A multiscale approach to magnetization dynamics simulations
Date issued
Authors
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
License
Abstract
Simulations of magnetization dynamics in a multiscale environment enable rapid evaluation of the Landau-Lifshitz-Gilbert equation in a mesoscopic sample with nanoscopic accuracy in areas where such accuracy is required. I have developed a multiscale magnetization dynamics simulation approach that can be applied to large systems with spin structures that vary on small length scales locally. To implement this, the conventional micromagnetic simulation framework was expanded to include a multiscale solving routine. The software selectively simulates different regions of a ferromagnetic sample according to the spin structures located within in order to employ a suitable discretization and use either a micromagnetic or an atomistic model. A tracking algorithm was developed in order to shift the atomistic region within the sample to follow the spin structures which vary on a short length scale.
In the first part of this thesis, the theory necessary for the development and the comprehension of this approach was introduced. This includes: the derivation of the LLG equation, the phenomenological background and the evaluation of the energy contributions in the two models, a review on magnetic structures of fundamental and technological interest, with a focus on some structures which cannot be modeled using micromagnetism only, and an analysis of the computational algorithms used in the multiscale simulation.
The second part of the thesis is focused on describing in detail the implementation of the multiscale approach, as well as demonstrating its necessity and validity. To demonstrate the validity of the approach, we simulate the spin wave transmission across the regions simulated with the two different models and different discretizations. We find that the interface between the regions is fully transparent for spin waves with frequency lower than a certain threshold set by the coarse scale micromagnetic model with no noticeable attenuation due to the interface between the models. One further demonstration consists in the comparison of a multiscale DMI spiral with the analytical theory. To demonstrate the reliability of the tracking algorithm, the motion of a domain wall in a magnetic nanostrip was simulated. The approach was then applied to magnetic Skyrmions to quantify their stability. Skyrmions belong to the most interesting spin structures for the development of future information technology as they have been predicted to be topologically protected. As a demonstration for the necessity of a multiscale approach, we first show how the stability of a Skyrmion is influenced by the refinement of the computational mesh and reveal that conventionally employed traditional micromagnetic simulations are inadequate for this task. Furthermore, we determine the stability quantitatively using our multiscale approach.
As a key operation for devices and as a first application of the approach, the process of annihilating a Skyrmion by exciting it with a spin polarized current pulse is analyzed, showing that different transformations in the topology of the system can be reliably induced by designing the pulse shape.