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Direct Determination of Atomic Structure and Magnetic Coupling of Magnetite Twin Boundaries Chunlin Chen,*,†,‡ Hongping Li,‡,¶ Takehito Seki,§ Deqiang Yin,‡,⊥ Gabriel Sanchez-Santolino,§ Kazutoshi Inoue,‡ Naoya Shibata,§ and Yuichi Ikuhara*,‡,§,# †
Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China ‡ Advanced Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan ¶ Institute for Advanced Materials, School of Materials Science and Engineering, Jiangsu University, Zhenjiang 212013, China § Institute of Engineering Innovation, The University of Tokyo, 2-11-16 Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan ⊥ College of Aerospace Engineering, Chongqing University, Chongqing 400044, China # Nanostructures Research Laboratory, Japan Fine Ceramics Center, 2-4-1 Mutsuno, Atsuta, Nagoya 456-8587, Japan S Supporting Information *
ABSTRACT: Clarifying how the atomic structure of interfaces/ boundaries in materials affects the magnetic coupling nature across them is of significant academic value and will facilitate the development of state-of-the-art magnetic devices. Here, by combining atomic-resolution transmission electron microscopy, atomistic spinpolarized first-principles calculations, and differential phase contrast imaging, we conduct a systematic investigation of the atomic and electronic structures of individual Fe3O4 twin boundaries (TBs) and determine their concomitant magnetic couplings. We demonstrate that the magnetic coupling across the Fe3O4 TBs can be either antiferromagnetic or ferromagnetic, which directly depends on the TB atomic core structures and resultant electronic structures within a few atomic layers. Revealing the one-to-one correspondence between local atomic structures and magnetic properties of individual grain boundaries will shed light on in-depth understanding of many interesting magnetic behaviors of widely used polycrystalline magnetic materials, which will surely promote the development of advanced magnetic materials and devices. KEYWORDS: transmission electron microscopy, grain boundary, magnetic coupling, first-principles calculations, differential phase contrast interfaces of magnetic thin films/layers, studies on the magnetic intergrain coupling across individual grain boundaries (GBs) are more challenging due to the much more abundant and complex atomic structures of GBs. Efforts to investigate the interplay between local atomic structures and magnetic coupling of GBs are greatly hampered by the technical difficulties in determining accurately and simultaneously the atomic structure and magnetic properties of individual GBs. Clarifying how the atomic structure of GBs affects the magnetic coupling nature across them is an intriguing but challenging research subject in materials science, which is of essential
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agnetic coupling across interfaces/boundaries of magnetic materials has attracted great attention over the past years because it is of not only fundamental scientific interest but also practical significance for magnetic applications.1−4 For decades, extensive efforts have been devoted to developing ways for tailoring the interfacial/ intergranular magnetic coupling which is important for developing higher performance of magnetic materials and devices.5−8 However, the roles of interface/boundary local structures on the magnetic coupling across them have remained poorly understood since such investigations have hitherto been based mainly on indirect comparisons between single-crystal and polycrystalline samples9−14 or the study of interface roughness of heteroepitaxial structures.6,15 Compared to the magnetic interlayer coupling across the well-defined hetero© XXXX American Chemical Society
Received: December 13, 2017 Accepted: February 22, 2018
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DOI: 10.1021/acsnano.7b08802 ACS Nano XXXX, XXX, XXX−XXX
