Diffraction Effects in Lorentz Microscopy

Abstract

Several electron optical techniques are in use to study microscopic magnetic field distributions through deflection by the Lorentz force (Lorentz microscopy). It is shown that for most cases of practical interest the deflected electrons must be treated quantum mechanically in order to extract quantitatively information on the structure of the field inhomogeneity from the experimental electron record. The lateral wave-length of an electron deflected in a weak magnetic field is independent of the initial electron momentum and is often of the order of the lateral extent of the structure under investigation. For instance, in ferromagnetic thin films, λlat≈1000 Å behind domain walls 3000 Å wide, or λlat≈10 μ behind ripples with 2 μ period. It is well known that the geometric approach to contrast formation can break down in such cases (Abbe's sine condition). High-resolution micrographs of ferromagnetic layers are shown. In the defocused mode, one interference fringe appears in the image per flux unit h/2e in the layer near convergent walls. In the Foucault mode, the transition from bright to dark areas of the image occurs across a finite distance due to diffraction. This distance corresponds to the width of one flux unit h/2e in the layer. Ripple contrast is smaller than one and is a complicated function of defocusing distance, ripple period, and initial electron momentum due to diffraction. High-frequency-ripple Fourier components tend to be damped in the image, and certain components cannot at all produce any contrast. Lorentz contrast from the Abrikosov lattice in hard superconductors is expected to be qualitatively similar to, but weaker than, ripple contrast. The Foucault mode is shown to be inferior to the defocused mode for quantitative high-resolution Lorentz microscopy.