Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-24T08:47:02.906Z Has data issue: false hasContentIssue false
  • English
  • Français

Spin-Dependent Nonlinear Contrast Transfer in Transmission Electron Microscopy

Published online by Cambridge University Press:  14 September 2022

Markus Lentzen Open the ORCID record for Markus Lentzen [Opens in a new window]
Markus Lentzen*
Affiliation:
Forschungszentrum Jülich GmbH, Ernst Ruska Centre, Jülich 52425, Germany
*
Email: [email protected]
Get access

Abstract

In this study, the spin-dependent nonlinear contrast transfer in transmission electron microscopy is derived from the eikonal expansion of the Dirac equation. The transmission cross-coefficient of the standard imaging theory is amended by a spin-dependent factor, whose effect is investigated for single scattering in the object by an electrical field under polarized and unpolarized illumination, and it is illustrated with numerical results and plots for a kinetic energy of 80 keV. The resulting image displacement and image convolution increase with decreasing kinetic energy but are always smaller than a wavelength. General features of the cross-coefficient are discussed to identify favorable conditions for the measurement of the small spin effects, possibly in an unmodified instrument.

Keywords

contrast theoryDirac equationelectron diffractionelectron spintransmission electron microscopy
Type
Original Article
Information
Microscopy and Microanalysis , First View , pp. 1 - 9
Check for updates
Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of the Microscopy Society of America

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bargmann, V, Michel, L & Telegdi, VL (1959). Precession of the polarization of particles moving in a homogeneous electromagnetic field. Phys Rev Lett 2, 435–436.CrossRefGoogle Scholar
Dirac, PAM (1928). The quantum theory of the electron. Proc R Soc London Ser A 117, 610–624.Google Scholar
Ferwerda, HA, Hoenders, BJ & Slump, CH (1986 a). Fully relativistic treatment of electron-optical image formation based on the Dirac equation. Opt Acta 33, 145–157.CrossRefGoogle Scholar
Ferwerda, HA, Hoenders, BJ & Slump, CH (1986 b). The fully relativistic foundation of linear transfer theory in electron optics based on the Dirac equation. Opt Acta 33, 159–183.CrossRefGoogle Scholar
Forbes, BD, D'Alfonso, AJ, Findlay, SD, Van Dyck, D, LeBeau, JM, Stemmer, S & Allen, LJ (2011). Thermal diffuse scattering in transmission electron microscopy. Ultramicroscopy 111, 1670–1680.CrossRefGoogle ScholarPubMed
Fujiwara, K (1961). Relativistic dynamical theory of electron diffraction. J Phys Soc Jpn 16, 2226–2238.CrossRefGoogle Scholar
Glaser, W (1933). Über geometrisch-optische Abbildung durch Elektronenstrahlen. Z Phys 80, 451–464.CrossRefGoogle Scholar
Gordon, W (1926). Der Comptoneffekt nach der Schrödingerschen Theorie. Z Phys 40, 117–133.CrossRefGoogle Scholar
Houben, L, Thust, A & Urban, K (2006). Atomic-precision determination of the reconstruction of a 90° tilt boundary in YBa2Cu3O7−δ by aberration corrected HRTEM. Ultramicroscopy 106, 200–214.CrossRefGoogle Scholar
Ishizuka, K (1980). Contrast transfer of crystal images in TEM. Ultramicroscopy 5, 55–65.CrossRefGoogle Scholar
Jia, CL, Houben, L, Thust, A & Barthel, J (2010). On the benefit of the negative-spherical-aberration imaging technique for quantitative HRTEM. Ultramicroscopy 110, 500–505.CrossRefGoogle Scholar
Klein, O (1926). Quantentheorie und fünfdimensionale Relativitätstheorie. Z Phys 37, 895–906.CrossRefGoogle Scholar
Kuwahara, M, Kusunoki, S, Jin, XG, Nakanishi, T, Takeda, Y, Saitoh, K, Ujihara, T, Asano, H & Tanaka, N (2012). 30-kV spin-polarized transmission electron microscope with GaAs-GaAsP strained superlattice photocathode. Appl Phys Lett 101, 033102.Google Scholar
Kuwahara, M, Yoshida, Y, Nagata, W, Nakakura, K, Furui, M, Ishida, T, Saitoh, K, Ujihara, T & Tanaka, N (2021). Intensity interference in a coherent spin-polarized electron beam. Phys Rev Lett 126, 125501.Google Scholar
Lichte, H (2008). Performance limits of electron holography. Ultramicroscopy 108, 256–262.CrossRefGoogle ScholarPubMed
Linck, M, Hartel, P, Uhlemann, S, Kahl, F, Müller, H, Zach, J, Haider, M, Niestadt, M & Bischoff, M (2016). Chromatic aberration correction for atomic resolution TEM imaging from 20 to 80 kV. Phys Rev Lett 117, 076101.CrossRefGoogle ScholarPubMed
Molière, G (1947). Theorie der Streuung schneller geladener Teilchen I – Einzelstreuung am abgeschirmten Coulomb-Feld. Z Naturforsch A 2, 133–145.CrossRefGoogle Scholar
Pulvermacher, H (1981). Der Transmissions-Kreuz-Koeffizient für die elektronenmikroskopische Abbildung bei partiell kohärenter Beleuchtung und elektrischer Instabilität. Optik 60, 45–60.Google Scholar
Rosen, M (1964). A three-dimensional WKB approximation for the Dirac equation. Il Nuovo Cimento 33, 1667–1679.CrossRefGoogle Scholar
Rother, A & Scheerschmidt, K (2009). Relativistic effects in elastic scattering of electrons in TEM. Ultramicroscopy 109, 154–160.CrossRefGoogle ScholarPubMed
Rubinow, SI & Keller, JB (1963). Asymptotic solution of the Dirac equation. Phys Rev 131, 2789–2796.CrossRefGoogle Scholar
Thust, A (2009). High-resolution transmission electron microscopy on an absolute contrast scale. Phys Rev Lett 102, 220801.Google Scholar
Uhlemann, S, Müller, H, Hartel, P, Zach, J & Haider, M (2013). Thermal magnetic field noise limits resolution in transmission electron microscopy. Phys Rev Lett 111, 046101.CrossRefGoogle ScholarPubMed
Urban, KW (2008). Studying atomic structures by aberration-corrected transmission electron microscopy. Science 321, 506–510.CrossRefGoogle ScholarPubMed