Thin line of a Rashba-type spin texture: Unoccupied surface resonance of Tl/Si(111) alongΓ¯M¯

Abstract

The Tl/Si(111)-(1 × 1) surface features outstanding properties with a unique spin pattern in momentum space. Along¯ K (¯ K ), surface states with rotating spin had been observed. Here, the focus is put on the unoccupied surface electronic structure along the¯ M high-symmetry direction. Spin-and angle-resolved inversephotoemission experiments with sensitivity to the in-plane and out-of-plane components of the spin-polarization vector are conducted with the help of our recently developed rotatable spin-polarized electron source (ROSE). In agreement with our theoretical findings, we identify a surface resonance with giant spin-orbit-induced spin splitting, which exhibits an exclusive Rashba-type spin texture, i.e., a pure in-plane spin polarization perpendicular to¯ M , in compliance with the mirror-plane symmetry of the¯ M direction. Notably, for slight deviations from the high-symmetry line, this constraint is lifted and additional spin-polarization components emerge. This highlights the importance of a correct alignment of the experiment when investigating samples with spin textures that are more complex than in simple Rashba systems or in ferromagnets.

Spin texture with a twist in momentum space for Tl/Si(111)

“…For a more detailed discussion, see Ref. [20]. The calculated dispersions of S 3 and S 4 are in nice agreement with the experimental findings.…”

“…3(c) and Ref. [20]). With this data, we model the measured band structure with the help of a simple approach using an effective Hamiltonian H eff , which takes into account the C 1h symmetry of theM point (with k x chosen along the mirror-plane directionM¯ ) and first-order Rashba parameters α [27]:…”

“…(b) Corresponding reciprocal lattice points (crosses) with two adjacent surface Brillouin zones and respective high-symmetry points (dots). Surface-derived states discussed in this manuscript are purely in-plane spin polarized along¯ M¯ (red and blue arrows)[20] and almost completely out-of-plane spin polarized atK (K ) (purple and orange markers).…”

“…This leads to almost completely out-of-plane spin-polarized valleys at theK (K ) points [9,10,17]. On the other hand, along the mirror plane direction¯ M , the surface-derived states are purely in-plane spin polarized [20] and they are degenerate at¯ andM.…”

“…To address this question, spin-and angle-resolved inverse-photoemission and density-functional theory is used to investigate theMK direction. Light is shed onto the spin texture aroundM taking into account the results alongM¯ [20] and by fitting an effective Hamiltonian to the experimental data. Our results demonstrate that theM point is encircled by a surface-derived state, which is almost completely out-of-plane spin polarized at the intersections with theMK and theMK line and purely in-plane spin polarized at theM¯ intersections.…”