Proposal for Measuring Magnetism with Patterned Apertures in a Transmission Electron Microscope.

We propose a magnetic measurement method utilizing a patterned postsample aperture in a transmission electron microscope. While utilizing electron magnetic circular dichroism, the method circumvents previous needs to shape the electron probe to an electron vortex beam or astigmatic beam. The method can be implemented in standard scanning transmission electron microscopes by replacing the spectrometer entrance aperture with a specially shaped aperture, hereafter called a ventilator aperture. The proposed setup is expected to work across the whole range of beam sizes-from wide parallel beams down to atomic resolution magnetic spectrum imaging.

Blind identification of magnetic signals in electron magnetic chiral dichroism using independent component analysis.

Electron magnetic chiral dichroism (EMCD) is a promising technique to investigate local magnetic structures in the electron microscope. However, recognition of the EMCD signal, or also finding optimal parameter settings for given materials and sample orientations typically requires extensive simulations to aid the experiment. Here, we discuss how modern data processing techniques, in particular independent component analysis, can be used to identify magnetic signals in an unsupervised manner from energy filtered transmission electron microscopy (EFTEM) images. On the background of the recent advent of 4D scanning transmission electron microscopy, we discuss how this data processing may enable simultaneous tracking of all three spatial components of the magnetic momenta for arbitrary materials and several sample orientations without the previous need of complementary simulations.

Local low rank denoising for enhanced atomic resolution imaging.

Atomic resolution imaging and spectroscopy suffers from inherently low signal to noise ratios often prohibiting the interpretation of single pixels or spectra. We introduce local low rank (LLR) denoising as tool for efficient noise removal in scanning transmission electron microscopy (STEM) images and electron energy-loss (EEL) spectrum images. LLR denoising utilizes tensor decomposition techniques, in particular the multilinear singular value decomposition (MLSVD), to achieve a denoising in a general setting largely independent of the signal features and data dimension, by assuming that the signal of interest is of low rank in segments of appropriately chosen size. When applied to STEM images of graphene, LLR denoising suppresses statistical noise while retaining fine image features such as scan row-wise distortions, possibly related to rippling of the graphene sheet and consequent motion of atoms. When applied to EEL spectra, LLR denoising reveals fine structures distinguishing different lattice sites in the spinel system CoFe2O4.

Unmixing hyperspectral data by using signal subspace sampling.

This paper demonstrates how Signal Subspace Sampling (SSS) is an effective pre-processing step for Non-negative Matrix Factorization (NMF) or Vertex Component Analysis (VCA). The approach allows to uniquely extract non-negative source signals which are orthogonal in at least one observation channel, respectively. It is thus well suited for processing hyperspectral images from X-ray microscopy, or other emission spectroscopies, into its non-negative source components. The key idea is to resample the given data so as to satisfy better the necessity and sufficiency conditions for the subsequent NMF or VCA. Results obtained both on an artificial simulation study as well as based on experimental data from electron-microscopy are reported.

The usage of data compression for the background estimation of electron energy loss spectra.

Quantitative analysis of noisy electron spectrum images requires a robust estimation of the underlying background signal. We demonstrate how modern data compression methods can be used as a tool for achieving an analysis result less affected by statistical errors or to speed up the background estimation. In particular, we demonstrate how a multilinear singular value decomposition (MLSVD) can be used to enhance elemental maps obtained from a complex sample measured with energy electron loss spectroscopy. Furthermore, the usage of vertex component analysis (VCA) for a basis vector centered estimation of the background is demonstrated. Arising computational benefits in terms of model accuracy and computational costs are studied.

Towards sub-nanometer real-space observation of spin and orbital magnetism at the Fe/MgO interface.

