Detecting magnetic ordering with atomic size electron probes
© The Author(s) 2016
Received: 28 January 2016
Accepted: 9 May 2016
Published: 27 May 2016
Although magnetism originates at the atomic scale, the existing spectroscopic techniques sensitive to magnetic signals only produce spectra with spatial resolution on a larger scale. However, recently, it has been theoretically argued that atomic size electron probes with customized phase distributions can detect magnetic circular dichroism. Here, we report a direct experimental real-space detection of magnetic circular dichroism in aberration-corrected scanning transmission electron microscopy (STEM). Using an atomic size-aberrated electron probe with a customized phase distribution, we reveal the checkerboard antiferromagnetic ordering of Mn moments in LaMnAsO by observing a dichroic signal in the Mn L-edge. The novel experimental setup presented here, which can easily be implemented in aberration-corrected STEM, opens new paths for probing dichroic signals in materials with unprecedented spatial resolution.
KeywordsAberration correction STEM EELS EMCD Aberrated probes Vortex beams
In the presence of a magnetic field, ferromagnets, paramagnets, antiferromagnets, and ferrimagnets exhibit different photon absorption cross sections that depend on the polarization of the incident photons. This effect, known as dichroism, has allowed polarized X-ray spectroscopy techniques, i.e., X-ray magnetic linear  and circular  dichroism (XMLD and XMCD), to probe the magnetic properties of materials since the mid-1980s. More recently, it was recognized that in transmission electron microscopy (TEM), under particular scattering conditions, magnetic dichroism could also be probed via energy-loss magnetic circular dichroism (EMCD) spectroscopy . Utilizing crystal as the beam splitter, it was possible to achieve spatial resolutions of about 1–2 nm [4, 5].
Until now, the goal of aberration correction in STEM has been to produce electron probes with sizes as small as possible. The reasoning is that smaller probes result in images and spectra with better spatial resolutions [6–8]. However, it has been recently argued on theoretical grounds that in some cases, it is desirable to have an atomic size electron probe with customized aberrations . According to inelastic electron diffraction calculations, aberrated probes can have tails with a phase distribution that plays an analogous role to polarization of X-rays when interacting with a material. These novel aberrated probes then can be utilized to obtain chiral dichroic signals in materials via electron energy-loss spectroscopy (EELS) with high spatial resolution. Furthermore, the aberrated probes allow the collection of EEL spectra using the transmitted beam, which results in EMCD with intrinsically larger signal-to-noise ratios than those obtained via nanodiffraction techniques , where most of the transmitted electrons are discarded.
In this study, we experimentally verify the theoretical prediction of Rusz et al. . We use an aberrated electron probe, which still maintains an atomic size, and detect the antiferromagnetic ordering of Mn moments in LaMnAsO by observing a dichroic signal in the Mn L-edge.
EMCD in STEM has been identified previously only in ferromagnets, because the size of the electron probes has been larger than the period over which the magnetic moment directions vary in antiferromagnets or ferrimagnets. However, according to Rusz et al. calculations , the key to reveal EMCD signals emerging from different magnetic orderings is to set a phase distribution of an atomic size electron probe that maximizes the symmetric component of EMCD at the spectrometer plane. EMCD arising from magnetic moments aligned along the electron beam direction, in a crystal with in-plane fourfold symmetry, can be detected using an aberrated electron probe containing fourfold astigmatism (known as C34 in Krivanek’s notation , or A3 in Haider’s notation ). Crystals with different symmetries require electron probes with different phase distributions . Here, we use a LaMnAsO as a model system, because it presents an antiferromagnetic ordering at room temperature, which is ideal to test if an aberrated probe can reveal an EMCD signal.
Sample preparation and susceptibility measurement
LaMnAsO was synthesized from LaAs and MnO. An equimolar mixture of the starting materials was mixed and compacted into a pellet. The pellet was sealed inside an evacuated silica glass ampoule and heated at 1000 °C for 24 h. X-ray diffraction showed the reaction product to be nearly single-phase LaMnAsO, with only 2–3 wt percent MnO and La2O3 detected as impurities. Neither of these phases is expected to influence the magnetic properties near or above room temperature.
