Application of the dynamical theory of electron diffraction to ferromagnetic crystals

Abstract

Following the qualitative results of a previous paper (Jakubovics 1964), the effect of magnetization on diffraction contrast in transmission electron niicroscopy is investigated in terms of the dynaniical theory of diffraction. It is shown that the effect of a uniform magnetization is equivalent to that of an elastic deformation in which the lattice planes are bent about the component of the magnetization normal to the incident electron beam. Differential equations for the variation of the transmitted and diffracted amplitudes are derived and integrated numerically. The main features of the results can be derived from the symmetry properties of the scattering matrix, given by Howie and Whelan (1961) for the bright-field image, and Ball (1964) for the dark-field image. These symmetry considerations show that the effect of magnetization on the bright-field image is approximately the same as that of changing the deviation parameter w by an amount corresponding to half the Lorentz deflection. The effect on the dark-field image is more complicated. Intensity measurements on the dark field image allow the anomalous absorption parameter to be determined. The results of the theory are confirmed experimentally.