Micromagnetic Monte Carlo method with variable magnetization length based on the Landau–Lifshitz–Bloch equation for computation of large-scale thermodynamic equilibrium states

Abstract

An efficient method for computing thermodynamic equilibrium states at the micromagnetic length scale is introduced, based on the Markov chain Monte Carlo method.Trial moves include not only rotations of spins, but also a change in their magnetization length.The method is parameterized using the longitudinal susceptibility, reproduces the same Maxwell-Boltzmann distribution as the stochastic Landau-Lifshitz-Bloch equation, and is applicable both below and above the Curie temperature. The algorithm is fully parallel, can be executed on graphical processing units, and efficiently includes the long range dipolar interaction. This method is generally useful for computing finite-temperature relaxation states both for uniform and non-uniform temperature profiles, and can be considered as complementary to zero-temperature micromagnetic energy minimization solvers, with comparable computation time. However, unlike quasi-zero temperature approaches which do not take into account the magnetization length distribution and stochasticity, the method is better suited for structures with unbroken symmetry around the applied field axis, granular films, and at higher temperatures and fields. In particular, applications to finite-temperature hysteresis loop modelling, chiral magnetic thin films, granular magnetic media, and artificial spin ices are discussed.

BORIS – Micromagnetic, Spin Transport and Multiscale Atomistic Software for Modelling Magnetic Information Storage

“…In Ref. [30] a new Monte Carlo algorithm was introduced, specifically for modelling at the micromagnetic length scale (MMC), where a variable magnetization length was used based on the LLB equation. A number of applications were discussed, where in addition to finite-temperature hysteresis loop modelling, chiral magnetic thin films, granular magnetic media, and artificial spin ices were also modelled.…”

“…An example computation using the MMC algorithm is shown in Figure 5, as discussed in Ref. [30]. Here a hysteresis loop is computed at 350 K in a 2 nm thin Co film with interfacial DMI interaction and perpendicular anisotropy.…”

“…The insets show the perpendicular magnetization component at the indicated points on the increasing field sweep, with blue denoting magnetization into the plane, and red out of the plane. Image adapted from Ref [30]…”

Accelerating micromagnetic and atomistic simulations using multiple GPUs

“…The multi-GPU implementation uses the red-black checkerboard decomposition scheme [35], previously used to implement the Monte Carlo algorithm on a single GPU [36], and such a scheme has already been implemented for multi-GPU acceleration of the 2D Ising model [37]. The same method is used to implement the micromagnetic Monte Carlo method [38] on multiple GPUs, which additionally includes the demagnetizing interaction. The speedup factors obtained for the atomistic Monte Carlo method are shown in Figure 7, where maximum efficiency factors between 0.94 to 0.98 are obtained for 2, 3, and 4 GPUs.…”