Computation of magnetization, exchange stiffness, anisotropy, and susceptibilities in large-scale systems using GPU-accelerated atomistic parallel Monte Carlo algorithms
arXiv:2103.03517 · doi:10.1016/j.jmmm.2021.168460
Abstract
Monte Carlo algorithms are frequently used in atomistic simulations, including for computation of magnetic parameter temperature dependences in multiscale simulations. Even though parallelization strategies for Monte Carlo simulations of lattice spin models are known, its application to computation of magnetic parameter temperature dependences is lacking in the literature. Here we show how, not only the unconstrained algorithm, but also the constrained atomistic Monte Carlo algorithm, can be parallelized. Compared to the serial algorithms, the parallel Monte Carlo algorithms are typically over 200 times faster, allowing computations in systems with over 10 million atomistic spins on a single GPU with relative ease. Implementation and testing of the algorithms was carried out in large-scale systems, where finite-size effects are reduced, by accurately computing temperature dependences of magnetization, uniaxial and cubic anisotropies, exchange stiffness, and susceptibilities. In particular for the exchange stiffness the Bloch domain wall method was used with a large crosssectional area, which allows accurate computation of the domain wall width up to the Curie temperature. The exchange stiffness for a simple cubic lattice closely follows an mk scaling at low temperatures, with k < 2 dependent on the anisotropy strength. However, close to the Curie temperature the scaling exponent tends to k = 2. Furthermore, the implemented algorithms are applied to the computation of magnetization temperature dependence in granular thin films with over 15 million spins, as a function of average grain size and film thickness. We show the average Curie temperature in such systems may be obtained from a weighted Bloch series fit, which is useful for analysis of experimental results in granular thin films.
References in corpus (19)
- Parallel Tempering: Theory, Applications, and New Perspectives
- Fokker-Planck and Landau-Lifshitz-Bloch Equations for Classical Ferromagnets
- Quantitative simulation of temperature dependent magnetization dynamics and equilibrium properties of elemental ferromagnets
- Constrained Monte Carlo Method and Calculation of the Temperature Dependence of Magnetic Anisotropy
- Spirit: Multifunctional Framework for Atomistic Spin Simulations
- Multi-GPU Accelerated Multi-Spin Monte Carlo Simulations of the 2D Ising Model
- Magnetization switching in a Heisenberg model for small ferromagnetic particles
- Self-Consistent Gaussian Approximation for Classical Spin Systems: Thermodynamics
- Quantum thermodynamics of complex ferrimagnets
- Quantum rescaling, domain metastability and hybrid domain-walls in two-dimensional CrI3 magnets
- Calculating temperature-dependent properties of NdFeB permanent magnets by atomistic spin model simulations
- Transition to linear domain walls in nano-constrictions
- Temperature scaling of the Dzyaloshinsky-Moriya interaction in the spin wave spectrum
- Boris Computational Spintronics -- High Performance Multi-Mesh Magnetic and Spin Transport Modelling Software
- Emergence of Transient Domain Wall Skyrmions after Ultrafast Demagnetisation
- GPU accelerated Monte Carlo simulations of lattice spin models
- Magnetisation dynamics of granular HAMR media by means of a multiscale model
- Monte Carlo simulation of the effects of higher order anisotropy on the spin reorientation transition in the two dimensional Heisenberg model with long range interactions
- Vegas: Software package for the atomistic simulation of magnetic materials