## 5. Simulation of magnetization processes and dynamics of magnetically ordered materials and systems

The rapid progress of nanotechnology will lead to novel concepts in the application of magnetic materials. New areas such as spin electronic devices, magnetic sensors, and composite and functional materials will be of practical interest within the next years. A prerequisite for the application of structured magnetic materials is the detailed knowledge of the correlation between the physical and magnetic structure of the system. The design of smart materials requires predicting the response of the system to external fields, stress and temperature as a function of time. In magnetic recording the microstructure plays an important role in order to increase the storage density. Ultra high density storage media with low noise require a small grain size. For a given material its maximum real density is ultimately limited by the so called superparamagnetic effect. If the energy barrier between the two states representing the two bits becomes smaller than the thermal energy the stored information is no longer stable.

Modern computer facilities will be used by the group of Dieter Suess, Jehyun Lee, and Josef Fidler to explore new concepts of multi-scale (in the sense of time and length scale) micromagnetic simulations on composite soft/hard nanoand mesoscopic structures. The main work will base on high coercive materials with a typical characterisitic exchange length in the range of (only) nanometers, such as FePt, CoPd and CoPt nanoparticles, thin films and multilayers, which are promising candidates for future high density recording media. In a soft/hard magnetic nanostructured device the finite element micromagnetic model typically consists of several million tetrahedral elements. The intrinsic material properties like the magnetization and magneto-crystalline anisotropy will be taken from ab initio calculations or experiments, and will then be used in micromagnetic simulations that describe the hysteresis properties. As an example the knowledge of the high coercive materials will be used to design new recording media systems or magnetic nano-sensor devices. Using this multi-scale approach, it is possible to bridge the length scales and to calculate write performance and media noise from first principles.

Numerical micromagnetics relates the microscopic distribution of the magnetization to the physical and chemical microstructure of a material. The micromagnetic equations are time-dependent coupled partial differential equations. The so called Landau Lifshitz-Gilbert equation describes the time evolution of the magnetization under the action of an effective field. The effective field can be calculated by solving the static Maxwell equations. An exchange field that arises from quantum theory is taken into account in a continuous limit. To solve the static Maxwell equation a hybrid finite element / boundary element method is used. The advantage is that no mesh is required outside the magnetic parts.

All information concerning the mutual interaction of the different parts is stored in the boundary element matrix. In order to avoid the matrix elements to be recomputed at each time step due to the movement of the head, we compute the scalar potential at the surface of a so-called field box which moves together with the external field coil. The above combination of the finite element method, the fast boundary element method, and the finite difference method gives a highly efficient micromagnetics solver.