## Introduction

In the 88 years since the seminal invention of the transmission electron microscope (TEM) by Ruska and Knoll in 19311, researchers have always pursued better and better spatial resolution. As electrons are charged particles, electromagnetic fields have been utilized as lenses for electrons following the discovery of Busch in 19262. Because of their stability and controllability, high-power magnetic lenses have been considered the best lens systems for modern TEMs. Historically, the spatial resolution of TEMs has been strongly limited not by the wavelength of the incident electrons but rather by the performance of the magnetic objective lens: it forms the primary image and diffraction pattern, which will be magnified by all the other lenses, and so the quality of the final image is severely affected by its lens aberrations. To achieve better spatial resolution, the design of magnetic objective lenses with smaller lens aberration coefficients (such as for spherical aberration, Cs, and chromatic aberration, Cc) has been at the heart of modern TEM developments. The 1995 development by Haider et al.3 of a practical spherical aberration correcting lens systems produced breakthrough improvements in spatial resolution4. Since then, aberration correcting lens systems for scanning TEM (STEM)5 have achieved sub-Å spatial resolution in real-space6, with sub-0.5 Å resolution having been recently reported with 300 kV accelerating voltage7. Nowadays, individual single atoms can be routinely imaged by commercially available electron microscopes. Electronic structures within single atoms can even be probed in real-space8,9,10.

Even after the advent of aberration correction technology, magnetic objective lenses with minimal lens aberration coefficients remain indispensable for atomic-resolution TEMs/STEMs. One critical drawback of the current magnetic condenser-objective lens systems for atomic-resolution TEMs/STEMs is that the samples have to be inserted into very high magnetic fields, up to 2~3 T, to realize the short focus length condition essential for atomic-resolution imaging. Figure 1a, b show a schematic cross section of a conventional magnetic objective lens and the magnetic field distribution it produces along the optical axis (z-direction) within the sample region, respectively. In this configuration, samples are inserted between the upper and lower polepieces, which are surrounded by a coil of copper wires. When an electrical current passes through the coil, a magnetic field is created within the bore of the polepieces, and this field is used to focus the incoming high-energy electron beam. Figure 1b also schematically plots the z-component of the magnetic field distribution across the upper and lower polepieces. The maximum field strength is found near the sample position. This high magnetic field can severely hamper atomic-resolution imaging of many important soft/hard magnetic materials such as silicon steel because the material’s magnetic and sometimes physical structures can be largely altered, even destroyed, by the strong magnetic field. Thus, Lorentz imaging mode11, in which the magnetic objective lens is completely switched off or exchanged for so-called Lorentz type lenses12,13,14, has been used to observe magnetic materials in TEMs/STEMs at the expense of high spatial resolution. There have been several attempts to develop magnetic field-free objective lens systems for high spatial resolution TEM/STEM imaging, but atomic-resolution imaging under magnetic field-free conditions is still extremely challenging even with the aid of the state-of-the-art aberration correctors and ultrahigh voltage electron sources (see Supplementary Table 1 for a summary of previously reported attainable spatial resolution by TEMs/STEMs in a magnetic field-free environment).

In the present study, we develop a new magnetic objective lens system combined with a state-of-the-art aberration corrector and thereby simultaneously realize atomic resolution electron microscopy (with sub-Å spatial resolution) and a magnetic field-free sample environment. We first confirm the environment around the sample position is magnetic field free through the direct measurement of the three-dimensional magnetic field distribution within the magnetic objective lens, and then observe non-magnetic crystals to prove through annular dark-field (ADF) STEM imaging that sub-Å spatial resolution is achieved. Finally, we directly observe atomic structures of a typical soft magnetic material (silicon steel) to demonstrate the capability of this new magnetic objective lens system for characterizing atomic structures of magnetic materials.

