The properties of modern magnetic materials are strongly influenced by their microstructure. The continuing improvement of the properties of SmCo based magnets has been made possible by additives like Cu and Zr and a refined processing route and heat treatment, which have a great impact on the resulting cellular precipitation structure [12]. The typical size of the cells is in the order of 100 nm with an intercellular phase of around 10 nm. The particle size in magnetic recording tapes is of the same order of magnitude. The typical grain size in current hard disk storage media is about 8 nm with an intergranular region of about 2 nm for exchange decoupling of the grains.
These structures are so small that quantum mechanical effects like exchange have to be taken into account. However, they are too large for a pure quantum mechanical description, which would exceed the capabilities of today's ab-initio computational models. On this intermediate level between the macroscopic world and a description with atomic resolution, micromagnetic models have proved to be a useful tool [13]. These computational models provide great freedom in the choice of experiment conditions and in the variation of material parameters. In addition to measurements of the remanent magnetization and the coercive field, it is possible to study the details of the magnetization distribution and the magnetization reversal processes, which are difficult to investigate experimentally. In this thesis temperature dependent effects have not been considered explicitly, but they are included in the temperature dependent material parameters. Also eddy current effects, which should be taken into account in materials with high conductivity and in high speed switching experiments, are only implicitly included in the Gilbert damping constant.
In various fields of computer aided engineering like structural analysis, fluid dynamics, and electromagnetic field computation, as well as micromagnetics [14] the finite element method has been successfully applied. Especially its flexibility in modeling arbitrary geometries has made it very popular. In the light of the importance of the microstructure of magnetic materials the finite element method has been chosen for the implementation of a micromagnetic model.
There are several commercial and open source micromagnetics packages available (cf. App. A), however all of them use the finite difference method. In addition, the work on this thesis required static energy minimization methods for the study of SmCo permanent magnets as well as dynamic time integration methods for the investigation of the magnetization dynamics in magnetic nanoparticles.
Therefore, a finite element micromagnetics package has been implemented which combines several unique features:
It is
An introduction to the finite element method is given in chapter 2. The basic micromagnetic equations and their discretization in the context of the finite element method are outlined in chapter 3, while the appropriate solution methods are described in chapter 4. The details of the implementation of the micromagnetics package are discussed in chapter 5 and the optimization strategies are explained in chapter 6.
This micromagnetics model has been applied to study domain wall pinning effects in SmCo permanent magnets. The results are presented in chapter 7. Nucleation and magnetization reversal processes in FePt nanoparticles for magnetic storage media are studied in chapter 8, while the static and dynamic properties of permalloy nanodots are investigated in chapter 9. Finally, in chapter 10 the properties of elliptical and rectangular permalloy nanoparticles and the influence of magnetostatic coupling in chains of particles are examined. This thesis is completed by an appendix including a list of publicly available micromagnetics packages, the list of software packages, which has been used for the implementation of the parallel code, and a list of typical material parameters.