Lorentz electron microscopy is a powerful tool for high resolution studies of magnetic structure in thin films.1-3 The physical mechanism that underlies all known modes of Lorentz microscopy is the interaction between the propagating electron wave and the magnetic vector potential field. For a given electron trajectory the interaction, commonly known as the Aharonov-Bohm effect, results in a phase delay directly proportional to the path integral of the vector potential.4 Lorentz microscopy is therefore a branch of phase contrast microscopy whose various modes (e.g., Fresnel, Foucault, differential phase contrast, small angle diffraction, electron interference, and holography) simply represent different designs for capturing the information contained in the phase of the beam after passage through the sample. This paper introduces a general technique for computing the phase imparted to the electron beam by a two dimensional pattern of magnetization. The vector potential field for a thin film with arbitrary magnetization is calculated using fast Fourier transforms. This field is then used to compute the phase modulation of the electron beam. Calculated phase patterns and the corresponding Fresnel/Foucault intensity distributions for several magnetic configurations of practical interest (e.g., ripples, vortices, sinks, and sources) are presented..
ASJC Scopus subject areas
- Physics and Astronomy(all)