Convergent‐Beam
EMCD
: Benefits, Pitfalls, and Applications
Authors: Löffler Stefan , Hetaba Walid 
Published: December 2016

Energy‐loss magnetic chiral dichroism (EMCD) [1] is a state‐of‐the‐art technique to measure magnetic properties on the nanoscale using TEM and EELS. Since its first experimental realization a decade ago, it has seen tremendous progress and many applications, including the analysis of phase transitions [2] or of magnetic nanoparticles [3,4].

EMCD exploits the spin‐orbit interaction in the sample that gives rise to different probabilities for the transfer of ±1ħ of orbital angular momentum (OAM) to the probe beam. The net OAM of the probe beam is then measured interferometrically in the diffraction plane. The classical EMCD approach uses an incident plane wave and a “point‐like” detector placed on the Thales circle through two diffraction spots. This, however, has two major shortcomings: on the one hand, it limits the best achievable spatial resolution to the size of the selected area aperture; on the other hand, it places the detector far off‐axis where the intensity is very low. Thus, it is difficult or even impossible to use for many applications, including many application‐relevant cases such as nanoparticles, interfaces, defects, or beam‐sensitive materials where long exposure times are not possible.

Here, we investigate the benefits of using a convergent incident beam for EMCD [5,6] by simulating the EMCD effect using the multislice algorithm [7] together with the mixed dynamic form factor (MDFF) approach [8] for a 10 nm Fe sample oriented in a systematic row condition including the (2 0 0) diffraction spot and an incident beam energy of 300 kV. As shown in fig. 1 for an Fe model system, a visible EMCD signal occurs up to large convergence angles as used in contemporary, Cs‐corrected STEMs. However, the region of large EMCD signal is “pushed out” away from the Thales circle towards the rim of the diffraction disks with increasing convergence angles. This is natural as the overall effect is expected to average out inside the diffraction disks. At the same time, it gives a good rule of thumb regarding the optimal position of the detector.

In addition, we investigate the signal‐to‐noise ratio (SNR) as a function of convergence and collection angles. For practical applications, the SNR actually plays a much more important role than the theoretical expected EMCD effect as even a high EMCD signal is useless if it is well below the noise level. As shown in fig. 2, the SNR is highest for medium convergence and collection angles of the order of the Bragg angle (~7 mrad for the present model system), while the EMCD effect under these conditions is only slightly smaller than for the “classical” case of small convergence and collection angles and a detector positioned on the Thales circle. Thus, it is not necessary (and, indeed, counter‐productive) to use a “point‐like” detector and parallel illumination which severely limits the recorded intensity as well as the spatial resolution.

Our analysis shows that convergent beam EMCD is not only possible, but actually is superior to classical EMCD in several aspects – most notably spatial resolution and SNR. This makes it the ideal tool for characterizing magnetic properties on the nanoscale, including the technologically relevant question of how the magnetic behavior changes at interfaces.