One-dimensional Rashba states with unconventional spin texture in Bi chains

P. M. Sheverdyaeva, D. Pacilè, D. Topwal, U. Manju, M. Papagno, V. Feyer, M. Jugovac, G. Zamborlini, I. Cojocariu, C. Tusche, X. L. Tan, K. Hagiwara, Y.-J. Chen, J. Fujii, P. Moras, L. Ferrari, E. Vescovo, G. Bihlmayer, and C. Carbone

Phys. Rev. B 106, 045108 – Published 7 July 2022

Abstract

Spin-polarized electrons confined in low-dimensional structures are of high interest for spintronics applications. Here, we investigate the electronic structure of an ordered array of Bi monomer and dimer chains on the Ag(110) surface. By means of spin-resolved photoemission spectroscopy, we find Rashba-Bychkov split bands crossing the Fermi level with one-dimensional constant energy contours. These bands are up-spin polarized for positive wave vectors and down-spin polarized for negative wave vectors, at variance with the Rashba-Bychkov model that predicts a pair of states with opposite spin in each half of the surface Brillouin zone. Density functional theory shows that spin-selective hybridization with the Ag bulk bands originates this unconventional spin texture.

Received 20 May 2022
Accepted 16 June 2022

DOI:https://doi.org/10.1103/PhysRevB.106.045108

Physics Subject Headings (PhySH)

1-dimensional spin chains Interfaces Surfaces

Angle-resolved photoemission spectroscopy GGA Spin-resolved photoemission spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

P. M. Sheverdyaeva ¹, D. Pacilè ^2,*, D. Topwal ^3,4, U. Manju⁵, M. Papagno ², V. Feyer⁶, M. Jugovac^1,6,†, G. Zamborlini ⁶, I. Cojocariu⁶, C. Tusche^6,7, X. L. Tan⁶, K. Hagiwara⁶, Y.-J. Chen^6,7, J. Fujii⁸, P. Moras ¹, L. Ferrari ⁹, E. Vescovo¹⁰, G. Bihlmayer¹¹, and C. Carbone¹

¹Istituto di Struttura della Materia-CNR (ISM-CNR), SS 14, Km 163,5, I-34149, Trieste, Italy
²Dipartimento di Fisica, Università della Calabria, 87036 Arcavacata di Rende (CS), Italy
³Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
⁴Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, India
⁵CSIR - Institute of Minerals and Materials Technology, Bhubaneswar 751013, India
⁶Peter Grünberg Institut PGI, Forschungszentrum Jülich, 52425 Jülich, Germany
⁷Fakultät für Physik, Universität Duisburg-Essen, Duisburg 47057, Germany
⁸Istituto Officina dei Materiali (IOM)-CNR, Laboratorio TASC, S.S.14, Km 163.5, 34149 Trieste, Italy
⁹Istituto di Struttura della Materia, Consiglio Nazionale delle Ricerche, 00133 Roma, Italy
¹⁰National Synchrotron Light Source, Brookhaven National Laboratory, Upton, New York 11973, USA
¹¹Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, D-52425 Jülich, Germany

^*daniela.pacile@fis.unical.it
^†Present address: Elettra - Sincrotrone Trieste, S. S. 14 km 163.5 34149 Trieste, Italy.

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Vol. 106, Iss. 4 — 15 July 2022

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Images

Figure 1
LEED images taken with electron energy of 72 eV of (a) clean Ag(110); (b) Bi/Ag(110) $p$ ( $4 \times 1$ ). (c)–(e) STM images on different length scales of the sample in (b) acquired with constant-current mode (bias voltage was $- 380$ mV and tunneling current 1 nA). Line profiles extracted from (d) and (e) images along the pink and light blue lines, marking the apparent width and vertical displacement of the chains, as well as the step edge between adjacent Ag(110) terraces, are shown. (f) Schematics of the surface structure. The yellow rectangle is the surface unit cell. ${Bi}^{1}$ are Bi atoms in substitutional sites and ${Bi}^{2}$ in the topmost layer. ${Ag}^{1}$ and ${Ag}^{2}$ are Ag atoms of the topmost substrate layer, slightly rumpled due to the Bi atomic chains.
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Figure 2
Energy-momentum dispersion of Bi/Ag(110) $p$ ( $4 \times 1$ ) along: (a) $\bar{Γ} − \bar{Y}$ of the first SBZ; (b) $\bar{Γ} − \bar{Y}$ of the second SBZ; (c) along $\bar{X} − \bar{S}$ ; the corresponding $k_{y}$ positions of the cuts are indicated in (d). (d)–(e) 2D momentum maps taken at 0.55 eV binding energy with and without SBZ on top. Blue and red dashed lines indicate $R_{1}$ – $R_{3}$ pair of RB states. Solid grey lines indicate the SBZ. (f) SBZ of Bi/Ag(110) $p$ ( $4 \times 1$ ). The sketch of blue and red arrows show the spin texture at the Fermi surface from this work. (g) Spin-resolved photoemission intensities for the data shown in panel (e). Red and blue intensities correspond to spin-up and spin-down electronic states as shown in the legend. All measurements were taken at 120 eV of photon energy with $s$ -polarized light. The directions of the light polarization and of the SQA are shown in panel (g).
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Figure 3
(a), (b) Energy-momentum dispersion of Bi/Ag(110) $p$ ( $4 \times 1$ ): (a) along $\bar{Γ} − \bar{X}$ direction; (b) along $\bar{Γ} − \bar{Y}$ direction. The corresponding $k_{y}$ and $k_{x}$ positions of the cuts are indicated in the panel (c). (c) 2D momentum map, taken at 3.0 eV binding energy. (d) Spin-resolved photoemission intensities of the data shown in panel (c). Blue and red dashed lines indicate $R_{4}$ – $R_{5}$ pair of RB states. Solid grey lines indicate the SBZ. All measurements were taken at 120 eV of photon energy with $s$ -polarized light. (e) SBZ of Bi/Ag(110) $p$ ( $4 \times 1$ ). The sketch of blue and red arrows show the spin texture at about 3.0 eV binding energy from this work.
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Figure 4
(a) Theoretical band structure of Bi/Ag(110) $p$ ( $4 \times 1$ ) parallel to the Bi chains, that is along $\bar{Γ} − \bar{Y}$ . The color and size of the symbols indicate the orientation and size of the spin-polarization at the Bi atoms in the $k_{y}$ direction. (b) The same representation perpendicular to the Bi chains, i. e., along $\bar{Γ} − \bar{X}$ , with SQA referred to $k_{x}$ direction. (c) Ag(110) bands along $\bar{Γ} − \bar{X}$ and $\bar{Γ} − \bar{Y}$ folded according to the $4 \times 1$ periodicity. Different colors indicate a different density of states. (d)–(g) Charge density plots of states $R_{1}$ (d), $R_{2}$ (e), $R_{4}$ (f), and $R_{5}$ (g) pairs in the plane of the ${Bi}^{2}$ dimers (d), (g) or the ${Bi}^{1}$ alloyed atoms (e), (f). (d), (e) are extracted at 0.6 eV; (f) at 1.4 eV; (g) at 2.3 eV binding energy. Bi atoms are shown in blue, Ag atoms in grey.
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