Spin-Dependent Nonlinear Contrast Transfer in Transmission Electron Microscopy

Abstract

Abstract In this study, the spin-dependent nonlinear contrast transfer in transmission electron microscopy is derived from the eikonal expansion of the Dirac equation. The transmission cross-coefficient of the standard imaging theory is amended by a spin-dependent factor, whose effect is investigated for single scattering in the object by an electrical field under polarized and unpolarized illumination, and it is illustrated with numerical results and plots for a kinetic energy of 80 keV. The resulting image displacement and image convolution increase with decreasing kinetic energy but are always smaller than a wavelength. General features of the cross-coefficient are discussed to identify favorable conditions for the measurement of the small spin effects, possibly in an unmodified instrument.