Magnetic measurements with atomic-plane resolution

Noise-dependent bias in quantitative STEM-EMCD experiments revealed by bootstrapping

Electron magnetic circular dichroism (EMCD) is a powerful technique for estimating element-specific magnetic moments of materials on nanoscale with the potential to reach atomic resolution in transmission electron microscopes. However, the fundamentally weak EMCD signal strength complicates quantification of magnetic moments, as this requires very high precision, especially in the denominator of the sum rules. Here, we employ a statistical resampling technique known as bootstrapping to an experimental EMCD dataset to produce an empirical estimate of the noise-dependent error distribution resulting from application of EMCD sum rules to bcc iron in a 3-beam orientation. We observe clear experimental evidence that noisy EMCD signals preferentially bias the estimation of magnetic moments, further supporting this with error distributions produced by Monte-Carlo simulations. Finally, we propose guidelines for the recognition and minimization of this bias in the estimation of magnetic moments.

The influence of residual plural scattering after deconvolution in electron magnetic chiral dichroism

This work investigated the existence and influence of residual plural scattering in electron magnetic chiral dichroism (EMCD) spectra. A series of low-loss, conventional core-loss, and q-resolved core-loss spectra at Fe-L2,3 edges were detected from areas of different thicknesses in a plane-view sample of Fe/MgO (001) thin film. It reveals by comparison that there remains noticeable plural scattering in q-resolved spectra acquired at two particular chiral positions after deconvolution, and the residual scattering is more significant in thicker areas than thinner ones. Accordingly, the orbital-to-spin moment ratio extracted from EMCD spectra, which is the difference between the two q-resolved spectra after deconvolution, would be in principle increased with increasing sample thickness. The randomly fluctuated moment ratios displayed in our experiments are greatly attributed to a slight and irregular variation of local diffraction conditions due to the bending effect and imperfect epitaxy in detected areas. We suggest EMCD spectra should be acquired from sufficiently thin samples to minimize the plural scattering effect in originally detected spectra before any deconvolution. In addition, great care should be taken for slight misorientation and imperfect epitaxy when performing EMCD investigation on epitaxial thin films using a nano beam.

Single scan STEM-EMCD in 3-beam orientation using a quadruple aperture

The need to acquire multiple angle-resolved electron energy loss spectra (EELS) is one of the several critical challenges associated with electron magnetic circular dichroism (EMCD) experiments. If the experiments are performed by scanning a nanometer to atomic-sized electron probe on a specific region of a sample, the precision of the local magnetic information extracted from such data highly depends on the accuracy of the spatial registration between multiple scans. For an EMCD experiment in a 3-beam orientation, this means that the same specimen area must be scanned four times while keeping all the experimental conditions same. This is a non-trivial task as there is a high chance of morphological and chemical modification as well as non-systematic local orientation variations of the crystal between the different scans due to beam damage, contamination and spatial drift. In this work, we employ a custom-made quadruple aperture to acquire the four EELS spectra needed for the EMCD analysis in a single electron beam scan, thus removing the above-mentioned complexities. We demonstrate a quantitative EMCD result for a beam convergence angle corresponding to sub-nm probe size and compare the EMCD results for different detector geometries.

Prospect for measuring two-dimensional van der Waals magnets by electron magnetic chiral dichroism

Two-dimensional (2D) van der Waals magnets have drawn considerable attention in recent years triggered by the huge interest in novel magnetism and spintronic devices. Magnetic measurement of 2D van der Waals (vdW) magnets is crucial to understand the physical origin of magnetism in 2D limits. Therefore, advanced magnetic characterization techniques are highly required. However, only a limited number of such techniques are available due to the extremely small volume of 2D vdW magnets. Here, we introduce the electron magnetic chiral dichroism (EMCD) technique in transmission electron microscope (TEM) to measure 2D vdW crystals. In comparison with some other already-employed techniques in 2D magnets, EMCD is able to quantitatively measure magnetic parameters in three orthogonal directions at nanometer or even at atomic scale. We then perform EMCD simulations on several typical 2D vdW magnets with respect to the accelerating voltage, the number of atomic layers and beam tilt under zone axial orientation. The intensity and distribution of EMCD signals in three orthogonal directions are given in the diffraction plane, thereby providing an optimized design to achieve EMCD measurements. Finally, we discuss the signal-to-noise-ratio and required electron dose in order to obtain a measurable EMCD signal for 2D vdW magnets. Our results provide a feasibility analysis and guideline to measure 2D vdW magnets in future experiments.

