Investigation of the Geometrical-Optical Theory of Magnetic Structure Imaging in the Electron Microscope

Abstract

The imaging of domain walls in thin ferromagnetic films by off‐focus transmission electron microscopy is generally considered in terms of a simple geometrical‐optical theory in which the electron beam is deviated by the Lorentz force exerted by the internal magnetic flux of the film. Calculated intensity profiles of the wall images are rectangular in form for large off‐focus distances where the geometrical‐optical approach is valid. The width of the images is simply related to the thickness and internal magnetic flux of the film and to the off‐focus distance of the observation plane and the electron beam accelerating potential. An experimental investigation of these relationships for vacuum‐condensed films of iron, nickel, and their alloys shows general agreement with the theoretical relationships derived for 180° Néel walls. The observed electron beam deflections within the films are about half of the calculated values. This is largely due to the wall angles being less than 180° and to the film density being below that of the bulk material. Domain wall widths in 80–20 Ni–Fe films about 200 Å thick were found to be approximately 2000 Å, leading to a value for the exchange constant of this material of around 8×10⁻⁷ erg·cm⁻¹.