Abstract

The phase of electrons contains a wealth of information on the physics of nanomaterials. In addition to spatial high-resolution, typical of modern Transmission Electron Microscopy, the sensitivity of electrons to electromagnetic fields generated by nanostructures of interests enables us to establish a quantitative link between the retrieved signal and the properties of magnetic (and electronic) materials at the nanoscale. Such link, and its benefits in terms of gained knowledge, will be illustrated while exploring magnetic phase diagrams of shape-controlled nanostructured arrays: from the basic physics governing the magnetic response and hysteretic properties, configurational models are developed as a function of shape, geometry, composition, and other external parameters; the electron-optical phase shift is then evaluated and compared with the signal retrieved from holography experiments; the goal is to establish a quantitative framework where the expected magnetic ground state is determined univocally. In this perspective, the key element is a computational strategy developed recently that relies on the reciprocal representation of the physical quantities (fields and potentials) responsible for phase-shifting the electron beam.