) and from the primitive cell only to obtain the magnetic interactions up to long distances, instead of first-principles calculations of many different magnetic configurations and large supercells. The output of TB2J can be used directly for the adiabatic magnon band structure and spin dynamics calculations. A minimal user input is needed, which allows for easy integration into high-throughput workflows.
Program Title: TB2J
CPC Library link to program files:https://doi.org/10.17632/dm45fcn69d.1
Developer’s repository link:https://github.com/mailhexu/TB2J
Code Ocean capsule:https://codeocean.com/capsule/6486145
Licensing provisions: BSD 2-clause
Programming language: Python
Nature of problem: TB2J is a package for the computing of parameters in the extended Heisenberg model of the magnetic interaction, including the isotropic exchange, anisotropic exchange and Dzyaloshinskii–Moriya interactions from first principles result. It can make use of the Wannier function Hamiltonian, which can be constructed from many first principles codes, or localized orbital based codes.
Solution method: It uses the magnetic force theorem and takes the rigid spin rotation as a perturbation to the electronic structure. The energy variation is calculated from the Green’s functions from tight-binding like Hamiltonian based on Wannier functions or localized orbitals.
Additional comments including restrictions and unusual features: Isotropic exchange, anisotropic exchange, and Dzyaloshinskii–Moriya interactions can all be computed with the input of many DFT codes through the interface of Wannier90, or directly from localized orbital codes. The magnetic interaction parameters up to any distance can be computed from one DFT calculation. A minimum user-input is required which provides a black-box like experience. It generates output for several spin dynamics codes and thus bridges the first principles electronic structure simulation with the large scale spin dynamics simulation.
Frustrated magnetic compounds, in particular low-dimensional, are topical research due to the persistent uncovering of novel nontrivial quantum states and potential applications. The problem of this ...field is that many important results are scattered over the localized parameter ranges, while areas in between still contain hidden interesting effects. We consider the Heisenberg model on the square lattice and use the spherically symmetric self-consistent approach for spin-spin Green's functions in 'quasielastic' approximation. We have found a new local order in spin liquids: antiferromagnetic isotropical helices. On the structure factor we see circular concentric dispersionless structures, while on any radial direction the excitation spectrum has 'roton' minima. That implies nontrivial magnetic excitations and consequences in magnetic susceptibility and thermodynamics. On the exchange parameters globe we discover a crossover between antiferromagnetic-like local order and ferromagnetic-like; we find stripe-like order in the middle. In fact, our 'quasielastic' approach allows investigation of the whole globe.
•The critical temperature of FeNi and FePt alloys using Heisenberg interaction is closer to the experimental value than the Ising interaction.•The FeNi and FePt alloys prefer a ferromagnetic phase ...over the ferrimagnatic phase.•The Ising interaction predicts higher critical temperature for the FeNi alloy than the Heisenberg interaction.•The Heisenberg interaction predicts higher critical temperature for the FePt alloy than the Ising interaction.
A Monte Carlo simulation has been used to explore the magnetic properties of L10 ordered FeNi and FePt binary alloys. Our Hamiltonians include Heisenberg interaction or Ising interaction. Our calculations of variations of specific heat Cv, magnetic susceptibility χ and the magnetization M with the temperature T showed that predicted critical temperature for ferromagnetic phase is very close to the experimental values for these alloys. Also, thermal hysteresis loops, magnetic remanence, and the coercive field have been calculated. Moreover, the magnetic properties of the ferrimagnetic phase are presented.
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