The distribution of charge density in materials dictates their chemical bonding, electronic transport, and optical and mechanical properties. Indirectly measuring the charge density of bulk materials is possible through X-ray or electron diffraction techniques by fitting their structure factors1,2,3, but only if the sample is perfectly homogeneous within the area illuminated by the beam. Meanwhile, scanning tunnelling microscopy and atomic force microscopy enable us to see chemical bonds, but only on the surface4,5,6. It remains a challenge to resolve charge density in nanostructures and functional materials with imperfect crystalline structures—such as those with defects, interfaces or boundaries at which new physics emerges. Here we describe the development of a real-space imaging technique that can directly map the local charge density of crystalline materials with sub-ångström resolution, using scanning transmission electron microscopy alongside an angle-resolved pixellated fast-electron detector. Using this technique, we image the interfacial charge distribution and ferroelectric polarization in a SrTiO3/BiFeO3 heterojunction in four dimensions, and discover charge accumulation at the interface that is induced by the penetration of the polarization field of BiFeO3. We validate this finding through side-by-side comparison with density functional theory calculations. Our charge-density imaging method advances electron microscopy from detecting atoms to imaging electron distributions, providing a new way of studying local bonding in crystalline solids.
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The datasets generated or analysed here are available from the corresponding authors on reasonable request.
Midgley, P. A. Electronic bonding revealed by electron diffraction. Science 331, 1528–1529 (2011).
Zuo, J. M., Kim, M., O’Keeffe, M. & Spence, J. C. H. Direct observation of d-orbital holes and Cu–Cu bonding in Cu2O. Nature 401, 49–52 (1999).
Nakashima, P. N. H., Smith, A. E., Etheridge, J. & Muddle, B. C. The bonding electron density in aluminum. Science 331, 1583–1586 (2011).
Han, Z. et al. Imaging the halogen bond in self-assembled halogenbenzenes on silver. Science 358, 206–210 (2017).
Altman, E. I., Baykara, M. Z. & Schwarz, U. D. Noncontact atomic force microscopy: an emerging tool for fundamental catalysis research. Acc. Chem. Res. 48, 2640–2648 (2015).
Mohn, F., Gross, L., Moll, N. & Meyer, G. Imaging the charge distribution within a single molecule. Nat. Nanotechnol. 7, 227–231 (2012).
Shibata, N. et al. Differential phase-contrast microscopy at atomic resolution. Nat. Phys. 8, 611–615 (2012).
Shibata, N. et al. Direct visualization of local electromagnetic field structures by scanning transmission electron microscopy. Acc. Chem. Res. 50, 1502–1512 (2017).
Müller-Caspary, K. et al. Measurement of atomic electric fields and charge densities from average momentum transfers using scanning transmission electron microscopy. Ultramicroscopy 178, 62–80 (2017).
Müller, K. et al. Atomic electric fields revealed by a quantum mechanical approach to electron picodiffraction. Nat. Commun. 5, 5653 (2014).
LeBeau, J. M., Findlay, S. D., Allen, L. J. & Stemmer, S. Position averaged convergent beam electron diffraction: theory and applications. Ultramicroscopy 110, 118–125 (2010).
Wang, J. et al. Epitaxial BiFeO3 multiferroic thin film heterostructures. Science 299, 1719–1722 (2003).
Seshadri, R. & Hill, N. A. Visualizing the role of Bi 6s “lone pairs” in the off-center distortion in ferromagnetic BiMnO3. Chem. Mater. 13, 2892–2899 (2001).
Kim, Y.-M. et al. Direct observation of ferroelectric field effect and vacancy-controlled screening at the BiFeO3/LaxSr1−xMnO3 interface. Nat. Mater. 13, 1019–1025 (2014).
Nelson, C. T. et al. Spontaneous vortex nanodomain arrays at ferroelectric heterointerfaces. Nano Lett. 11, 828–834 (2011).
Gauss, C. F. in Werke: Fünfter Band 3–22 (Springer, 1877).
Moon, E. J. et al. Spatial control of functional properties via octahedral modulations in complex oxide superlattices. Nat. Commun. 5, 5710 (2014).
Thomas, S. et al. Localized control of Curie temperature in perovskite oxide film by capping-layer-induced octahedral distortion. Phys. Rev. Lett. 119, 177203 (2017).
