Abstract
Atomic-scale observations of a specific local area would be considerably beneficial when exploring new fundamental materials and devices. The development of hardware-type aberration correction1,2 in electron microscopy has enabled local structural observations with atomic resolution3,4,5 as well as chemical and vibration analysis6,7,8. In magnetic imaging, however, atomic-level spin configurations are analysed by electron energy-loss spectroscopy by placing samples in strong magnetic fields9,10,11, which destroy the nature of the magnetic ordering in the samples. Although magnetic-field-free observations can visualize the intrinsic magnetic fields of an antiferromagnet by unit-cell averaging12, directly observing the magnetic field of an individual atomic layer of a non-uniform structure is challenging. Here we report that the magnetic fields of an individual lattice plane inside materials with a non-uniform structure can be observed under magnetic-field-free conditions by electron holography with a hardware-type aberration corrector assisted by post-digital aberration correction. The magnetic phases of the net magnetic moments of (111) lattice planes formed by opposite spin orderings between Fe3+ and Mo5+ in a ferrimagnetic double-perovskite oxide (Ba2FeMoO6) were successfully observed. This result opens the door to direct observations of the magnetic lattice in local areas, such as interfaces and grain boundaries, in many materials and devices.
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Data availability
The data that support the findings of this study are available from the corresponding author upon request and with the permission of the Japanese government sponsors who funded the work.
Code availability
The code used for the analyses is available from the corresponding author upon request and with the permission of the Japanese government sponsors that funded the work.
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Acknowledgements
This research was supported by a grant from the Japan Society for the Promotion of Science (JSPS) through the ‘Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program)’ initiated by the Council for Science, Technology, and Innovation and by a Japan Science and Technology Agency (JST) CREST programme (Grant No. JPMJCR 1664). X.Z.Y. was supported in part by a grant-in-aid for scientific research (A) (Grant No. 19H00660) from JSPS and a JST CREST programme (Grant No. JPMJCR 20T1). Y. Tokura was supported in part by a grant-in-aid for scientific research (S) (Grant No. 23H05431) from JSPS and a JST CREST programme (Grant No. JPMJCR1874).
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T.T., T.A., K.H., Y.M. and H.S. conceived and designed the experiments. T.T., T.A., T.Y. and Y.M. performed the experiments and carried out the analysis. T.T., T.Y., K.I., M.I. and K.M. performed the simulations. Y. Tomioka, X.Z.Y. and Y. Tokura contributed to materials design and synthesized the single crystal. All authors discussed the results and commented on the manuscript.
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Extended data figures and tables
Extended Data Fig. 1 Experimental setup for high-resolution magnetic-field observation and transmission electron microscopic cross-sectional image of the observed sample.
a, Schematic of electron-holography experiment. An 1.2-MeV coherent electron wave passes through the sample (object wave) and vacuum (reference wave). A high-resolution object wave formed by the aberration-corrected imaging system is overlapped with the reference wave by a biprism, and an electron hologram is formed at the image plane, where a direct electron-detection camera is placed. To separate the electrostatic and magnetic phases, pairs of electron holograms with opposite directional magnetizations in the sample are acquired. The magnetization direction in the sample is reversed by using a pulsed magnetic field generated by coils placed near two sides of the sample. b, Schematic of the rectangular sample used to create [\(\bar{1}\bar{1}\)2] or [11\(\bar{2}\)] directional magnetization along the (111) lattice plane. c, Full view of the cross section. The cross-sectional thin TEM sample of the area observed by electron holography was fabricated after the holography experiment. Carbon is deposited as a protection layer in the sample preparation for cross-sectional observation. d, Enlarged image of the left end of c. The black arrow indicates the observation area subjected to the high-resolution analysis of the magnetic field.
Extended Data Fig. 2 Defocus, astigmatism, and spherical aberration corrections by electron holography.
