Micromagnetism and the microstructure in nanocrystalline materials

Abstract

Micromagnetic calculations using computational techniques are a pre-requisite to treat complex magnetization processes in ensembles of ferromagnetic grains. Applying the finite element method spin structures of small spherical prismatic and platelet-like particles and the critical fields for the reversal of magnetization have been determined as a function of grain size, isotropic and textured distribution of easy axes and different magnetic properties of grain boundaries. Adapting the mesh sizes of finite elements to the gradients of the direction cosines of the spontaneous magnetization, inhomogeneous spin distributions could be determined within the grains as well as within grain boundaries. Numerical results have been obtained for nanocrystalline single phase and composite materials taking into account exchange and dipolar coupling between grains and inhomogeneous magnetic material parameters within the grain boundaries. The results of these investigations show clearly that large coercivities require exchange decoupling between the grains. Dipolar long-range magnetic stray fields reduce the coercivity mainly for large grain sizes, whereas the remanence enhancing by exchange coupling becomes effective for grain sizes of the order of twice the domain wall widhh of the hard-magnetic phase. For larger grain sizes the coercivity breaks down. From the model calculations general rules for the development of optimized nanocrystalline materials with large remanences and large coercivities are derived.