Advanced numerical micromagnetics

The development and application of modern magnetic materials requires a basic understanding of the magnetization processes that determine the magnetic properties. Micromagnetics relates the microscopic distribution of the magnetization to the physical and chemical microstructure of a material. Recently, micromagnetic modeling has become an important tool to characterize the magnetic behavior of such different materials as thin film heads, recording media, patterned magnetic elements, and nanocrystalline permanent magnets. The rapid progress of nanotechnoloy will lead to novel application of magnetic materials in spin electronic devices, magnetic sensors, and functional materials 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 to predict the response of the system to external fields, stress and temperature as a function of time. This proposal aims to develop advanced numerical methods to simulate the functional behavior of future novel magnetic devices. The length- and timescales involved in these simulations vary widely. The lengthscales range from nano-meters for the nucleation of reversed domains at material interfaces to micrometers for the simulation of the magnetostatic interactions of the entire system. The timescales vary from nanoseconds for high speed response of the magnetization to 101 to 104 seconds for slow thermal decay of the magnetization. The proposed use of advanced numerical techniques and new formalisms will allow simulations over the full length- and timescales and thus will extent current state of the art numerical micromagnetics which is often limited to small volumes of material and small times scales. The new algorithms to be developed in the first phase of the project involve matrix compression techniques for fast field calculation, highly adaptive hierarchic solvers for the micromagnetic equations, numerical continuation methods to calculate nucleation fields of complex systems, and randomized hybrid Monte Carlo schemes to simulate thermally activated processes. In the second phase of the project, the newly developed methods will be applied to tackle two topical issues in the field of magnetism and magnetic materials: Coercivity mechanisms of highest energy density permanent magnets and the thermal stability of recorded bits in ultra-high storage density recording media. Novel functional magnetic devices will be simulated in the third phase of the project. This includes the extension of standard micromagnetics taking into account spin transport and magneto-elastic effects. The innovative combination of micromagnetic theory with advanced numerical techniques for the solution of partial differential equations gives rise to realistic simulations of modem magnetic materials with a physically complete formalism. The development of new magnetic materials used for permanent magnets, data storage, or magnetic sensors is linked with the ability to make accurate predictions of their magnetic properties. Advanced numerical micromagnetic simulations will have a great impact on the structural design of novel magnetic materials and devices. Influence of the proposed work on the development of the field The proposed research will have an impact in different areas of the highly active field of magnetism and magnetic materials: The advanced numerical techniques will overcome the current limits on the length- and time scale of micromagnetic calculations. Numerical nucleation field theory detects bifurcation points during the calculation of the hysteresis loops and will provide the grounds for highly accurate simulations of magnetic properties. The clarification of the magnetic hardening of highest energy density permanent magnets may open ways to enhance the coercive field of Nd-Fe-B sintered magnets. This is of vital importance, in order to meet the increasing demand for high performance magnets for application to high power motors. Micromagnetic analysis of the correlation between the microstructure and the stability of written bits in ultra-high density storage media is crucial for a further increase of data storage densities as required by the demands of computer and information technologies. The ability to simulate the functional behavior of entire magnetic devices will have a great impact on the design and development of novel, structured magnetic materials.