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Three-Dimensional Spin Rotations at the Fermi Surface of a Strongly Spin-Orbit Coupled Surface System

P. Höpfner, J. Schäfer, A. Fleszar, J. H. Dil, B. Slomski, F. Meier, C. Loho, C. Blumenstein, L. Patthey, W. Hanke, and R. Claessen
Phys. Rev. Lett. 108, 186801 – Published 30 April 2012
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    Abstract

    The spin texture of the metallic two-dimensional electron system (3×3)−Au/Ge(111) is revealed by fully three-dimensional spin-resolved photoemission, as well as by density functional calculations. The large hexagonal Fermi surface, generated by the Au atoms, shows a significant splitting due to spin-orbit interactions. The planar components of the spin exhibit a helical character, accompanied by a strong out-of-plane spin component with alternating signs along the six Fermi surface sections. Moreover, in-plane spin rotations toward a radial direction are observed close to the hexagon corners. Such a threefold-symmetric spin pattern is not described by the conventional Rashba model. Instead, it reveals an interplay with Dresselhaus-like spin-orbit effects as a result of the crystalline anisotropies.

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    • Received 11 November 2011

    DOI:https://doi.org/10.1103/PhysRevLett.108.186801

    © 2012 American Physical Society

    Authors & Affiliations

    P. Höpfner1, J. Schäfer1, A. Fleszar2, J. H. Dil3,4, B. Slomski3,4, F. Meier3,4, C. Loho1, C. Blumenstein1, L. Patthey3, W. Hanke2, and R. Claessen1

    • 1Physikalisches Institut, Universität Würzburg, 97074 Würzburg, Germany
    • 2Institut für Theoretische Physik und Astrophysik, Universität Würzburg, 97074 Würzburg, Germany
    • 3Swiss Light Source, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland
    • 4Physik-Institut, Universität Zürich, 8057 Zürich, Switzerland

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    Vol. 108, Iss. 18 — 4 May 2012

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    • Figure 1
      Figure 1
      DFT FS in the 1st SBZ, exhibiting a surface state split into two bands (S1A, S1B) due to the spin-orbit interaction. Small arrows along the FS and their lengths indicate the in-plane spin component. The spin is rotated by up to 75° out of (into) the surface [red/light gray (blue/dark gray)], highlighted by additional large arrows. Green (the longest thin arrows) indicates fully in-plane alignment. The magnitude ΔkR of the Rashba splitting between S1A and S1B varies with its position along the FS. For experimental scans (e.g., the dashed line), we use a local coordinate system (x,y,z).Reuse & Permissions
    • Figure 2
      Figure 2
      (a) Spin-resolved intensities derived from scattering asymmetries for the x component of the spin from an MDC in the 2nd SBZ along M¯−Γ¯−M¯. Upward (downward) pointing triangles correspond to the spin orientation in positive (negative) direction of x. (b) Scattering asymmetries for the y direction and (c) the z direction. (d) Total intensity MDC Itot. The peak doublets below originate from a two-step fitting routine [30] using the data in (a) to (c). Their maxima represent the spin-split band positions of S1A and S1B.Reuse & Permissions
    • Figure 3
      Figure 3
      Measured MDC spin-polarization for the z component as a function of k∥ along three different scan positions of the FS in the 2nd SBZ. The curved lines are fits to the data. The coordinate axes x, y, and z are strictly bound to the scan position.Reuse & Permissions
    • Figure 4
      Figure 4
      (a)–(c) z, y, and x components (Pz,Py,Px) of the spin-polarization vector for each individual state obtained from both a fit of the SARPES data and DFT as a function of the SP 1, 2, …, 7. (d) Rashba splitting ΔkR as a function of the corresponding SP. (e) 3D view of the spin-vector orientation as determined by SARPES. The SPs are the same as in Fig. 3. (f) CHCT model of (3×3)−Au/Ge(111) with the unit cell and high-symmetry directions as indicated.Reuse & Permissions
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