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Fe3O4 is on the (111) crystal plane and the twin axis is along the [11̅0] direction. The diffraction spots are elongated since the thickness of the Fe3O4 twin lamellae is thin. To offer more structural details, we also performed TEM imaging of the Fe3O4 twin lamellae from the orthogonal [112̅] projection. As shown in Figure 1c, the TBs of Fe3O4 are also edge-on viewing along the [112̅] zone axis. The corresponding SAED pattern in Figure 1d confirms again the (111) crystal plane as the twin plane, in which the diffraction spots of twins and matrix are overlapped. To clearly determine the atomic structure of the Fe3O4 TBs, we conduct atomic-resolution STEM investigation from two orthogonal projections. Extensive STEM observations reveal that three types of twin boundary structures coexist in Fe3O4 simultaneously. Figure 2 presents three groups of high-angle annular dark-field (HAADF) and annular bright-field (ABF) STEM images of the TBs. The red arrows indicate the TBs. The electron beam is projected from the [110̅ ] direction. In the HAADF image, heavier atoms appear brighter due to the stronger intensity which directly depends on the atomic number (Z).30 Moreover, a higher atomic density will also induce a brighter contrast. The HAADF images in Figure 2 show only Fe atomic columns because the O columns are invisible due to the much weaker scattering. The different contrast of Fe atomic columns comes from the different atomic density of Fe atoms. The brighter columns have double atomic density of Fe atoms compared to the darker ones. Although the low-mag BF TEM images show similar image contrasts in TBs, it is revealed that there exists three different types of TB core structures in this material. As can be seen from the HAADF images, the arrangement of Fe cations of the type I TB is symmetric, while those of the other two TBs (type II and III) are asymmetric. To directly resolve all the atomic columns, we show in Figure 2 the corresponding ABF STEM images of the three types of TBs collected simultaneously with the HAADF STEM images. The ABF STEM images can clearly show both light and heavy atomic columns even if the specimen thickness is not very thin.31 As indicated by the inserted atomic models, the ABF STEM images unambiguously present both Fe and O atomic columns at the TBs, which are important for the theoretical calculations. As can be seen from the ABF images, the twin planes of all the three types of TBs are located at the O planes. The O sublattices of all three types of TBs are the same and symmetric. Different arrangements of the Fe cations in the O sublattices induce the formation of three different types of Fe3O4 TBs. The STEM images in Figure 2 also suggest that the type I and II Fe3O4 TBs are stoichiometric boundaries, while the type III TB is a nonstoichiometric one including Fe vacancies (as represented by solid circles). To obtain more profound information on the atomic structure, we also record the atomic-resolution HAADF and ABF images for the Fe3O4 TBs from the orthogonal [112̅] direction (Figure 3). The red arrows indicate the TBs. Every elongated spot in the HAADF and ABF images represents three neighboring Fe atomic columns too closely spaced to be resolved by using the present STEM microscope. Comparison of the STEM images in Figure 3 confirms again that the O lattices of all three types of Fe3O4 TBs are the same, in which different arrangements of the Fe cations lead to the formation of three types of TB structures. Atomic models are inserted in the ABF images to indicate the atomic structure of the TBs. Viewing along this projection, the arrangements of Fe cations are also symmetric for the type I TB and asymmetric for the type II and III TBs. The Fe vacancies of the type III TB (as
importance for understanding the magnetic behaviors and tailoring the magnetic properties of polycrystalline magnetic materials. Recent technical development in atomic-resolution scanning transmission electron microscopy (STEM) and differential phase contrast (DPC) imaging,16−18 which very successfully determines the local magnetic and electrical fields in materials,19−23 has offered a fertile ground for probing GBs to obtain simultaneously the atomic-scale structural information and the magnetic properties, which facilitates the direct investigation of the interplay between them. Magnetite (Fe3O4), being an abundant magnetic material and the oldest one known to mankind, attracts continuous attention due to its intriguing electronic and magnetic properties.24−29 In a previous study, we predicted the antiferromagnetic coupling of an antiphase boundary in Fe3O4 by first-principles calculations.27 Due to lack of direct experimental evidence for the magnetic coupling, the findings have remained as deductions/predictions. Here, we reduce a hematite (Fe2O3) single crystal into the Fe3O4 phase under high temperature and successfully prepare a high density of Fe3O4 twins. By combining atomic-resolution STEM, DPC STEM, and atomistic first-principles calculations, we revealed that the magnetic coupling across the Fe3O4 twin boundaries (TBs) can be either antiferromagnetic (AFM) or ferromagnetic (FM) depending on the difference in atomic core structures and resultant electronic structures of the TBs.
