Fig. 1: Electron holography for complex spin textures.

a Schematic and simplified setup for capturing phase images within a transmission electron microscope. b Tilt series of phase-images and decomposition of a single phase-image into magnetic and electronic components as exemplified for a hopfion. The illustrated phase images are the basic ingredients for a 3D reconstruction of the spin texture, ultimately enabling tomography, which is not the focus of our study. The electronic component consists of three contributions that depend on the rotation of the magnetic moment and the presence of spin-orbit coupling. For the simulation, we used a common value of 300 keV for the acceleration voltage.