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Spin mapping of surface and bulk Rashba states in ferroelectric α-GeTe(111) films

H. J. Elmers, R. Wallauer, M. Liebmann, J. Kellner, M. Morgenstern, R. N. Wang, J. E. Boschker, R. Calarco, J. Sánchez-Barriga, O. Rader, D. Kutnyakhov, S. V. Chernov, K. Medjanik, C. Tusche, M. Ellguth, H. Volfova, St. Borek, J. Braun, J. Minár, H. Ebert, and G. Schönhense
Phys. Rev. B 94, 201403(R) – Published 9 November 2016
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    Abstract

    The breaking of bulk inversion symmetry in ferroelectric semiconductors causes a Rashba-type spin splitting of electronic bulk bands. This is shown by a comprehensive mapping of the spin polarization of the electronic bands in ferroelectric α-GeTe(111) films using a time-of-flight momentum microscope equipped with an imaging spin filter that enables a simultaneous measurement of more than 10 000 data points. The experiment reveals an opposite spin helicity of the inner and outer Rashba bands with a different spin polarization in agreement with theoretical predictions, confirming a complex spin texture of bulk Rashba states. The outer band has about twice larger spin polarization than the inner one, giving evidence of a spin-orbit effect being related to the orbital composition of the band states. The switchable inner electric field of GeTe implies new functionalities for spintronic devices.

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    • Received 4 June 2016
    • Revised 5 September 2016

    DOI:https://doi.org/10.1103/PhysRevB.94.201403

    ©2016 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    FerroelectricityRashba coupling
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    H. J. Elmers1,*, R. Wallauer1, M. Liebmann2, J. Kellner2, M. Morgenstern2, R. N. Wang3, J. E. Boschker3, R. Calarco3, J. Sánchez-Barriga4, O. Rader4, D. Kutnyakhov1, S. V. Chernov1, K. Medjanik1, C. Tusche5,6, M. Ellguth1,5, H. Volfova7, St. Borek7, J. Braun7, J. Minár7,8, H. Ebert7, and G. Schönhense1

    • 1Institut für Physik, Johannes Gutenberg-Universität, Staudingerweg 7, D-55099 Mainz, Germany
    • 2II. Physikalisches Institut B and JARA-FIT, RWTH Aachen University, D-52074 Aachen, Germany
    • 3Paul-Drude-Institut für Festkörperelektronik, Hausvogteiplatz 5-7, 10117 Berlin, Germany
    • 4Helmholtz-Zentrum Berlin für Materialien und Energie, Elektronenspeicherring BESSY II, Albert-Einstein-Straße 15, D-12489 Berlin, Germany
    • 5Max-Planck-Institut für Mikrostruktur Physik, Weinberg 2, D-06120 Halle, Germany
    • 6Peter Grünberg Institut (PGI-6), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
    • 7Department Chemie, Ludwig-Maximilians-Universität München, 81377 Munich, Germany
    • 8New Technologies-Research Center, University West Bohemia, Univerzitni 8, 306 14 Pilseň, Czech Republic

    • *elmers@uni-mainz.de

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    Issue

    Vol. 94, Iss. 20 — 15 November 2016

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    Images

    • Figure 1
      Figure 1

      (a) Bulk and surface Brillouin zone of GeTe with marked high symmetry points and the projection of the hexagonal face of the Brillouin zone encircled in green. (b) Constant energy slice I(EF,kx,ky) of the photoelectron intensity distribution for a photon energy of hν=18.5 eV covering the complete bulk Brillouin zone projection. (c) Constant energy slice I(Eb,kx,ky) with Eb=0.4 eV for hν=22 eV with larger magnification. The two surface bands (S1,2) and the bulk band B1 are marked. Full lines at constant kx indicate positions of cuts shown in (d)–(f). (d)–(f) Photoelectron intensity I(0.4eV,kx,ky,kz) for fixed values kx=0 and kx=±0.2Å−1. kz is measured relative to the Z point in k space, which is probed for hν=19.5 eV. Dash-dotted lines indicate bulk bands.

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    • Figure 2
      Figure 2

      (a)–(g) Energy isosurfaces of the photoelectron spin-polarization component Px(Eb,kx,ky) combined with the corresponding intensity distribution measured without spin resolution for hν=22 eV. Each slice averages over an energy interval of 43 meV. The corresponding color code for Px and I is indicated in (h). Arrows in (a) and (f) mark the deduced spin direction assuming a negligible perpendicular spin component.

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    • Figure 3
      Figure 3

      (a), (b) Constant momentum cut Px(Eb,kx,ky) for kx=0 and kx=+0.1Å−1 combined with the corresponding intensity distribution. For the color scale see Fig. 2. The cuts are averaged over a momentum interval of Δkx=0.05Å−1. Red (dashed) and blue (dotted) lines are guides to the eye; arrows and the dotted rectangle denote hybridization regions of bulk (BR) and surface states (SR). (c), (d) Calculations of the photoemission spin polarization and intensity shown in a similar representation as in (a) and (b): constant momentum cut Px(Eb,kx,ky) for kx=0 (c) and kx=+0.1Å−1 (d). Red (dashed) and blue (dotted) lines are guides to the eye; arrows and dotted rectangle (d) denote the energy region of the surface resonance. (e) Intensity line profile I(Eb,kx,ky) for kx=0.11Å−1 and Eb=0.565 eV along the line indicated in (b). (f) Corresponding line profile of the spin polarization Px. (g) Resulting intensity for spin-up and spin-down electrons. Arrows in (f) and (g) mark the extrema positions.

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