More importantly, ferromagnetic MnAs (T C = 318 K) is not present in the sample, as confirmed by the linear M vs H data shown in Fig. 1b. Magnetization measurements were performed with a magnetic properties measurement system (Quantum Design). Note that the previous reports of TN via magnetization measurements have been masked by the presence of a ferromagnetic MnAs impurity with a Curie temperature of 317 K [13, 15]. However, the experimental measurement indicate that no ferromagnetic impurities are present in the synthesized sample, and that the magnetization of one formula unit of LaMnAsO in 2 T magnetic field is less than 0.2 % of the reported ordered moment per Mn atom . The low magnetization of LaMnAsO under the presence of an external magnetic field indicates that its checkerboard antiferromagnetic structure is basically unperturbed during the electron microscopy experiments—which were performed with a field of ~2T and at 295 K.
Inelastic electron scattering calculations
The calculations were performed using a combined multislice/Bloch-waves method . Elastic propagation of an aberrated probe was done by multislice calculations, using supercell of size 12 × 12 unit cells (4.9 × 4.9 nm2) in lateral directions and a real-space grid spacing of 6.4 pm. The energy-integrated inelastic transition matrix elements were calculated using the method of sum rules inversion . Cut-off parameter in Bloch waves calculations was set to 5 × 10−6, and the energy-filtered diffraction patterns were calculated on a grid from −5G to 5G in both directions with a step size of 0.2G, where G = (100). Convergence and collection angles, acceleration voltage were set according to the experiment. The energy-filtered STEM images were evaluated on a grid of 16 × 16 pixels within a unit cell. These calculations only obtain the integrated signal of the L3 peak for 3d transition metals. Quenching of the Mn L2 peak intensity due to multiple scattering effects and effects beyond dipole approximation in inelastic transition matrix elements is not considered.
STEM–EEL spectrum imaging experiments
The experiments were performed in an aberration-corrected STEM Nion UltraSTEM™ 100, equipped with a cold field emission electron source and a corrector of the third- and fifth-order aberrations, operating with a probe current of ~110 pA at 100 kV accelerating voltage . EEL spectra were collected using a Gatan Enfina spectrometer, with 0.3 eV/channel dispersion, giving an energy resolution of 0.9 eV. The convergence semi-angle for the incident probe and the EELS collection semi-angle were 30 mrad and 48 mrad, respectively. The sample’s thickness was obtained using the log-ratio method with an inelastic mean free path calculated using Lenz’ equation as described by Egerton . The EEL spectra data set shown in Fig. 5b (5e) contains 96 × 215 (50 × 130) spectra, and they were collected with a linear spectral density of ~29.1 spectra/nm using 20 ms/pixel dwell time acquisition. The spectra’s total acquisition time was from 8 to 13 min. The Z-contrast images were collected using ~86–200 mrad half-angle range.
The sample was in the electron microscope at a constant temperature of 22 °C (295 K). The temperature of the whole microscope system (both column and room separately) was constantly monitored and controlled with accuracy better than ±0.1 °C/h. This temperature stability over long periods of time in the electron microscope is one of the main factors that allow the acquisition of spectrum images with atomic resolution. Moreover, the determination of T N = 360 K and the negligible net magnetization at room temperature (Fig. 1b) clearly indicates that the electron microscopy experiments were performed within the antiferromagnetic regime. Sample heating due to the electron beam is calculated to be negligible here, considering the thermal conductivity of the material and its low thickness resulting in a small relative amount of inelastically scattered electrons .
Evaluation of the signal-to-noise ratio of the measured EMCD spectra
Configuring an atomic size fourfold (C34)-aberrated electron probe
The C34-aberrated electron probe was achieved using the following approach
Measure the relative angle of one of the main axes of the corrector with the horizontal direction of the CCD camera.
Measure the relative angle between one of the two main axes (a or b) of the studied LaMnAsO crystal and the horizontal direction of the CCD camera. This can be obtained by identifying a main Kikuchi line in the sample, for a grain previously aligned in a main zone axis. It is not important, which Kikuchi line is selected in this case. One can select the line that has the smallest angle with respect to the horizontal axis. However, the relative angles of both the corrector and the sample with the horizontal axis need to be defined consistently (either both clockwise or both counterclockwise) .
