Abrupt Rotation of the Rashba Spin to the Direction Perpendicular to the Surface

Abstract

The polarization vector of the Rashba spin, which must be parallel to the two-dimensional (2D) plane in an ideal system, is found to change abruptly and definitely to the direction perpendicular to the surface at the K̅ point of the Brillouin zone of a real hexagonal system, the Tl/Si(111)-(1×1) surface. This finding obtained experimentally by angle-resolved and spin-resolved photoemission measurements is fully confirmed by a first-principles theoretical calculation. We found that the abrupt rotation of the Rashba spin is simply understood by the 2D symmetry of the hexagonal structure

Relativistic effects and fully spin-polarized Fermi surface at the Tl/Si(111) surface

“…The calculations on the A termination are in very good agreement with spin-resolved ARPES photoemission experiments. 31 Our analysis demonstrates that the band gap of this surface is reduced to a value of ∼0.1 eV as a direct consequence of the spin-orbit interaction, the Fermi level being completely surrounded by fully spinpolarized surface states. In overall, both terminations show a highly complex spin-polarization structure in momentum space, particularly the Tl/Si(111)B termination.…”

“…31 In an analogous way, the S ↓ A2 and S ↑ A2 bands suffer a maximum splitting of ∼0.6 eV, an extraordinarily large value for a spin-orbit energy shift. The energy band gap of this termination reduces roughly from a value of 0.2 eV in scalar relativistic calculations to the 0.1 eV found in fully relativistic bands.…”

“…reveals that close to the K and K symmetry points, the spin-state of the surface electrons becomes predominantly polarized along the z direction, in agreement with recent spin-resolved ARPES measurements. 31 This characteristic property is a consequence of the C3 rotational symmetry of the honeycomb layered structure of the surface. 11 In Fig.…”

Current-induced spin–orbit torques

“…Note that, in the presence of an external magnetic field [41] or exchange splitting [34,42,43], both time-reversal and inversion symmetry may be broken, leading to a more complex relationship between k and spin depending on the relative strength of the SO relative to exchange splitting ( §4a). In real two-dimensional systems, the point-group symmetry of the surface lattice and the presence of in-plane electric field gradients between dissimilar atomic species may further lead to out-of-plane components of the k-dependent spin polarization [39,44]. It is easy to understand how either BIA or SIA result in magnetic field-like interactions by considering the motion of electrons in an asymmetric crystal field potential (V ).…”

Spin-flip transitions and departure from the Rashba model in the Au(111) surface

“…The family of bismuth alloy surfaces, 2,5,6 for instance, exhibits giant spin-orbit energy shifts of nearly 400 meV. Other interesting examples include the semiconducting surfaces Tl/Si(111)−(1 × 1), [7][8][9] Tl/Ge(111)−(1 × 1), 10 and Pb/Ge(111)−β √ 3 × √ 3R30 • , 11,12 among many others. In these systems, the bulk bands present a gap near the Fermi level, and thus the electron transport properties are strongly influenced by the spin-split metallic surface states.…”