Li, J. et al. Dramatically enhanced polarization in (001), (101), and (111) BiFeO3 thin films due to epitiaxial-induced transitions. Appl. Phys. Lett. 84, 5261–5263 (2004).
Yu, P., Chu, Y.-H. & Ramesh, R. Oxide interfaces: pathways to novel phenomena. Mater. Today 15, 320–327 (2012).
Spaldin, N. A., Cheong, S.-W. & Ramesh, R. Multiferroics: past, present, and future. Phys. Today 63, 38–43 (2010).
Bert, J. A. et al. Direct imaging of the coexistence of ferromagnetism and superconductivity at the LaAlO3/SrTiO3 interface. Nat. Phys. 7, 767–771 (2011).
Li, L., Richter, C., Mannhart, J. & Ashoori, R. C. Coexistence of magnetic order and two-dimensional superconductivity at LaAlO3/SrTiO3 interfaces. Nat. Phys. 7, 762–766 (2011).
Reyren, N. et al. Superconducting interfaces between insulating oxides. Science 317, 1196–1199 (2007).
Tsukazaki, A. et al. Quantum hall effect in polar oxide heterostructures. Science 315, 1388–1391 (2007).
Zhang, Y. et al. Discovery of a magnetic conductive interface in PbZr0.2Ti0.8O3/SrTiO3 heterostructures. Nat. Commun. 9, 685 (2018).
Guo, R. et al. Non-volatile memory based on the ferroelectric photovoltaic effect. Nat. Commun. 4, 1990 (2013).
Ohtomo, A., Muller, D. A., Grazul, J. L. & Hwang, H. Y. Artificial charge-modulation in atomic-scale perovskite titanate superlattices. Nature 419, 378–380 (2002).
Tan, H., Verbeeck, J., Abakumov, A. & Van Tendeloo, G. Oxidation state and chemical shift investigation in transition metal oxides by EELS. Ultramicroscopy 116, 24–33 (2012).
Rojac, T. et al. Domain-wall conduction in ferroelectric BiFeO3 controlled by accumulation of charged defects. Nat. Mater. 16, 322–327 (2017).
Jang, H. W. et al. Metallic and insulating oxide interfaces controlled by electronic correlations. Science 331, 886–889 (2011).
Ohtomo, A. & Hwang, H. Y. A high-mobility electron gas at the LaAlO3/SrTiO3 heterointerface. Nature 427, 423–426 (2004); corrigendum 441, 120 (2006).
Lee, H. et al. Direct observation of a two-dimensional hole gas at oxide interfaces. Nat. Mater. 17, 231–236 (2018).
Zuo, J. M. & Spence, J. C. H. Electron Microdiffraction (Plenum, 1991).
Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).
Kresse, G. & Hafner, J. Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium. Phys. Rev. B 49, 14251–14269 (1994).
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).
Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).
Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).
Dudarev, S. L., Botton, G. A., Savrasov, S. Y., Humphreys, C. J. & Sutton, A. P. Electron-energy-loss spectra and the structural stability of nickel oxide: an LSDA+U study. Phys. Rev. B 57, 1505–1509 (1998).
Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188–5192 (1976).
Elsässer, C., Fähnle, M., Chan, C. T. & Ho, K. M. Density-functional energies and forces with Gaussian-broadened fractional occupations. Phys. Rev. B 49, 13975–13978 (1994).
Wang, Z., Wang, H., Yu, C. C. & Wu, R. Q. Hydrogen as a source of flux noise in SQUIDs. Phys. Rev. B 98, 020403 (2018).
Wang, H. et al. Candidate source of flux noise in SQUIDs: adsorbed oxygen molecules. Phys. Rev. Lett. 115, 077002 (2015).
Wang, H. et al. Possibility of realizing quantum spin Hall effect at room temperature in stanene / Al2O3 (0001). Phys. Rev. B 94, 035112 (2016).
Kohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133–A1138 (1965).
Shannon, R. D. Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallogr. A 32, 751–767 (1976).
Henkelman, G., Arnaldsson, A. & Jónsson, H. A fast and robust algorithm for Bader decomposition of charge density. Comput. Mater. Sci. 36, 354–360 (2006).
Bader, R. F. W. Atoms in Molecules—A Quantum Theory (Oxford Univ. Press, 1990).
