page_title: Scanning transmission electron microscopy
section_title: Differential phase contrast
hierarchical_section_title: Scanning transmission electron microscopy / STEM detectors and imaging modes / Differential phase contrast
caption_attribution_description: English: In Scanning Transmission Electron Microscopy (STEM) it is possible image magnetic fields using a technique called differential phase contrast, which relies on the electron beam being deflected by the magnetic field. This figure shows a schematic of this, with an electron beam passing through two different regions in a material, where the magnetic domains point in opposite directions. This leads to a beam deflection which can be imaged on a camera, represented by the grid patterns towards the bottom of the plot. In a real STEM the electron beam would be scanning in a raster pattern across the material, and the detector would be far away from the material.
context_page_description: A scanning transmission electron microscope is a type of transmission electron microscope. Pronunciation is [stɛm] or [ɛsti:i:ɛm]. As with a conventional transmission electron microscope, images are formed by electrons passing through a sufficiently thin specimen. However, unlike CTEM, in STEM the electron beam is focused to a fine spot which is then scanned over the sample in a raster illumination system constructed so that the sample is illuminated at each point with the beam parallel to the optical axis. The rastering of the beam across the sample makes STEM suitable for analytical techniques such as Z-contrast annular dark-field imaging, and spectroscopic mapping by energy dispersive X-ray spectroscopy, or electron energy loss spectroscopy. These signals can be obtained simultaneously, allowing direct correlation of images and spectroscopic data.
  A typical STEM is a conventional transmission electron microscope equipped with additional scanning coils, detectors and necessary circuitry, which allows it to switch between operating as a STEM, or a CTEM; however, dedicated STEMs are also manufactured.
context_section_description: Differential phase contrast (DPC) is an imaging mode which relies on the beam being deflected by electromagnetic fields. In the classical case, the fast electrons in the electron beam is deflected by the Lorentz force, as shown schematically for a magnetic field in the figure to the left. The fast electron with charge −1 e passing through an electric field E and a magnetic field B experiences a force F:
  For a magnetic field, this can be expressed as the amount of beam deflection experienced by the electron, βL:
  where  is the wavelength of the electron,  the Planck constant and  is integrated magnetic induction along the trajectory of the electron. This last term reduces to  when the electron beam is perpendicular to a sample of thickness  with constant in-plane magnetic induction of magnitude . The beam deflection can then be imaged on a segmented or pixelated detector. This can be used to image magnetic and electric fields in materials. While the beam deflection mechanism through the Lorentz force is the most intuitive way of understanding DPC, a quantum mechanical approach is necessary to understand the phase-shift generated by the electromagnetic fields through the Aharonov–Bohm effect.
  Imaging most ferromagnetic materials require the current in the objective lens of the STEM to be reduced to almost zero. This is due to the sample residing inside the magnetic field of the objective lens, which can be several Tesla, which for most ferromagnetic materials would destroy any magnetic domain structure. However, turning the objective lens almost off drastically increase the amount of aberrations in the STEM probe, leading to an increase in the probe size, and reduction in resolution. By using a probe aberration corrector it is possible to get a resolution of 1 nm.
caption: Schematic of differential phase contrast imaging, with the beam being deflected by a magnetic field in the material.
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