Maze-Bubble Pattern Magnetic Domain Simulation Based on the Lengyel-Epstein Model

TL;DR

This work addresses the challenge of simulating remanent magnetic-domain topology, specifically maze-bubble patterns in PMA thin films, by adopting the Lengyel-Epstein reaction-diffusion model. The authors reinterpret two RD variables $M_1$ and $M_2$ as outward and inward magnetization components and derive a modified LE system with parameters $a$ (external-field analogue) and $w$ (thickness analogue) to reproduce observed patterns under varying thickness and magnetic field. Through linear stability analysis and numerical simulations, they demonstrate qualitative agreement with MFM images, map Hopf and Turing bifurcation regimes, and capture transitions from labyrinth to bubble patterns as physical conditions change. Extensions to magnetic skyrmions and a discussion of a Turing-pattern analogy further illustrate the RD perspective’s potential, while limitations are acknowledged and pathways for quantitative refinement are outlined.

Abstract

This study is based on the Lengyel-Epstein (LE) model, governed by a system of nonlinear partial differential equations, to simulate the maze-bubble pattern magnetic domains in magnetic thin films with perpendicular magnetic anisotropy (PMA). Through numerical simulations, we successfully reproduce the maze, bubble, and intermediate-state magnetic domains observed in PMA multilayer films under the influence of material thickness and external magnetic fields. The topological structures of the magnetic domains shown in the simulation closely resemble those observed under a microscope, demonstrating the effectiveness of the LE model in simulating changes in the magnetic domain topology of magnetic thin films. This study also innovatively applies the concept of reaction-diffusion, commonly used in biochemistry, by drawing an analogy to electromagnetism. This approach holds significant implications for the study of magnetic domains.

Figures (11)

• Figure 1: Schematic of a collection of magnetic domains in a ferromagnetic materialF1.
• Figure 2: Remanent magnetic domain observed in $[Co/Pt]_N$ multilayers. Extracted from 6.
• Figure 3: Short-range interaction-induced spin wave phenomenon in micromagnetic simulation spin
• Figure 4: The images shown in red and yellow are MFM micrographs of PMA thin-film magnetic domains 796. The black-and-white images are maze-bubble phase diagrams simulated using the simulation model from Section 4.1 in MATLAB.
• Figure 5: The topological structure change of PMA multilayers in the remanent magnetization state depends on the thickness of the film and the applied magnetic field6.