While the performance of magnetic tunnel junctions based on metal/oxide interfaces is determined by hybridization, charge transfer, and magnetic properties at the interface, there are currently only limited experimental techniques with sufficient spatial resolution to directly observe these effects simultaneously in real-space. In this letter, we demonstrate an experimental method based on Electron Magnetic Circular Dichroism (EMCD) that will allow researchers to simultaneously map magnetic transitions and valency in real-space over interfacial cross-sections with sub-nanometer spatial resolution. We apply this method to an Fe/MgO bilayer system, observing a significant enhancement in the orbital to spin moment ratio that is strongly localized to the interfacial region. Through the use of first-principles calculations, multivariate statistical analysis, and Electron Energy-Loss Spectroscopy (EELS), we explore the extent to which this enhancement can be attributed to emergent magnetism due to structural confinement at the interface. We conclude that this method has the potential to directly visualize spin and orbital moments at buried interfaces in magnetic systems with unprecedented spatial resolution.

Tensor decompositions for the analysis of atomic resolution electron energy loss spectra.

A selection of tensor decomposition techniques is presented for the detection of weak signals in electron energy loss spectroscopy (EELS) data. The focus of the analysis lies on the correct representation of the simulated spatial structure. An analysis scheme for EEL spectra combining two-dimensional and n-way decomposition methods is proposed. In particular, the performance of robust principal component analysis (ROBPCA), Tucker Decompositions using orthogonality constraints (Multilinear Singular Value Decomposition (MLSVD)) and Tucker decomposition without imposed constraints, canonical polyadic decomposition (CPD) and block term decompositions (BTD) on synthetic as well as experimental data is examined.

Analysis of electron energy loss spectroscopy data using geometric extraction methods.

A set of geometric data decomposition methods is discussed. In particular, randomized vertex component analysis (RVCA), an extension of vertex component analysis (VCA) for the application to noisy data, is established. Minimum volume simplex analysis (MVSA), a recent technique for the extraction of endmembers in the absence of pure pixels, is presented. A comparison between MVSA and the previously presented technique of Bayesian Linear Unmixing (BLU) is drawn. Lastly, the efficiency of these methods for high-dimensional data is examined. Improvement on the extracted source components spectral signatures are achieved by establishing Gaussian mixture modeling as extraction technique.

Can we use PCA to detect small signals in noisy data?

Principal component analysis (PCA) is among the most commonly applied dimension reduction techniques suitable to denoise data. Focusing on its limitations to detect low variance signals in noisy data, we discuss how statistical and systematical errors occur in PCA reconstructed data as a function of the size of the data set, which extends the work of Lichtert and Verbeeck, (2013) [16]. Particular attention is directed towards the estimation of bias introduced by PCA and its influence on experiment design. Aiming at the denoising of large matrices, nullspace based denoising (NBD) is introduced.

Magnetic measurements with atomic-plane resolution.

Rapid development of magnetic nanotechnologies calls for experimental techniques capable of providing magnetic information with subnanometre spatial resolution. Available probes of magnetism either detect only surface properties, such as spin-polarized scanning tunnelling microscopy, magnetic force microscopy or spin-polarized low-energy electron microscopy, or they are bulk probes with limited spatial resolution or quantitativeness, such as X-ray magnetic circular dichroism or classical electron magnetic circular dichroism (EMCD). Atomic resolution EMCD methods have been proposed, although not yet experimentally realized. Here, we demonstrate an EMCD technique with an atomic size electron probe utilizing a probe-corrected scanning transmission electron microscope in its standard operation mode. The crucial element of the method is a ramp in the phase of the electron beam wavefunction, introduced by a controlled beam displacement. We detect EMCD signals with atomic-plane resolution, thereby bringing near-atomic resolution magnetic circular dichroism spectroscopy to hundreds of laboratories worldwide.

A multislice theory of electron scattering in crystals including backscattering and inelastic effects.

In the framework of the slice transition operator technique, a general multislice theory for electron scattering in crystals is developed. To achieve this generalization, we combine the approaches for inelastic scattering derived by Yoshioka [J. Phys. Soc. Jpn. 12, 6 (1957)] and backscattering based on the formalism of Chen and Van Dyck [Ultramicroscopy 70, 29-44 (1997)]. A computational realization of the obtained equations is suggested. The proposed computational scheme is tested on elastic backscattering of electrons, where we consider single backscattering in analogy to the computational scheme proposed by Chen and Van Dyck.