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Lothar Collatz Center for Computing in Science
Lothar Collatz Center
for Computing in Science

Photo: c3s

Project A6 (finished)

Project A6 - Discrete mathematical concepts in micromagnetic computations

Principal investigators: Michael Hinze, Guido Meier

Background and Motivation

Micromagnetic simulations are a well established tool for the numerical treatment of magnetization dynamics in ferromagnetic microstructures. Insights into magnetization dynamics of microstructures are of interest for the development of microscopic magnetic devices such as non-volatile storage devices and magnetoresistive sensors.

Aims and Objectives

The goal of this project is the development of mathematical methods for the micromagnetic simulation of ferromagnetic nanostructures. The theory of micromagnetism describes the dynamics of a continuous magnetization field in an effective magnetic field by the Landau-Lifshitz-Gilbert equation. The dipole-dipole interaction as well as the exchange interaction of the magnetic moments are modeled in the effective field. Other contributions to the effective field include the external Zeeman field and anisotropy terms. The Landau-Lifshitz-Gilbert equation can be solved analytically only for simple problems. Hence computer simulations are applied in order to obtain the time evolution of the magnetization of arbitrary systems. Micromagnetic simulations are computational expensive and despite fast hardware there are hard limits for the size of the simulated sample and the simulation time. The goal of this project is the development and implementation of novel simulation techniques in order to speed up micromagnetic simulations and increase their reliability.

Ultimately the developed methods will be included in the micromagnetic simulation code MicroMagnum.

PhD student: Claas Abert (member of the Research Training Group 1286 (RTG 1286) entitled Maßgeschneiderte Metall-Halbleiter-Hybridsysteme Functional Metal-Semiconductor Hybrid Systems, speaker Ulrich Merkt, Department of Physics)

Claas Abert successfully defended his PhD on September 3, 2013

Publications

1. Abert, C., Exl, L., Bruckner, F., Drews, A., & Suess, D. (2013). magnum. fe: A micromagnetic finite-element simulation code based on FEniCS. Journal of Magnetism and Magnetic Materials.

2. Abert, C., Exl, L., Selke, G., Drews, A., & Schrefl, T. (2012). Numerical methods for the stray-field calculation: A comparison of recently developed algorithms. Journal of Magnetism and Magnetic Materials.

3. Abert, C., Selke, G., Krüger, B., & Drews, A. (2012). A fast finite-difference method for micromagnetics using the magnetic scalar potential. Magnetics, IEEE Transactions on, 48(3), 1105-1109.