Electron Energy Loss Spectroscopy of oriented targets and magnetic transitions

Abstract

Electron beam energies in Transmission Electron Microscopes (TEMs) reach the relativistic realm constituting Quantum Electrodynamics (QED) the appropriate framework for the study of electron matter interaction in TEMs. We focus on the inelastic scattering of relativistic electrons from a generic oriented target. The inelastic differential cross section factorizes to the fast electron part which is calculated analytically, and the dynamic form factor of the target, which encodes the response of the medium to the interaction with the beam. The properties of the dynamic form factor of oriented targets are analyzed. We then derive the scattering cross section of electrons by magnetic targets where spin-flip transitions are induced. We comment on the kinematic regimes where the coefficient of the transverse magnetic interaction is amplified compared to the coulomb matrix element.

Figures (8)

• Figure 1: Feynman diagram for the scattering of a high-energy electron from a heavy target.
• Figure 2: Feynman diagram for the excitation of heavy target by an external electromagnetic field.
• Figure 3: The scattering coefficients as functions of the angle, for $V_{beam} = 300 kV$ and $E_{loss} = 0.1eV$. a) $C_L$ and $C_T$. c) The ratio $C_T/C_L$. The shape of the plots does not depend strongly at the value of the energy loss.
• Figure 4: The scattering coefficients as a function of the angle in the area of the steepest slope (small angles $\sim \mu rads$). For higher energy loss the steep curve extends to a few mrads. a) $C_L$ and $C_T$. c) The ratio $C_T/C_L$. $V_{beam} = 300 kV$. $E_{loss} = 0.1eV$.
• Figure 5: The scattering coefficients as functions of energy loss and angle. a) $C_L$. b) $C_T$. c) The ratio $C_T/C_L$. $E_{beam} = 300 keV$