Three-Dimensional Measurement of Magnetic Moment Vectors Using Electron Magnetic Chiral Dichroism at Atomic Scale

Here we have developed an approach of three-dimensional (3D) measurement of magnetic moment vectors in three Cartesian directions using electron magnetic chiral dichroism (EMCD) at atomic scale. Utilizing a subangstrom convergent electron beam in the scanning transmission electron microscopy (STEM), beam-position-dependent chiral electron energy-loss spectra (EELS), carrying the EMCD signals referring to magnetization in three Cartesian directions, can be obtained during the scanning across the atomic planes. The atomic resolution EMCD signals from all of three directions can be separately obtained simply by moving the EELS detector. Moreover, the EMCD signals can be remarkably enhanced using a defocused electron beam, relieving the issues of low signal intensity and signal-to-noise-ratio especially at atomic resolution. Our proposed method is compatible with the setup of the widely used atomic resolution STEM-EELS technique and provides a straightforward way to achieve 3D magnetic measurement at atomic scale on newly developing magnetic-field-free TEM.

Exploiting the Acceleration Voltage Dependence of EMCD

Energy-loss magnetic chiral dichroism (EMCD) is a versatile method for measuring magnetism down to the atomic scale in transmission electron microscopy (TEM). As the magnetic signal is encoded in the phase of the electron wave, any process distorting this characteristic phase is detrimental for EMCD. For example, elastic scattering gives rise to a complex thickness dependence of the signal. Since the details of elastic scattering depend on the electron's energy, EMCD strongly depends on the acceleration voltage. Here, we quantitatively investigate this dependence in detail, using a combination of theory, numerical simulations, and experimental data. Our formulas enable scientists to optimize the acceleration voltage when performing EMCD experiments.

Simultaneous mapping of EMCD signals and crystal orientations in a transmission electron microscope

When magnetic properties are analysed in a transmission electron microscope using the technique of electron magnetic circular dichroism (EMCD), one of the critical parameters is the sample orientation. Since small orientation changes can have a strong impact on the measurement of the EMCD signal and such measurements need two separate measurements of conjugate EELS spectra, it is experimentally non-trivial to measure the EMCD signal as a function of sample orientation. Here, we have developed a methodology to simultaneously map the quantitative EMCD signals and the local orientation of the crystal. We analyse, both experimentally and by simulations, how the measured magnetic signals evolve with a change in the crystal tilt. Based on this analysis, we establish an accurate relationship between the crystal orientations and the EMCD signals. Our results demonstrate that a small variation in crystal tilt can significantly alter the strength of the EMCD signal. From an optimisation of the crystal orientation, we obtain quantitative EMCD measurements.

Denoising of series electron holograms using tensor decomposition

In this study, a noise-reduction technique for series low-dose electron holograms using tensor decomposition is demonstrated through simulation. We treated an entire dataset of the series holograms with Poisson noise as a third-order tensor, which is a stack of 2D holograms. The third-order tensor, which is decomposed into a core tensor and three factor matrices, is approximated as a lower-rank tensor using only noise-free principal components. This technique is applied to simulated holograms by assuming a p-n junction in a semiconductor sample. The peak signal-to-noise ratios of the holograms and the reconstructed phase maps have been improved significantly using tensor decomposition. Moreover, the proposed method was applied to a more practical situation of time-resolved in situ electron holography by considering a nonuniform fringe contrast and fringe drift relative to the sample. The accuracy and precision of the reconstructed phase maps were quantitatively evaluated to demonstrate its effectiveness for in situ experiments and low-dose experiments on beam-sensitive materials.

Single-pass STEM-EMCD on a zone axis using a patterned aperture: progress in experimental and data treatment methods

Measuring magnetic moments in ferromagnetic materials at atomic resolution is theoretically possible using the electron magnetic circular dichroism (EMCD) technique in a (scanning) transmission electron microscope ((S)TEM). However, experimental and data processing hurdles currently hamper the realization of this goal. Experimentally, the sample must be tilted to a zone-axis orientation, yielding a complex distribution of magnetic scattering intensity, and the same sample region must be scanned multiple times with sub-atomic spatial registration necessary at each pass. Furthermore, the weak nature of the EMCD signal requires advanced data processing techniques to reliably detect and quantify the result. In this manuscript, we detail our experimental and data processing progress towards achieving single-pass zone-axis EMCD using a patterned aperture. First, we provide a comprehensive data acquisition and analysis strategy for this and other EMCD experiments that should scale down to atomic resolution experiments. Second, we demonstrate that, at low spatial resolution, promising EMCD candidate signals can be extracted, and that these are sensitive to both crystallographic orientation and momentum transfer.

