Separating Magnetic and Non‐magnetic Signals at the Fe/MgO Interface

Abstract

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.