Model-based magnetization retrieval from holographic phase images

The phase shift of the electron wave is a useful measure for the projected magnetic flux density of magnetic objects at the nanometer scale. More important for materials science, however, is the knowledge about the magnetization in a magnetic nano-structure. As demonstrated here, a dominating presence of stray fields prohibits a direct interpretation of the phase in terms of magnetization modulus and direction. We therefore present a model-based approach for retrieving the magnetization by considering the projected shape of the nano-structure and assuming a homogeneous magnetization therein. We apply this method to FePt nano-islands epitaxially grown on a SrTiO₃ substrate, which indicates an inclination of their magnetization direction relative to the structural easy magnetic [001] axis. By means of this real-world example, we discuss prospects and limits of this approach.