Enhancing Micromagnetics Simulations with a Third-Order Semi-Implicit Projection Method

TL;DR

This paper introduces a third-order semi-implicit projection method for micromagnetics that improves accuracy and efficiency in simulating magnetization dynamics, validated through nanostrip simulations.

Contribution

It presents a novel third-order temporal scheme for the Landau-Lifshitz-Gilbert equation, enhancing accuracy and computational efficiency over existing methods.

Findings

Achieves rigorous third-order accuracy surpassing current methods.

Provides higher computational efficiency with stable convergence.

Maintains stability for a wide range of damping parameters.

Abstract

Micromagnetics depends on high-fidelity numerical methods for magnetization dynamics. This work proposes a third-order temporal accuracy scheme for the Landau-Lifshitz-Gilbert equation, addressing accuracy-efficiency trade-offs in existing methods. Validated via nanostrip simulations (representative of real devices), the scheme offers two key advantages: rigorous third-order accuracy (surpassing existing simulation methods) and higher computational efficiency, ensuring fast convergence without precision loss. It maintains stability for Gilbert damping \(\alpha\) from $0.1$ to $10$, avoiding non-physical states. The magnetic microstructures it captures are consistent with established methods, confirming reliability for physical analysis.