## Results

### Development of a new magnetic field-free objective lens system

Figure 1c, d show a schematic cross section of the newly designed objective lens system in this study and the magnetic field distribution it produces along the z-direction within the sample region, respectively. This lens system is basically composed of two round lenses15. The front objective lens (FOL) is located in front of the specimen and the back objective lens (BOL) is located behind the specimen, with respect to the incoming electron beam. The magnetic polepieces and coils of the FOL and BOL are in an exact mirror symmetric configuration with respect to the sample plane. However, the polarities of their excitations are opposite, resulting in an anti-symmetric magnetic field distribution across the sample plane. Thus, the z-component of the magnetic fields of the FOL and BOL can be ideally canceled out at the sample plane. In addition, the radial component of the magnetic field is minimal near the optic axis because of the symmetry of the round lenses. This new lens system should, in principle, realize extremely small residual magnetic fields at the sample position, while placing the strongly excited FOL and BOL close enough to the sample to realize the short focus length condition indispensable for atomic-resolution imaging. Note that the present magnetic objective lens should also be applicable to the aberration-corrected TEM configuration due to its symmetric structure about the sample plane. This magnetic objective lens thus has huge potential for application to other existing TEM/STEM imaging and analytical techniques, such as high-resolution TEM, conventional TEM, electron holography, Lorentz TEM, differential phase contrast STEM imaging, ptychography, electron energy loss spectroscopy and energy dispersive X-ray spectroscopy.

To test this new objective lens concept in practice, we developed such an objective lens system and installed it into a STEM (200 kV accelerating voltage) equipped with a state-of-the-art higher-order aberration corrector, which can correct lens aberrations up to 5th order sixfold astigmatism16. Figure 2 shows the experimental three-dimensional magnetic field distribution inside the objective lens directly measured through Hall devices placed on a TEM specimen holder. Figure 2a shows the three-dimensional magnetic field strength map within a 800 × 800 × 200 μm3 volume in between the FOL and BOL. Since atomic-resolution TEM/STEM observation is normally carried out for very small sample regions, typically within 100 nm in the x and y direction and with a thickness of <50 nm or so, the above volume well covers the region of interest of typical samples for atomic-resolution TEM/STEM observation. Figure 2b–d show two-dimensional magnetic field vector maps on xy (z = 0), xz (y = 0), and yz (x = 0) planes, respectively, with the measured local magnetic field modulus at each position shown in color scale. It is seen that, while the FOL and BOL are strongly excited, the residual magnetic fields near the sample center become much <0.2 mT, >10,000 times smaller than the value in a conventional magnetic objective lenses used for atomic resolution TEM/STEM imaging. The aberration corrector was also excited during the magnetic field measurement. Thus, we conclude that the stray magnetic fields from the FOL, BOL, and all the other possible sources are well compensated and that an essentially magnetic field-free environment is realized at the sample position.

### Atomic-resolution ADF STEM imaging of a non-magnetic crystal

Atomic-resolution ADF STEM observations of a GaN crystal were performed using the new objective lens system combined with the higher-order aberration corrector. The aberration corrector was situated between the electron gun and the objective lens so as to correct the lens aberrations of the probe-forming FOL. The lens parameters of the BOL alone (the FOL should have the same value by the symmetry) were experimentally estimated at the accelerating voltage of 200 kV as follows: Cs = 16.9 mm, Cc = 3.45 mm and a focal length of 3.14 mm. The details of the evaluation can be found in the Methods section. The experimental Ronchigram, which is the shadow image of the probe, is shown in Supplementary Fig. 1, obtained with an amorphous carbon film on the sample position. It is seen that the flat phase region extends up to 26 mrad in semiangle. Using a 200 kV accelerated electron beam with a probe-forming aperture of 20 mrad in semiangle, we observed a GaN single crystal along the [111] direction by ADF STEM as shown in Fig. 3a. In the ADF image, only the atomic columns of Ga are visible because of the strong atomic number-dependent contrast. Figure 3b shows the experimental repeat-unit averaged image and the crystal structure model of GaN from the same viewing direction. The Ga-Ga dumbbells of 0.92 Å separation are clearly resolved in real-space. The Fourier transform of the ADF image shown in Supplementary Fig. 2 also confirms sub-Å spatial resolution.

