Simulation of magnetic circular dichroism in the electron microscope

As electron energy-loss spectroscopy (EELS) and x-ray absorption spectroscopy (XAS) probe the same transitions from core-shell states to unoccupied states above the Fermi energy, it should always be possible to apply the two techniques to the same physical phenomena, such as magnetic dichroism, and obtain the same information. Indeed, the similarity in the expression of the electron and x-ray cross-sections had been already exploited to prove the equivalence of x-ray magnetic linear dichroism and anisotropy in EELS, by noting that the polarization vector of a photon plays the same role as the momentum transfer in electron scattering. Recently, the same was proven true for x-ray magnetic circular dichroism (XMCD) by establishing a new TEM technique called EMCD (electron energy-loss magnetic chiral dichroism) (Schattschneider P et al 2006 Nature 441 486-8), which makes use of special electron scattering conditions to force the absorption of a circularly polarized virtual photon. The intrinsic advantage of EMCD over XMCD is the high spatial resolution of electron microscopes, which are readily available. Among the particular obstacles in EMCD that do not exist for synchrotron radiation, is the notoriously low signal and the very particular scattering conditions necessary to observe a chiral dichroic signal. In spite of that, impressive progress has been made in recent years. The signal strength could be considerably increased, and some innovations such as using a convergent beam have been introduced. EMCD has evolved into several techniques, which make full use of the versatility of the TEM and energy filtering, spectroscopy or STEM conditions (Rubino S 2007 Magnetic circular dichroism in the transmission electron microscope PhD Thesis Vienna University of Technology, Vienna, Austria).