Coherent rotation of magnetization in three dimensions: A geometrical approach

We propose a geometrical method to explore the problem of coherent magnetization rotation, for an arbitrary anisotropy and in three dimensions. This method is a nontrivial generalization of the astroid construction which is well known in two dimensions. Specific features to the three-dimensional (3D) problem are highlighted. In order to establish a connection with the thermal and quantum theories of magnetization relaxation, the local curvatures of the potential are also evaluated geometrically. As an application of the method to a real 3D problem, the determination of the effective anisotropy constants from 3D switching field measurements is discussed and first results shown.