Reconstructed amplitude (a) and phase (b) images with spatial frequency up to 1/0.23 nm−1. c, Fast Fourier transform (FFT) image of the amplitude image with digital defocus of −200 nm. The elongated ring pattern indicates two-fold astigmatism (A1). d, Thon diagram of the amplitude of the reconstructed wave. Minimum amplitude at df = 40 nm (yellow line) indicates that C1 in this reconstructed wave was −40 nm. Aberrations of focus (C1) and A1 values estimated from the Thon diagram are indicated in d. Aberration-corrected amplitude (e) and phase (f) images. g, FFT image of A1-corrected amplitude image with digital defocus of −200 nm. h, Thon diagram for amplitude of the C1-corrected wave. Experimental defocus (C1) was corrected, and minimum amplitude is shifted to df = 0 nm (red line). The blue pattern is the simulated Thon diagram matched with the aberration-corrected Thon diagram. It indicates the point resolution in the digitally aberration-corrected image is 0.26 nm. i, Thon diagram before spherical aberration correction. Green line shows bending of central black curve due to spherical aberrations (C3: −4.0 mm, C5: 2.14 km). j, Thon diagram after spherical aberration correction.
Extended Data Fig. 3 Aberration-corrected single-phase image and low-resolution magnetic phase.
a, Aberration-corrected phase image. The lattice image of the (111) plane is clearly seen. The scale bar is 2 nm. b, Low-resolution magnetic phase. c, Line profiles of low-resolution magnetic phase of the area indicated by the dashed light-blue rectangle. The phase slope of magnetic phase indicates [\(\bar{1}\bar{1}\)2] directional magnetization. A non-magnetic area is clearly visible at the edge of the sample.
Extended Data Fig. 4 Low-resolution simulated magnetic phase.
a, Rectangular model used in the simulation. The shape of the sample in the simulation was set to be similar to the experimental sample. b, Schematics of electron propagations of the object wave (φO) and reference wave (φR). The low-resolution magnetic phase was simulated considering surrounding demagnetizing field outside the sample in the ±4000-nm range in the z direction. c, Phase shift of the reference wave (φR). d, Phase shift of the object wave (φO). e, Observed phase shift (φO - φR). The background phase slopes (dashed lines) due to the demagnetization fields in φO and φR are almost the same, and those effects are subtracted from the hologram observation (φO - φR) for local high-resolution observation.
Extended Data Fig. 5 Calculated spin distribution, magnetic flux, and electromagnetic phase grating for multislice simulation.
a, Spin distribution per unit cell shown with the projection average. b, Magnetic flux with the [111] directional (in the original unit cell) component per unit cell. c, Magnetic flux with the [\(\bar{1}\bar{1}\)2] directional (in the original unit cell) component per unit cell. d, Electrostatic phase grating (conventional). e, Magnetic phase grating with [\(\bar{1}\bar{1}\)2] directional magnetization calculated by the Vienna Ab initio simulation package (VASP). The magnetic phase is magnified 10000 to visual inspection. f, Electromagnetic phase grating that is a simple sum of d and e. Please note this is not the electromagnetic phase grating used in the simulation, since the magnetic phase is amplified for visual inspection.
Extended Data Fig. 6 Magnetization properties of bulk Ba2FeMoO6.
The main graph is the temperature profile of magnetization for a single crystal of Ba2FeMoO6 taken at H// < 111 > = 0.5 T. The inset shows a magnetization hysteresis curve for the same crystal taken at 5 K.
Extended Data Fig. 7 Magnetic-flux distribution in the thin Ba2FeMoO6 sample and atomic arrangements and elemental ordering of Ba2FeMoO6 sample observed in the \([1\bar{1}0]\) direction.
a, TEM image of the thin sample. b, Magnetic flux in the area indicated by the white rectangle in a displayed with the cosine of phase φM amplified 10 times (cos10φM). Constant flux of h/10e flows between adjacent contour lines. The white dashed rectangle indicates the area used for evaluating magnetization. c and d, High-angle annular dark-field (HAADF) scanning transmission electron microscopic (STEM) images. e, Elemental mappings of Ba, Fe and Mo obtained by STEM energy-dispersive X-ray spectroscopy. Scale bar is 0.5 nm.