Calculate the aberration components C34a and C34b using the measured angle, δ, and the total magnitude of C34 (which for this experiment is defined as 15 μm), i.e., C34a = C34 cos δ, C34b = C34 sin δ. Here, δ is the difference of the relative angles between the sample and the corrector with respect to the horizontal axis . The calculated C34a and C34b values produce the desired antisymmetric phase distribution aligned with the axes of the LaMnAsO crystal as proposed in Ref. 9.
Run Nion’s Ronchigram aberration correction algorithm , using the calculated C34a and C34b as target values, until reaching convergence within the accuracy of the measurements.
Once the desired aberrations have been added to the electron probe, one can proceed to perform the experiments using any rotation angle in the scanning coils without affecting the measurements.
In a normal operation condition (i.e., used to achieve an aberration-corrected electron probe), Nion’s algorithm corrects all the aberrations in the electron optics up to the fifth order as described in Ref. . However, in the setup used here, all the aberrations (up to the fifth order) are corrected with the exception of C34a and C34b, which now have the values obtained in step (ii).
225, 129 (nm)
157, 196 (nm)
−185, 44.1 (nm)
−173, 48.7 (nm)
−1.78, 4.22 (μm)
5.08, 9.13 (μm)
0.67, −0.31 (μm)
9.95, 11.5 (μm)
−210.7, −262.3 (μm)
−210.7, −262.3 (μm)
348.5, −97.9 (μm)
348.5, −97.9 (μm)
68.0, −0.03 (μm)
68.0, −0.03 (μm)
−1.18, −7.41 (mm)
−1.18, −7.41 (mm)
−1.75, −0.14 (mm)
−1.75, −0.14 (mm)
−0.63, −0.17 (mm)
−0.63, −0.17 (mm)
DFT calculations of LaMnAsO were performed using an all-electron full-potential linearized augmented plane-waves method implemented in WIEN2k package . Spin-polarized local density approximation (LSDA) was used to describe exchange and correlation effects, including a +U correction (LSDA + U method) with U = 6 eV and J = 1 eV, using the around mean-field (AMF) double-counting correction . Spin-orbital coupling was included in the calculations. A large basis size of more than 120 basis functions per atom and 660 k-points in the irreducible wedge of the Brillouin zone were used to ensure a well-converged calculation.
Results and discussion
Figure 2e, f shows the experimental Z-contrast STEM images of a LaMnAsO grain oriented along the c-axis obtained with the corrected probe and the C34 aberrated probe, respectively. Noting that in the Z-contrast image acquired using the C34 aberrated probe (Fig. 2f), it is still possible to resolve individual La/As and Mn/O atomic columns, although an increase in the background and the Mn/O atomic column intensities can be observed when compared with the image acquired with the corrected probe. The increase in background is due to larger tails of the C34 aberrated probe.
In a previous theoretical study , it was noted that with electron vortex beams [24–27], an EMCD signal emerges only from probe positions that are close to the center of a magnetic atomic column. The localization of the EMCD signal contrasts to other EELS signals , which can, in principle, be non-local . We calculated the effective EMCD signal by taking the ratio between the inelastic scattering cross section evaluated solely using the imaginary part of the mixed dynamical form-factor (which corresponds to the magnetic signal—i.e., Mn↑–Mn↓) and the total inelastic scattering cross section arising in the EELS experiments . The calculations were performed with a 29-nm thick LaMnAsO sample (same thickness as the grain used in Fig. 2), for electrons accelerated at 100 kV, and with an added aberration C34 = 15 μm.
The Mn↑ and Mn↓ L-edge spectra (shown in Fig. 5b, e) were obtained by averaging all the spectra that are within a radius of 0.08 nm from the center of all the Mn sites, as shown schematically by the red and blue circles in the Z-contrast images (Fig. 5a, d), respectively. The Mn↑ and Mn↓ averaged spectra were obtained only from the affine-corrected data. The Mn↑–Mn↓ averaged spectra were background corrected using a power-law function (fitting energy region: 606–631 eV) and a non-parametric locally weighted scatterplot smoothing (LOWESS) algorithm .
