Hybrid FFT algorithm for fast demagnetization field calculations on non-equidistant magnetic layers

TL;DR

This paper introduces a hybrid FFT algorithm that efficiently computes the demagnetization field in multilayer magnetic systems with arbitrary thicknesses, significantly speeding up simulations for complex geometries.

Contribution

It combines FFT-based convolution with explicit convolution using generalized Newell formulas, enabling fast and accurate calculations for irregular multilayer geometries.

Findings

Significant speedups in demagnetization field calculations for multilayer systems.

Successful implementation on CPUs and GPUs.

Optimized magnetic memory cell geometry and simulated hysteresis behavior.

Abstract

In micromagnetic simulations, the demagnetization field is by far the computationally most expensive field component and often a limiting factor in large multilayer systems. We present an exact method to calculate the demagnetization field of magnetic layers with arbitrary thicknesses. In this approach we combine the widely used fast-Fourier-transform based circular convolution method with an explicit convolution using a generalized form of the Newell formulas. We implement the method both for central processors and graphics processors and find that significant speedups for irregular multilayer geometries can be achieved. Using this method we optimize the geometry of a magnetic random-access memory cell by varying a single specific layer thickness and simulate a hysteresis curve to determine the resulting switching field.