Projekt Details

Project ID

C15

Application Area

Project Title

Pattern formation in magnetic thin films

Description

Magnetic materials display a complex variety of patterns and singular structures on many different length scales. The way such patterns form and evolve in time is vitally important for many key technologies related to sensors, memory and recording devices where particularly magnetic thin films offer themselves in practice. Very recently strong interest in magnetic films stems from their combination with semiconductor elements in view of hybrid devices for future spin electronics, a rapidly developing new technology. A widely accepted theoretical framework for ferromagnetism is based on a continuum model due to Landau and Lifshitz. Within their theory, a universal energy functional, the micromagnetic energy, that captures in principle magnetic phenomena on every relevant length scale, including the coarse domain structures as well as fine substructures of domain walls and their mutual interaction. Mathematically, the formation of these patterns and structures is driven by the interplay of non-convexity and non-locality due to the coupling with Maxwell's equations. In practice, however, the general model is by far to complex in order to extract interesting predictions or to effectively perform suitable computations in high resolution. Hence there is a need for suitable reduced or effective models that capture specific features in parameter regimes of specific interest. Whereas in physics community micromagnetic theory is mainly used on the basis of computation, our main focus concerns rigorous model reductions and the investigation and derivation of qualitative features of patterns and microstructure. Mathematically, thin films distinguish themselves from bulk materials by a different form of induced stray-field interaction that becomes singular in dimensionally reduced theories and constitutes the main analytical challenge in such models. In recent time important analytic contribution have been made that were mostly focused on energy minimizing configuration. Particularly typical domain wall structures have been elucidated, and reduced models for soft magnetic films were rigorously derived on the basis of Gamma-convergence. To a much lesser extend, however, dynamic questions were addressed so far. This will be one of the main direction of research within the research group. On the other hand we aim to provide analytical background for phenomena that emerge in the production of new magnetic materials for which an adequate theoretical framework is still to be developed

Duration

06/05-09/08

Status

completed

Members

No assigned Project Members

Heads

Prof. Dr. Alexander Mielke

Guests

No assigned Project Guests

Publications

No assigned Publications