A clear EMCD signature in the EEL spectra, defined as (Mn↑–Mn↓) presenting a change of sign in its integrated intensity between the L3 and L2 peaks, is only visible for the Mn L-edge acquired using the C34 aberrated probe (Fig. 5e, f). Moreover, the strength of the EMCD signal obtained experimentally at the Mn L3 peak is comparable with that obtained with the inelastic electron scattering calculations shown in Fig. 4b.
The discrepancy of about an order of magnitude between the experimentally EMCD measured Mn m l/m s ratio and the DFT calculation most likely arises from a quenching of the Mn L2 peak intensity due to multiple scattering effects and channeling of the electron probe. Theoretical modeling of the EEL spectra needs to be performed to fully understand the origin of the experimentally overestimated Mn m l/m s ratio.
In this study, the EMCD signal was denoised using robust principal component analysis [29, 30]. However, in the near future, obtaining better EMCD signal-to-noise ratios in the EEL spectra should be possible by straightforward improvements in the software controlling the scanning of the electron probe, and by better spectrometers. For instance, the spectra shown in Fig. 5e only utilized 12.5 % of the entire acquired data set per Mn moment orientation (25 % total). The other 75 % of the data is discarded. Since the EMCD is localized in the vicinity of the atomic columns, it makes more sense to use a “selective data acquisition” scheme where only spectra around the center of the atomic columns are collected. This “selective data acquisition” scheme will allow more spectra nearby the center of the atoms to be collected per data set, resulting in a considerable improvement of the EMCD signal-to-noise ratio. Such an improvement would mean that in future EMCD experiments, it will be possible to reveal the magnetic ordering of individual atomic columns and atomic size defects in materials, allowing element-selective quantitative measurements with atomic resolution (and single atom sensitivity) of spin and orbital magnetic moments of ferromagnets, ferrimagnets, and antiferromagnets using EMCD sum rules [32, 33]. The novel experimental setup presented here could also be used to test candidate magnetic structure models on materials that cannot be made in forms suitable for neutron diffraction.
density functional theory
energy-loss magnetic circular dichroism
electron energy-loss spectroscopy
full width at half maximum
spin polarized local density approximation
robust principal component analysis
scanning transmission electron microscopy
transmission electron microscopy
X-ray magnetic circular dichroism
X-ray magnetic linear dichroism
JCI and JR conceived the project and designed the experiment. JCI conducted the STEM and EELS experiments, analyzed the data (with JS and JR) and wrote the paper. JR performed the inelastic electron scattering calculations. MAM synthesized the LaMnAsO sample and performed the magnetic susceptibility measurements. RPCA was performed by JS. Preliminarily statistical analysis was performed by CTS and RRV. CC performed further EELS experiments. ARL helped with the electron optics configuration for the aberrated electron probes. All authors discussed the results and commented on the manuscript. All authors read and approved the final manuscript.
This research was supported by the Center for Nanophase Materials Sciences (CNMS), which is sponsored at Oak Ridge National Laboratory by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy (JCI), by the Swedish Research Council, Göran Gustafsson Foundation and Swedish National Infrastructure for Computing (NSC center) (JR), and by the Materials Sciences and Engineering Division Office of Basic Energy Sciences, U.S. Department of Energy (MAM, CC, ARL), and by UT-Battelle, LLC, under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy (CTS, RRV). Helpful discussions on correlated noise with B. Violinist and T. Kuula, on EELS data analysis and EMCD with Maria Varela, Wu Zhou and Kristiaan Pelckmans, and on setting up aberrated probes in the electron microscope with Niklas Dellby are gratefully acknowledged. The authors would like to specially thank Ondrej Krivanek and Niklas Dellby for discussions on electron microscopy, and for introducing the authors (JCI, JR, and ARL) during Nion’s organized Swift Workshop in March 2014. Without their intervention this manuscript would not have been possible.
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
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