Extended Data Fig. 8 Magnetic-flux distribution in the rectangular-shaped thin Ba2FeMoO6 sample.
a, TEM image of the thin sample with rectangular shape. b, Magnetic flux obtained after applying a pulsed magnetic field of 207 kA/m in the area indicated by the white rectangle in a, as displayed with the cosine of phase φM amplified 15 times (cos15φM). Constant flux of h/15e flows between adjacent contour lines.
Extended Data Fig. 9 Procedure of data analysis and obtained data.
a, Flow chart of data analysis. b, Phase \({\varphi }_{\uparrow }\) with + M. c, Phase \({\varphi }_{\downarrow }\) with −M. d, Electrostatic phase. e, Magnetic phase. f, Line profiles of magnetic phase in the [111] direction in the area indicated by the yellow-dashed rectangle in e with different alignment positions for separating electrostatic and magnetic phases. g, Mean squared error of phase obtained from the \({\varphi }_{M}\) background with different alignment positions in the alignment area shown in f (also indicated by the yellow lines in e). h, Magnetic phase averaged in the (111) lattice plane with 2.5-nm range of the area indicated by the white rectangle in e. i, Magnetic phase when Gaussian blur with σ of 0.4 nm along the lattice plane after the averaging in the (111) lattice plane with 2.5-nm range for e. j, Enlarged image of the area indicated by the white rectangle in i. k, Derivative of magnetic phase i that reflects the in-plane magnetic field. l, Enlarged image of the area indicated by the white rectangle in k. The color wheel in l indicates how color and shade denote magnetic-field directions and strength (i.e., derivatives of magnetic phase range 0-0.06 rad/nm in absolute values). The areas indicated by white squares in j and l correspond to Figs. 2d and g. The white-dashed rectangles in i and l indicate the areas used for evaluating standard deviation. The red-dashed rectangles (W 2.8 nm × H 13.7 nm) in d, i and k show the areas used for evaluating the histograms (Figs. 2e, f and h) of the peak-to-peak values of electrostatic and magnetic phases and the +peak for the Mo plane and the −peak for the Fe plane of the derivative of the magnetic phase. The scale bar is 2 nm.
Extended Data Fig. 10 Simulations of electrostatic and magnetic phases with sample tilt in the [111] direction.
a, Electrostatic phase shift in the [111] direction without sample tilt β from the orientation of the [1\(\bar{1}\)0] zone axis shown in Fig. 3. Right-side green and light-green lines indicate two digital-focus conditions. Phase shifts at the Fe (Mo) layers are maximized in the thickness range indicated by the light-green (green) lines. b, Magnetic phase shift in the [111] direction without sample tilt from the orientation of the [1\(\bar{1}\)0] zone axis shown in Fig. 3 with the same digital focus conditions used in a. c, Electrostatic phase shift in the [111] direction with sample tilt β of 0.121 mrad in the [111] direction from the orientation of the [1\(\bar{1}\)0] zone axis shown in Fig. 3. Phase shifts at the Fe (Mo) layers are maximized with digital focus for the post process for obtaining magnetic phase. Right-side green and light-green lines indicate two digital-focus conditions. Phase shift at the Fe (Mo) layers is maximized in the thickness range indicated by the light-green (green) lines. d, Magnetic phase shift in the [111] direction with sample tilt β of 0.121 mrad from the orientation of the [1\(\bar{1}\)0] zone axis shown in Fig. 3 with the same digital focus conditions used in c.
Extended Data Fig. 11 Phase images without applying a 1/0.4 nm−1 filter and obtained data.
a, Phase \({\varphi }_{\uparrow }\) with + M. b, Phase \({\varphi }_{\downarrow }\) with −M. c, Electrostatic phase. d, Magnetic phase. e, Line profile of magnetic phase in the [111] direction (averaging width along lattice plane is 12.3 nm) in the area indicated by white rectangle in d. f, Derivative of magnetic phase profile shown in e. The gray-dashed areas in e and f indicate the areas used for evaluating standard deviation. The scale bar is 2 nm.
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Tanigaki, T., Akashi, T., Yoshida, T. et al. Electron holography observation of individual ferrimagnetic lattice planes. Nature 631, 521–525 (2024). https://doi.org/10.1038/s41586-024-07673-w
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DOI: https://doi.org/10.1038/s41586-024-07673-w
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