Application of machine learning techniques to electron microscopic/spectroscopic image data analysis

The combination of scanning transmission electron microscopy (STEM) with analytical instruments has become one of the most indispensable analytical tools in materials science. A set of microscopic image/spectral intensities collected from many sampling points in a region of interest, in which multiple physical/chemical components may be spatially and spectrally entangled, could be expected to be a rich source of information about a material. To unfold such an entangled image comprising information and spectral features into its individual pure components would necessitate the use of statistical treatment based on informatics and statistics. These computer-aided schemes or techniques are referred to as multivariate curve resolution, blind source separation or hyperspectral image analysis, depending on their application fields, and are classified as a subset of machine learning. In this review, we introduce non-negative matrix factorization, one of these unfolding techniques, to solve a wide variety of problems associated with the analysis of materials, particularly those related to STEM, electron energy-loss spectroscopy and energy-dispersive X-ray spectroscopy. This review, which commences with the description of the basic concept, the advantages and drawbacks of the technique, presents several additional strategies to overcome existing problems and their extensions to more general tensor decomposition schemes for further flexible applications are described.

Magnetic measurement by electron magnetic circular dichroism in the transmission electron microscope

Magnetic measurement by transmitted electrons at nanometer or even atomic scale is always an attractive and challenging issue in the transmission electron microscope. Electron magnetic circular dichroism, proposed in 2003 and realized in 2006, opens a new insight into the measurement of local magnetic properties. Later, it is developed into a powerful technique for quantitative magnetic measurement with site specificity and element specificity at high spatial resolution over years of efforts, both in the aspect of theory and experiments. The novel technique has been widely applied to the characterization of magnetic materials now. This present review gives an overview of its development and applications in the past fifteen years since its invention. The theory of electron magnetic circular dichroism and its development are reviewed. The diffraction geometry and experimental setups are summarized. The general way for quantitative measurement of magnetic parameters is presented with typical cases. Representative breakthroughs in method development and applications over a wide range of materials are then described. Finally, prospects for future development are briefly discussed.

Nanoscale measurement of giant saturation magnetization in α″-Fe16N2 by electron energy-loss magnetic chiral dichroism

Metastable α″-Fe₁₆N₂ thin films were reported to have a giant saturation magnetization of above 2200 emu/cm³ in 1972 and have been considered as candidates for next-generation rare-earth-free permanent magnetic materials. However, their magnetic properties have not been confirmed unequivocally. As a result of the limited spatial resolution of most magnetic characterization techniques, it is challenging to measure the saturation magnetization of the α″-Fe₁₆N₂ phase, as it is often mixed with the parent α'-Fe₈N phase in thin films. Here, we use electron energy-loss magnetic chiral dichroism (EMCD), aberration-corrected transmission electron microscopy, X-ray diffraction and macroscopic magnetic measurements to study α″-Fe₁₆N₂ (containing ordered N atoms) and α'-Fe₈N (containing disordered N atoms). The ratio of saturation magnetization in α″-Fe₁₆N₂ to that in α'-Fe₈N is determined to be 1.31 ± 0.10 from quantitative EMCD measurements and dynamical diffraction calculations, confirming the giant saturation magnetization of α″-Fe₁₆N₂. Crystallographic information is also obtained about the two phases, which are mixed on the nanoscale.

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.

Effect of cation ratio and order on magnetic circular dichroism in the double perovskite Sr2Fe1+xRe1-xO6

Superexchange-based magnetic coupling of the two B-site cations in rock-salt-ordered double perovskite oxides is extremely sensitive to the cation ratio and degree of order. However, as a result of the limited spatial resolution of most magnetic characterization techniques, it is challenging to establish a direct relationship between magnetic properties and structure in these materials, including the effects of elemental segregation and cation disorder. Here, we use electron energy-loss magnetic chiral dichroism together with aberration-corrected electron microscopy and spectroscopy to record magnetic circular dichroism (MCD) spectra at the nm scale, in combination with structural and chemical information at the atomic scale from the very same region. We study nanoscale phases in ordered Sr₂[Fe][Re]O₆, ordered Sr₂[Fe][Fe_1/5Re_4/5]O₆ and disordered Sr[Fe_4/5Re_1/5]O₃ individually, in order to understand the role of cation ratio and order on local magnetic coupling. When compared with ordered Sr₂[Fe][Re]O₆, we find that antiferromagnetic Fe³⁺-O^2--Fe³⁺superexchange interactions arising from an excess of Fe suppress the MCD signal from Fe cations in ordered Sr₂[Fe][Fe_1/5Re_4/5]O₆, while dominant Fe³⁺-O^2--Fe³⁺antiferromagnetic coupling in disordered Sr[Fe_4/5Re_1/5]O₃ leads to a decrease in MCD signal down to the noise level. Our work demonstrates a protocol that can be used to correlate crystallographic, electronic and magnetic information in materials such as Sr₂Fe_1+xRe_1-xO₆, in order to provide insight into structure-property relationships in double perovskite oxides at the atomic scale.