RESULTS AND DISCUSSION Figure 1 shows the microstructure of the Fe3O4 twin lamellae fabricated by annealing Fe2O3 single crystal under a pressure of
Figure 1. Microstructure of the Fe3O4 twin lamellae fabricated by reduction of Fe2O3 single crystal viewing from two orthogonal projections. (a) Bright-field TEM image showing the Fe3O4 twin lamellae and (b) SAED pattern recorded from the [11̅0] direction. (c) Bright-field TEM image and (d) SAED pattern viewed from [112̅] zone axis. The twin plane is the (111) crystal plane of Fe3O4. The subscripts “T” and “M” indicate the twins and the matrix of Fe3O4, respectively.
1.5 × 10−4 Pa at 973 K for 1 h. As can be seen from the brightfield TEM image in Figure 1a which was recorded along the twin axis, many Fe3O4 twin lamellae are formed during the annealing treatment of Fe2O3 single crystal. Indexing of the corresponding selected-area electron diffraction (SAED) pattern shown in Figure 1b reveals that the twin plane of B
DOI: 10.1021/acsnano.7b08802 ACS Nano XXXX, XXX, XXX−XXX
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Figure 2. Identifying atomic-scale structure of the Fe3O4 TBs from the [11̅0] projection. (a, c, e) HAADF STEM images showing atomic structure of the type I, II, and III TBs, respectively. (b, d, f) Corresponding ABF STEM images showing atomic structure of these three types of TBs, which were taken simultaneously with the HAADF images and revealed all the atomic columns at the TBs including O. Atomic models showing the double occupied Fe (purple), single occupied Fe (green), and oxygen (red) columns, are inserted in the ABF images for easy understanding of the atomic structure of TBs. The solid circles in (e) and (f) represent Fe vacancies. The TB planes are indicated by red arrows.
boundaries with interface formation energies 0.11 J m−2 and 0.30 J m−2 lower than those of FM couplings, respectively. These magnetic configurations for the Fe3O4 TBs are further evidenced in the spin-polarized density of states (DOS) plots. As one can see in Figure 4a, the spin polarization retains the same direction across the twin plane, indicating a FM coupling nature between the two conjugated twin lamellae for the type I TB. In sharp contrast to the case of type I TB, the spin polarization reverses the direction across the twin planes of the type II and III TBs, as shown in Figure 4b,c, verifying their AFM coupling nature. The total DOS projected onto both conjugated twin lamellae for each type of TB is shown respectively in Supplementary Figure S3, which clearly confirms again the FM coupling nature of the type I TB and the AFM ones of the type II and III TBs. The spin-polarized DOS directly at the three types of TBs are shown in Supplementary Figure S4. The direction of spin polarization maintains unchanged across the core region of the type I TB, which is consistent with its FM coupling nature, while the spin polarization gradually inverts the direction across the core regions of the type II and III TBs, suggesting their AFM coupling nature. The TB magnetic coupling should be induced by the Fe−O−Fe superexchange interactions across the TBs. The dominant Fe−O−Fe bond angles across the type I, II and III TBs are 75.6°, 131.8°, and 130.4°, respectively (Supplementary Figure S5). Obviously, the Fe−O−Fe bond angles
represented by solid circles) can also be visualized from this direction. To reveal the magnetic and electronic properties of three types of Fe3O4 TBs, density functional theory (DFT) calculations were carried out (see details in the Methods section). Several possible candidate atomic models for each type of TB are constructed based on the experimental STEM images (i.e., Figures 2 and 3). The formation energy is adopted to pick out the most energetically stable atomic structure for each type. The formation energies of the type I, II, and III TBs were calculated to be 0.47 J m−2, 0.12 J m−2 and 0.88 J m−2, respectively. We totally checked 237 TBs in the samples. The numbers of the type I, II, and III TBs were found to be 72, 118, and 47, respectively. The appearance ratio of each type TB is well consistent with their calculated formation energies. The atomistic structures for the lowest-energy configuration of each type are shown clearly in Supplementary Figure S1. Using these relaxed atomic models, we conduct STEM image simulations, and the results are shown Supplementary Figure S2, matching well with the experimental counterparts. For each type of TB, we determine the most stable magnetic configuration through comparison of the energies for FM and AFM coupling configurations. It is found that the type I TB prefers to form a FM coupling across the boundary with an interface formation energy 0.16 J m−2 lower than that of AFM coupling, whereas the type II and III TBs tend to form AFM couplings across the C
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Figure 3. Identifying atomic-scale structure of the Fe3O4 TBs along the [112̅] zone axis. (a, c, e) HAADF STEM images showing atomic structure of the type I, II, and III TBs, respectively. (b, d, f) Corresponding ABF STEM images with inserted atomic models, showing the double occupied Fe (purple), single occupied Fe (green), and oxygen (red) columns, reveal the atomic structure of these three types of TBs including O. The solid circles in (e) and (f) represent Fe vacancies. The TB planes are indicated by red arrows.
