Abstract
Theoretical models capture very precisely the behaviour of magnetic materials at the microscopic level. This makes computer simulations of magnetic materials, such as spin dynamics simulations, accurately mimic experimental results. New approaches to efficient spin dynamics simulations are limited by integration time step barrier to solving the equations-of-motions of many-body problems. Using a short time step leads to an accurate but inefficient simulation regime whereas using a large time step leads to accumulation of numerical errors that render the whole simulation useless. In this paper, we use a Deep Learning method to compute the numerical errors of each large time step and use these computed errors to make corrections to achieve higher accuracy in our spin dynamics. We validate our method on the 3D Ferromagnetic Heisenberg cubic lattice over a range of temperatures. Here we show that the Deep Learning method can accelerate the simulation speed by 10 times while maintaining simulation accuracy and overcome the limitations of requiring small time steps in spin dynamic simulations.
Highlights
Theoretical models capture very precisely the behaviour of magnetic materials at the microscopic level
Magnetic materials have a wide range of industrial applications such as in Nd–Fe–B-type permanent magnets used for motors in hybrid c ars[1,2], magnetoresistive random access memory (MRAM) based on the storage of data in stable magnetic states[3], ultrafast spins dynamics in magnetic nanostructures[4,5], heat assisted magnetic recording and ferromagnetic resonance methods for increasing the storage density of hard disk d rives[6,7], exchange bias related to magnetic recording[8], and magnetocaloric materials for refrigeration technologies[1]
Second order Suzuki–Trotter decomposition methods are used for all experiments in this paper
Summary
Theoretical models capture very precisely the behaviour of magnetic materials at the microscopic level. New approaches to efficient spin dynamics simulations are limited by integration time step barrier to solving the equations-of-motions of many-body problems. We use a Deep Learning method to compute the numerical errors of each large time step and use these computed errors to make corrections to achieve higher accuracy in our spin dynamics. Classical equations of motion of spin systems are solved numerically using well known integrators such as leapfrog, Verlet, predictor-corrector, and Runge-Kutta methods[11,12,13]. The accuracy of these simulations depends on a time integration step size. Is applied to simulation of the quantum spin d ynamics[26,27], identifying phase t ransitions[28], and solves the exponential complexity of the many body problem in quantum s ystems[29]
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