Despite various efforts, it remains an experimentally challenging task to access magnetic properties at
(sub) nanoscale. One route towards a direct measurement of magnetism is the measurement of electron
magnetic circular dichroism (EMCD) [1]. Being based on the measurement of electron energy loss
(EEL) spectra, EMCD can in principle be measured at atomic resolution and can open the door to study
exciting new area of physics such as magnetism in the vicinity of defects or interfaces. However, in
addition to general concerns of low signal to noise ratios of EMCD spectra measured at high
resolutions calling for a statistical data treatment, there might be other, non-magnetic contributions to
the signal which cause a change in the white line ratio of the L3/L2 edge peak of the magnetic species.
These white line changes might be related to the occurrence of a different chemical species of the same
element, e.g., due to in situ oxidation of the sample, or also to position dependent changes of the
electron wavefunction if the EMCD experiment is carried out at atomic resolution [2]. Such effects
may render the correct interpretation of EMCD signals impossible if they can not be clearly separated
from the true magnetic signal. The issue calls out for a statistical tool to separate the components.

We demonstrate how a canonical polyadic decomposition (CPD) [3],[4],[5] can be used to separate
magnetic and non-magnetic signals measured at the Fe/MgO interface. The system has recently
received a lot of attention as a candidate for magnetic tunnel junctions due to its large tunneling
magnetoresistance (e.g. [6],[7]), its magnetic properties, epecially at the interface are thus of interest.
Through the additional explanatory power of CPD, insight is gained on a perceived increase of orbital
to spin moment ratio at the interface [8]. Besides the spectral components and their spatial maps
(Fig.1), CPD also returns a vector containing the weight of the respective component in the data sets
measured with an aperture position such that the sign of the EMCD signal is positive, negative and
such that the magnetic component vanishes (Fig.2). The components shown below indicate a
significant non-magnetic white line branching towards the Fe/MgO interface.

CPD can not only be used as a technique to extract EMCD from noisy data and separate it from
potential non-magnetic signals, targeting both the aforementioned problems, but it can be generalized
to any problem of identifying different signal contributions in experiments where multiple data sets are
measured on the same sample area, such as momentum resolved EELS. It possesses desirable features
such as uniqueness while not constraining the components along either of the modes and comparatively
low computational costs. The assumptions on the tensor’s structure match the physical model and thus
lead to directly interpretable components. Hence, CPD is a useful addition to the set of statistical tools
for the analysis of microscopy data.

References:

[1] P. Schattschneider et al, Nature 441 (2006) 486.
[2] A. Gulec et al., Appl. Phys. Lett. 107 (2015) 143111.
[3] J. Carroll, J.-J. Chang, Psychometrika 35 (1970) 3.
[4] A. Cichocki et al, IEEE Signal Processing Magazine 145 (2015).
[5] J. Spiegelberg et al, submitted.
[6] S. Gautam et al, J. Appl. Phys. 115 (2014) 17C109.
[7] V. Serin et al, Phys. Rev. B 79 (2009) 144413.
[8] T. Thersleff et al, Manuscript.

Figures:

Figure 1: Spectra and abundancies of two components extracted with CPD. Both of them have an EMCD like spectral signature (d,e). d shows a component located over the bulk (a), whereas the component in e is centered at the interface (c, the interface is located at the bottom of the images above). b contains averaged, smoothened linescans taken over a (blue) and c (red).

Figure 2: Weights of the components above in the data sets measured at the three aperture positions. Between Chiral(+) and Chiral(-) position, a sign flip of the magnetic signal is expected, the on-axis data set does not include any EMCD signal. Only one of the components shows the expected weights (blue, bulk component in Fig.1), the other seems to be largely non-magnetic in nature.

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EMC Abstracts - https://emc-proceedings.com/abstract/separating-magnetic-and-non-magnetic-signals-at-the-femgo-interface/