the thickness of the TEM samples (ranging from 8.5 to 28.2 nm) is thinner than the Néel domain walls formed on the surface of magnetite bulk crystal,32,33 the magnetic domain walls formed in the Fe3O4 thin films are probably Néel domain walls.
across the type II and III TBs are slightly larger than those in the bulk (i.e., 121.9°), rendering the stronger superexchange interactions and the antiferromagnetic coupling nature across them. Meanwhile, the acute Fe−O−Fe bond angles induce the formation of ferromagnetic coupling across the type I TB. To confirm the prediction from first-principles calculations, we directly determined the magnetic coupling across the TBs by DPC STEM imaging. Using a segmented annular all-field detector, we are capable of measuring the beam deflections due to the effect of magnetic fields of specimens.21 Figure 5a,b shows the reconstructed in-plane magnetization vector color maps of the Fe3O4 twin lamellae obtained by DPC STEM using the as-prepared Fe3O4 TEM samples. The inserted color wheel indicates the magnetic field strength/direction. After the DPC measurements, we further checked the atomic structures of the twin lamellae using other microscopes. Figure 5c,d shows the bright-field TEM images of the Fe3O4 twin lamellae. Further atomic-scale HAADF STEM observations of the TBs were performed to confirm that their atomic structures are consistently identified as type I, II, and III TBs, respectively (Supplementary Figures S6 and S7). No steps were observed on these boundaries. As one can see, the in-plane magnetization vectors of the Fe3O4 twin lamellae maintain the same direction across the type I TB and reverse the magnetic direction across the type II and type III TBs. It suggests that the magnetic coupling across the type I TB is ferromagnetic and those across the type II and type III TBs are antiferromagnetic. These results are well consistent with the first-principles calculations. Since
CONCLUSIONS In summary, unveiling the interplay mechanism between atomic structure and magnetic coupling of GBs is a subject of fundamental significance for materials science. We have demonstrated a successful direct determination of atomic structure and magnetic coupling of Fe3O4 TBs by a combined study of atomic-resolution STEM observations, DPC STEM imaging, and atomistic first-principles calculations. It was found that the magnetic coupling across the Fe3O4 TBs can be either antiferromagnetic or ferromagnetic, which directly relies on the TB atomic core structures. Revealing the magnetic coupling nature across GBs, as well as interfaces in materials, can lead to a better understanding of the magnetic behaviors of polycrystalline magnetic materials, which will greatly benefit in developing advanced magnetic materials and devices. METHODS Materials and TEM/STEM Observations. A high-quality hematite (Fe2O3) single crystal was cut into slices with thickness of ∼800 μm along its [1010̅ ] and [1120̅ ] zone axes, respectively. For the preparation of TEM/STEM specimens, the single-crystalline Fe2O3 slices were mechanically grinded to ∼60 μm and then dimpled to ∼20 D
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Figure 5. Identifying magnetic couplings across the Fe3O4 TBs. (a, b) Reconstructed in-plane magnetization vector maps of these Fe3O4 twin lamellae obtained by DPC STEM. The inserted color wheel indicates the magnetic field strength/direction. (c, d) Brightfield TEM images of the Fe3O4 twin lamellae. The TBs were consistently identified as type I, II and III TBs, respectively. The inplane magnetization vectors of the Fe3O4 twin lamellae maintain the same direction across the type I TB and reverse the magnetic direction across the type II and III TBs. compared the Fe L2,3 edges and O K edges of the present samples with those of a commercial Fe3O4 single