Magnetic properties of single nanomagnets: Electron energy-loss magnetic chiral dichroism on FePt nanoparticles

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.

Probing magnetic properties at the nanoscale: in-situ Hall measurements in a TEM

We report on advanced in-situ magneto-transport measurements in a transmission electron microscope. The approach allows for concurrent magnetic imaging and high resolution structural and chemical characterization of the same sample. Proof-of-principle in-situ Hall measurements on presumably undemanding nickel thin films supported by micromagnetic simulations reveal that in samples with non-trivial structures and/or compositions, detailed knowledge of the latter is indispensable for a thorough understanding and reliable interpretation of the magneto-transport data. The proposed in-situ approach is thus expected to contribute to a better understanding of the Hall signatures in more complex magnetic textures.

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.

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.

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.

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.

Induction Mapping of the 3D-Modulated Spin Texture of Skyrmions in Thin Helimagnets

Envisaged applications of Skyrmions in magnetic memory and logic devices crucially depend on the stability and mobility of these topologically nontrivial magnetic textures in thin films. We present for the first time quantitative maps of the magnetic induction that provide evidence for a 3D modulation of the Skyrmionic spin texture. The projected in-plane magnetic induction maps as determined from in-line and off-axis electron holography carry the clear signature of Bloch Skyrmions. However, the magnitude of this induction is much smaller than the values expected for homogeneous Bloch Skyrmions that extend throughout the thickness of the film. This finding can only be understood if the underlying spin textures are modulated along the out-of-plane z direction. The projection of (the in-plane magnetic induction of) helices is further found to exhibit thickness-dependent lateral shifts, which show that this z modulation is accompanied by an (in-plane) modulation along the x and y directions.

Electron beam-based metrology after CMOS

The magnitudes of the challenges facing electron-based metrology for post-CMOS technology are reviewed. Directed selfassembly, nanophotonics/plasmonics, and resistive switches and selectors, are examined as exemplars of important post-CMOS technologies. Materials, devices, and architectures emerging from these technologies pose new metrology requirements: defect detection, possibly subsurface, in soft materials, accurate measurement of size, shape, and roughness of structures for nanophotonic devices, contamination-free measurement of surface-sensitive structures, and identification of subtle structural, chemical, or electronic changes of state associated with switching in non-volatile memory elements. Electron-beam techniques are examined in the light of these emerging requirements. The strong electron-matter interaction provides measurable signal from small sample features, rendering electron-beam methods more suitable than most for nanometer-scale metrology, but as is to be expected, solutions to many of the measurement challenges are yet to be demonstrated. The seeds of possible solutions are identified when they are available.

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.

EMCD with an electron vortex filter: Limitations and possibilities

We discuss the feasibility of detecting spin polarized electronic transitions with a vortex filter. This approach does not rely on the principal condition of the standard electron energy-loss magnetic chiral dichroism (EMCD) technique, the precise alignment of the crystal in order to use it as a beam splitter, and thus would pave the way for the application of EMCD to new classes of materials and problems, like amorphous magnetic alloys and interface magnetism. The dichroic signal strength at the L_{2, 3}-edge of ferromagnetic Cobalt (Co) is estimated on theoretical grounds using a single atom scattering approach. To justify this approach, multi-slice simulations were carried out in order to confirm that orbital angular momentum (OAM) is conserved in amorphous materials over an extended range of sample thickness and also in very thin crystalline specimen, which is necessary for the detection of EMCD. Also artefact sources like spot size, mask tilt and astigmatism are discussed. In addition, the achievable SNR under typical experimental conditions is assessed.

Effects of dynamic diffraction conditions on magnetic parameter determination in a double perovskite Sr2FeMoO6 using electron energy-loss magnetic chiral dichroism

Electron energy-loss magnetic chiral dichroism (EMCD) spectroscopy, which is similar to the well-established X-ray magnetic circular dichroism spectroscopy (XMCD), can determine the quantitative magnetic parameters of materials with high spatial resolution. One of the major obstacles in quantitative analysis using the EMCD technique is the relatively poor signal-to-noise ratio (SNR), compared to XMCD. Here, in the example of a double perovskite Sr₂FeMoO₆, we predicted the optimal dynamical diffraction conditions such as sample thickness, crystallographic orientation and detection aperture position by theoretical simulations. By using the optimized conditions, we showed that the SNR of experimental EMCD spectra can be significantly improved and the error of quantitative magnetic parameter determined by EMCD technique can be remarkably lowered. Our results demonstrate that, with enhanced SNR, the EMCD technique can be a unique tool to understand the structure-property relationship of magnetic materials particularly in the high-density magnetic recording and spintronic devices by quantitatively determining magnetic structure and properties at the nanometer scale.