### Atomic-resolution ADF STEM imaging of a magnetic crystal

We also observed the atomic structure of a grain-oriented silicon steel sheet (Fe-3wt%Si) as shown in Fig. 3c. Figure 3d shows the experimental repeat-unit averaged image and the crystal structure model of Fe-3wt%Si from the same viewing direction. Grain-oriented silicon steel is one of the most important engineering soft magnetic materials and atomic-resolution characterization of individual defects has long been sought. However, it has hitherto been extremely challenging to directly observe their atomic structures by TEMs/STEMs since samples are largely deformed or even destroyed by the strong lens magnetic field, and moreover the sample magnetic field makes it extremely difficult to reliably tune the lens astigmatism well enough to allow atomic-resolution observations. However, as shown in Fig. 3c, using our new objective lens system we can directly and clearly resolve the atomic structure of the silicon steel along the [110] direction (see also Supplementary Fig. 3 for an atomic-resolution image of a grain boundary in the silicon steel). Thus, direct atom-resolved imaging in a magnetic field-free environment is finally realized in electron microscopy, enabling unprecedented atomic-level structural characterization of magnetic materials.

In summary, atomic-resolution electron microscopy in a magnetic field-free environment is finally realized using a newly developed objective lens system combined with state-of-the-art aberration correction technology. This imaging capability should allow atomic structure characterization of any magnetic material, which has hitherto been extremely challenging in TEMs/STEMs. Since this objective lens can also be applied to other existing TEM/STEM imaging and analytical techniques, the present achievement should have considerable far-reaching effects across the entire field of transmission electron microscopy.

## Methods

### STEM sample preparation

GaN single crystal and grain-oriented Fe-3%Si alloy were mechanically polished with diamond suspension, and then thinned by Ar ion-beam milling to obtain electron transparency.

### Magnetic field distribution inside the new objective lens system

To map the three-dimensional (3D) magnetic field distribution inside the new magnetic objective lens system, we developed a sample holder with a small Hall device placed on the specimen position, which can measure the 3D magnetic field distribution at each sample position. We then systematically moved the sample positions in between the FOL and BOL and measured the 3D magnetic fields at each point within the range x: ± 400 µm, y: ± 400 µm, z: ± 100 µm. The step size between sample positions was 50 µm. The magnetic fields at 1445 points along three x, y, z directions were measured. The isosurfaces and the color maps were obtained by interpolating the measured values. In addition, we experimentally measured that the maximum magnetic field change on the sample position during the sample insertion into the objective lens, without turning off the objective lens, did not exceed 0.8 mT.

### Aberration coefficients of the new objective lens system

To experimentally estimate the lens parameters of the new magnetic field-free objective lens system, we first assumed the lens parameters of the FOL and BOL should be the same because of their structural symmetry. Then, we estimated the lens parameters of the BOL in TEM mode.

To estimate the focal length of the BOL, we used the following equation,

$$f = \frac{M}{{\left( {M + 1} \right)^2}}L$$
(1)

where f is the focal length, M is the magnification of the BOL and L is the distance between the sample and image planes. For a sample, we used MAGICAL (Norrox Scientific Ltd.), a standard sample for TEM magnification calibration. Here, we physically measured the distance between the sample and the image plane (selected area (SA) aperture plane) and used an already-known size SA aperture to measure the magnification. The focal length was estimated to be 3.14 mm.

To estimate the Cs of the BOL, we observed an Au nanoparticle sample under Scherzer focus condition and obtained the phase contrast transfer function (PCTF) by taking the Fourier transform of the image. Using the first zero of the PCTF, we defined the point resolution to be δ = 0.473 nm. Then, we estimated the Cs value of the BOL to be 16.9 mm.

To estimate the Cc (following the caution discussed in ref. 17) of the BOL, we changed the energy of incident electron beam and measured the defocus change systematically. The defocus change Δf due to the energy shift of the incident beam ΔE is given by

$$\Delta f = {\mathrm{Cc}}\frac{\Delta E}{E}$$
(2)

Using the experimental linear relationship between the defocus change (Δf) and the energy shift (ΔE) of incident electron beam as shown in Supplementary Fig. 4, we estimated the Cc value to be 3.45 mm.

These measured lens parameters are compared with another existing Lorentz type lens as shown in Supplementary Table 2.

### Microscope set-up

The base electron microscope for this experiment is a commercially available cold field emission type 200 kV STEM (ARM-200CF, JEOL Ltd.). We exchanged the normal objective lens system to the newly developed magnetic field-free type objective lens system. In this system, standard double-tilt sample holders are acceptable. The tilt angle ranges are x-axis: ± 10° and y-axis: ± 10°.