crystal (SurfaceNet GmbH). As shown in Supplementary Figure S8, both samples show very similar Fe L2,3 edges and O K edges. There is no splitting in the Fe L3 peak of both samples. These facts indicate that the present annealed samples are exactly Fe3O4, instead of other iron oxides. Bright-field TEM images and diffraction patterns were recorded using a conventional electron microscope (JEM-2010F, JEOL). We took the HAADF and ABF images using an aberration-corrected STEM (ARM200FC, JEOL) with a sub-Å resolution. The detailed parameters for the HAADF and ABF STEM imaging can be found in our previous study.34 The thickness of typical regions for STEM observations measured by the EELS technique ranges from 8.5 to 28.2 nm. We performed the DPC STEM imaging using an aberrationcorrected STEM (JEM-2100F, JEOL). As shown in our previous study, we installed in this STEM a segmented annular all-field (SAAF) detector and a Schottky field emission gun.17 The probe size used for the DPC STEM imaging is ∼2 nm in diameter. To avoid the effect of external magnetic fields, DPC imaging was performed using the magnetic-field-free imaging settings with the objective lenses turned off. Prior to the DPC observations, the as-prepared Fe3O4 TEM samples had never been inserted into a TEM and any other magnetic equipment. The atomic structures of the twin boundaries were investigated after the DPC measurements to establish the relation between DPC results and atomic-resolution STEM observations. Simulations of HAADF and ABF Images. We simulated the HAADF and ABF STEM images via the multislice method using the WinHREM package which is commercially available (HREM Res. Inc.).35 The detailed parameters for simulating the HAADF images were as follows: acceleration voltage of STEM 200 kV, aberration coefficient of probe 0.02 mm, convergence angle of probe 30 mrad, defocus value for imaging 30 Å, and semiangle of HAADF detector 68−280 mrad. To simulate the ABF images, the collection semiangle was selected as 12−24 mrad, and other parameters were maintained as
Figure 4. Spin-polarized DOS plots of the Fe3O4 TBs projected onto selective areas indicated by colored shading. (a) DOS of the type I TB, (b) DOS of the type II TB, and (c) DOS of the type III TB. The EF is represented by the red dashed lines. The relaxed atomistic models are also given for reference. The DOS results suggest that the magnetic coupling across the type I TB is ferromagnetic and those across the type II and III TBs are antiferromagnetic. μm. The Ar ion-milling process was performed with accelerating voltages of 1−4 kV using a precision ion polishing system (Model 691, GATAN). After that, the as-prepared Fe2O3 TEM/STEM samples were annealed under a pressure of 1.5 × 10−4 Pa at 973 K for 1 h. As a result, the Fe2O3 single crystal was reduced into the Fe3O4 phase. To confirm that the products of annealed samples are exactly Fe3O4, we E
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ACS Nano the same for HAADF images. The pixel size of 0.0833 Å was used for the display of HAADF and ABF images. DFT Calculations. For the DFT calculations, we used the commercial Vienna ab Initio Simulation Package (VASP)36,37 and adopted the projector augmented wave (PAW) method38 and the Perdew−Burke−Ernzerh generalized gradient approximation (GGA).39 We set a plane-wave energy cutoff of 400 eV for the expansion of valence-electron wave functions and employed a 7 × 5 × 1 Monkhorst−Pack k-point grid in the supercell calculations. We used the DFT+U approach40 and adopted 3.8 eV as the effective Hubbard parameter (Ueff = U − J) for accurately calculating Fe3O4.27,41 The Brillouin zone integration was performed via the tetrahedron method with Blöchl correction. For calculations, the total energies and forces were used as the convergence criterions which were
