Electron magnetic circular dichroism (EMCD) in the transmission electron microscope (TEM) is a relatively immature experimental technique, though it has already demonstrated quantitative results with a spatial resolution superior to what can be achieved with X-rays [1]. The main obstacles for widely sharing the method for routine use are (i) low SNR because of off-axis EELS detection, (ii) necessity of a very thin sample (a few nanometers) for quantitative analysis and (iii) unstable pre- and post-edge backgrounds by subsequent measurements in changing the aperture positions. There have been a number of attempts to overcome those difficulties, such as collecting a large quantity of data and applying statistical/information data processing methods [2,3]. In the present study we found a novel experimental condition that allowed us to solve almost all these issues and even applicable to atomic resolution EMCD measurements.

Consider the symmetrical 3-beam diffraction condition with an appropriate convergence angle, where the diffraction discs are partially overlapped, as shown in Fig. 1. In this configuration the magnetic signals included in a core-loss spectrum (e.g., Fe-L_{2,3} white-line) is expressed in a simplified form of Eq. (1), where T** _{G}** is the transmittance of the Bragg disc of

**G**, the argument of the sine function is the phase difference between the electron wavefunctions at a point of the disc overlapping regions, and

*S*(

**q**,

**q**–

**G**,

*E*) is the mixed dynamical form factor [4]. The first term stands for the classical EMCD signal. The second term is a new ‘phase-dependent EMCD’, which can be further simplified within the dipole approximation as in Eq. (2), where M

_{z}is the net magnetization in the direction of the optic axis and Δ

_{x}is the spatial coordinate in real space, measured perpendicular to the lattice planes with respect to the arbitrary atomic plane. Eq. (2) implies that a quite large fraction of chiral ± magnetic signals appear in an alternating manner in scanning the sub-nanometer electron probe on the sample perpendicular to the lattice fringes with the EELS entrance aperture covering an extended area over the either side of the diffraction discs with respect to the

*x*axis in Fig. 1.

The above proposed scheme was tested on the symmetrical 3-beam [110] diffraction condition in a 20 nm thick Fe film for STEM mode with the EELS aperture placed slightly off-axis on either side of the systematic row of the reflections. A focused electron probe with the convergence semi-angle of 10 mrad is scanned across the sample surface to find 1-dimensional lattice fringes as the ADF-STEM image, as shown in Figs. 2(a) and (b). The chiral ± EMCD signals should appear at the 1/4 of the lattice interval on both sides from the exact atomic column fringes, with the EMCD signal of the opposite sign appearing on the opposite sides of a lattice fringe, as shown in Fig. 2(c). Finally we applied a set of statistical treatments [5] to efficiently extract the EMCD signal. The extracted EMCD signal and its spatial localization map are shown in Fig. 3. Although the spatial distribution of the magnetic signal was quite noisy, the experimental intensity profiles of the non-magnetic and magnetic (EMCD) signals averaged over the direction parallel to the lattice planes showed the expected localization patterns, as shown in Fig. 4.

This method requires only a single scan to obtain the chiral ± EMCD signals and also exhibits stable signal fractions with the change in sample thickness. The present scheme solves most of the existing experimental difficulties and is a novel breakthrough for quantitative atomic scale EMCD measurements.

*References*

[1] Hebert and Schattschneider, *Ultramicrosc*. **96** (2003) 463-468.

[2] Muto*,* Tatsumi and Rusz, *Ultramicrosc*. **135** (2013) 89-96.

[3] Muto *et al*, *Nature Commun*. **5** (2014) 3138-1-5.

[4] J. Rusz, J. C. Idrobo, and S. Bhowmick, Phys. Rev. Lett. 113, 145501 (2014).

[5] C. Andersson, R. Bro, Chem. Int. Lab. Sys. 52, 1 (2000).

[6] This work was in part supported by Grant-in-Aid for Scientific Research of JSPS and Japan-Sweden Joint Research Program by JSPS and STINT.

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