## Micromagnetism

A precise understanding of magnetic processes is of major importance for the development and further improvement of novel data memories such as hard disks and magnetic random-access memories (RAM). The difficulty is that the device behavior needs to be known over a time scale of many years in order to guarantee a high reliability. Micromagnetic simulations are an important tool to compute the magnetic processes in such nano-structures. Reliable simulation results are usually obtained by a numerical integration of the Landau-Lifshitz-Gilbert equation (LLG), which is a nonlinear partial differential equation in space and time.

The research is concerned with finite element schemes for LLG. Difficulties arrise from a nonconvex side constraint, the proper handling of the nonlinearity, and the coupling with the magnetic potential. The latter yields the solution of a potential equation in the entire space for each time-step. Main objectives are the numerical computation of the energy barrier and the so-called attempt frequency for large-scale micromagnetic models. Complex micro-structures consisting of several hundred magnetic grains are simulated. The Ph.D. projects will be conducted with the participation of the following professors from physics and mathematics: Melenk, Praetorius, Suess.

Micromagnetic simulations are successfully applied at academia and industry in order to design new concepts of magnetic storage applications. The following movie shows the recording process of a perpendicular recording media, which recently became the standard technology in products:

We aim to represent our research results in state of the art visulations as it can be found in the following movie, showing the entire recording process of a harddisc drive in a common PC: More. Further applications of micromagnetism can be found at our homepage.