Our experimental work was supported by the US Department of Energy (DOE), Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under grant DE-SC0014430. TEM specimen preparation and sample thickness fitting were partially supported by the US National Science Foundation (NSF) under grant number DMR-1506535. DFT studies were supported by the US DOE (grant number DE-FG02-05ER46237) and the National Energy Research Scientific Computing Center (NERSC). Growth of BiFeO3 films at Cornell University was supported by the National Science Foundation (Nanosystems Engineering Research Center for Translational Applications of Nanoscale Multiferroic Systems) under grant number EEC-1160504, and film growth at Nanjing University was supported by the National Basic Research Program of China (grant number 2015CB654901). TEM experiments were conducted using the facilities in the Irvine Materials Research Institute (IMRI) at the University of California at Irvine. We thank H. Sawada from Jeol Ltd. for help with experiments.
The authors declare no competing interests.
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Extended data figures and tables
The electric-field strength at locations close to Sr atoms (black), farther away (red) and farthest away, in between the Sr and O atomic columns (blue), was calculated from simulated diffraction data with different sample thicknesses up to 6 nm. The measured electric-field strength is shown as points, and the dashed lines denote linear fitting. The inset shows the sampling locations for each line on a map of the simulated electric field. Diffraction data were generated using multi-slice simulations in which conditions were matched to experimental conditions.
a, HAADF-STEM image of SrTiO3. b, Least-squares fitting of the experimental PACBED results with the simulated PACBEDs (red line). The inset shows the PACBED acquired from the boxed region in the STEM image, and simulated PACBEDs of SrTiO3 with thicknesses from 0.8 nm to 10.4 nm.
Shown are the PACBED acquired in experiment and simulated PACBEDs for BiFeO3 with thicknesses of 2–10 nm.
a–c, Negative charge (a); positive charge (b); and overlapping of positive and negative charge (c) in the pseudo-cubic unit cell of BiFeO3. d, Positions of positive (blue) and negative (red) charge centres.
The EDS map was acquired using a JEM300CF AC-STEM system with EDS dual silicon-drift detectors (SDDs). Thirty scans (each with a 0.4-ms dwell time) in the same area across the interface were aligned and summed. The HAADF-STEM image and atomic-resolution EDS maps of Bi, Fe, Sr and Ti reveal an atomically sharp interface.
a, Atomic model of the BiFeO3/SrTiO3 interface, which is relaxed and then calculated by DFT. The rotation of O octahedra is readily visible from the splitting of the O atoms in this projection. b, Charge-density image calculated using DFT. The images of O charge become elongated and weak with higher O octahedron rotation. c, Intensity of O column charge (blue) and width of O intensity (red) plotted against O octahedron rotation measured using the atomic model from DFT calculations.
a, 2D charge-density image of SrTiO3. b, Charge-intensity profile drawn along the horizontal (red) and vertical (blue) directions as shown in a. Local minima in the charge-intensity profile are defined as the boundary of the area included for integrating the charge.
Histograms showing the integrated intensity of Bi columns, Fe + O columns, O columns, Sr columns and Ti + O columns from charge-density images of BiFeO3 and SrTiO3.
a, Integrated intensity in each atomic column in the charge-density image, plotted as a function of valence derived through DFT to show their correlation. The red line is the linear fit. b, Partial charge and valence states of all atoms derived through Bader charge analysis in DFT.
Extended Data Fig. 10 High-resolution core-loss EELS measurement of Ti, O and Fe at the SrTiO3/BiFeO3 interface.
a, HAADF-STEM image used for acquiring EELS data on the SrTiO3/BiFeO3 interface. Scale bar, 1 nm. b–d, Stacking EEL spectra of the Ti L2,3-edge (b); O K-edge (c); and Fe L2,3-edge (d) across the interface. The location of each coloured spectrum is marked by the colour bar in a. Each spectrum is averaged in the direction parallel with the SrTiO3/BiFeO3 interface. The purple, yellow and maroon arrows indicate respectively the top edge, interface and bottom edge of the mapping region in a.
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Gao, W., Addiego, C., Wang, H. et al. Real-space charge-density imaging with sub-ångström resolution by four-dimensional electron microscopy. Nature 575, 480–484 (2019). https://doi.org/10.1038/s41586-019-1649-6
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