Probing the localization of magnetic dichroism by atomic-size astigmatic and vortex electron beams

We report localization of a magnetic dichroic signal on atomic columns in electron magnetic circular dichroism (EMCD), probed by beam distorted by four-fold astigmatism and electron vortex beam. With astigmatic probe, magnetic signal to noise ratio can be enhanced by blocking the intensity from the central part of probe. However, the simulations show that for atomic resolution magnetic measurements, vortex beam is a more effective probe, with much higher magnetic signal to noise ratio. For all considered beam shapes, the optimal SNR constrains the signal detection at low collection angles of approximately 6–8 mrad. Irrespective of the material thickness, the magnetic signal remains strongly localized within the probed atomic column with vortex beam, whereas for astigmatic probes, the magnetic signal originates mostly from the nearest neighbor atomic columns. Due to excellent signal localization at probing individual atomic columns, vortex beams are predicted to be a strong candidate for studying the crystal site specific magnetic properties, magnetic properties at interfaces, or magnetism arising from individual atomic impurities.

Atomic scale imaging of magnetic circular dichroism by achromatic electron microscopy

In order to obtain a fundamental understanding of the interplay between charge, spin, orbital and lattice degrees of freedom in magnetic materials and to predict and control their physical properties^1-3, experimental techniques are required that are capable of accessing local magnetic information with atomic-scale spatial resolution. Here, we show that a combination of electron energy-loss magnetic chiral dichroism ⁴ and chromatic-aberration-corrected transmission electron microscopy, which reduces the focal spread of inelastically scattered electrons by orders of magnitude when compared with the use of spherical aberration correction alone, can achieve atomic-scale imaging of magnetic circular dichroism and provide element-selective orbital and spin magnetic moments atomic plane by atomic plane. This unique capability, which we demonstrate for Sr₂FeMoO₆, opens the door to local atomic-level studies of spin configurations in a multitude of materials that exhibit different types of magnetic coupling, thereby contributing to a detailed understanding of the physical origins of magnetic properties of materials at the highest spatial resolution.

An in-plane magnetic chiral dichroism approach for measurement of intrinsic magnetic signals using transmitted electrons

Electron energy-loss magnetic chiral dichroism is a powerful technique that allows the local magnetic properties of materials to be measured quantitatively with close-to-atomic spatial resolution and element specificity in the transmission electron microscope. Until now, the technique has been restricted to measurements of the magnetic circular dichroism signal in the electron beam direction. However, the intrinsic magnetization directions of thin samples are often oriented in the specimen plane, especially when they are examined in magnetic-field-free conditions in the transmission electron microscope. Here, we introduce an approach that allows in-plane magnetic signals to be measured using electron magnetic chiral dichroism by selecting a specific diffraction geometry. We compare experimental results recorded from a cobalt nanoplate with simulations to demonstrate that an electron magnetic chiral dichroism signal originating from in-plane magnetization can be detected successfully.

Electron energy-loss magnetic chiral dichroism enables the measurement of the local magnetic properties of a material using a transmission electron microscope, but is limited to signals in the electron-beam direction. Here, the authors demonstrate a method to extend this to in-plane magnetic signals too.

Atom size electron vortex beams with selectable orbital angular momentum

The decreasing size of modern functional magnetic materials and devices cause a steadily increasing demand for high resolution quantitative magnetic characterization. Transmission electron microscopy (TEM) based measurements of the electron energy-loss magnetic chiral dichroism (EMCD) may serve as the needed experimental tool. To this end, we present a reliable and robust electron-optical setup that generates and controls user-selectable single state electron vortex beams with defined orbital angular momenta. Our set-up is based on a standard high-resolution scanning TEM with probe aberration corrector, to which we added a vortex generating fork aperture and a miniaturized aperture for vortex selection. We demonstrate that atom size probes can be formed from these electron vortices and that they can be used for atomic resolution structural and spectroscopic imaging - both of which are prerequisites for future atomic EMCD investigations.