Measuring spin-polarized electronic states of quantum materials: $2H\ensuremath{-}{\mathrm{NbSe}}_{2}$

Measuring spin-polarized electronic states of quantum materials: $2 H - {NbSe}_{2}$

Chiara Bigi, Federico Mazzola, Jun Fujii, Ivana Vobornik, Giancarlo Panaccione, and Giorgio Rossi

Phys. Rev. B 103, 245142 – Published 25 June 2021

Abstract

Probing the energy and spin electron properties of materials by means of photoemission spectroscopy gives insights into the low-energy phenomena of matter driven by spin orbit coupling or exchange interaction. The information that can be derived from complete photoelectron spectroscopy experiments, beyond $E$ (k), is contained in the photoemission transition matrix elements that determine peak intensities. We present here a complete photoemission study of the spin-polarized bands of $2 H − {NbSe}_{2}$ , a material that presents a surface spin-texture. Circular dichroism in angular-resolved photoemission spectroscopy (CD-ARPES) data are compared with spin-polarized angular-resolved spectra (SARPES) as measured with linearly polarized radiation in a well-characterized experimental chirality, at selected photon energy values. CD-ARPES is due to a matrix element effect that depends strongly on photon energy and experimental geometry: we show that it cannot be used to infer intrinsic spin properties in $2 H − {NbSe}_{2}$ . On the other hand, SARPES data provide reliable direct information on the spin properties of the electron states. The results on $2 H − {NbSe}_{2}$ are discussed, and general methodological conclusions are drawn on the best experimental approach to the determination of the spin texture of quantum materials.

Received 25 November 2020
Revised 29 May 2021
Accepted 2 June 2021

DOI:https://doi.org/10.1103/PhysRevB.103.245142

Physics Subject Headings (PhySH)

Spin texture

Dichalcogenides Electronic structure

Angle-resolved photoemission spectroscopy Spin-resolved photoemission spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Chiara Bigi ^1,2, Federico Mazzola², Jun Fujii², Ivana Vobornik², Giancarlo Panaccione ², and Giorgio Rossi ^1,2

¹Department of Physics, University of Milano, 20133 Milano, Italy
²CNR-IOM TASC Laboratory, 34139 Trieste, Italy

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Vol. 103, Iss. 24 — 15 June 2021

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Figure 1
Scheme of the experimental geometry at the APE-LE beamline. The accumulation ring lies in the $y z$ plane. The photon beam is impinging the sample at an angle $α = 45^{\circ}$ with respect to the normal emission N.E. (i.e., the axis of the ARPES detector entrance optics). LH, CPR, and CPL light polarizations have been exploited to investigate the band structure of $2 H − {NbSe}_{2}$ . The sample is hosted on a manipulator with 5 degrees of freedom (3 translational and 2 angular). The DA30 Scienta analyzer is mounted with the slit parallel to the $x$ axis (i.e., perpendicular to the LH polarization vector) and collects the photoelectrons emitted at angle $Θ_{x}$ within $30^{\circ}$ maximum acceptance. The orange lines mark the photoelectron beam trajectory inside the analyzer body reaching the MCP where the ARPES spectrum is collected. The ARPES analyzer is fitted with a very low-energy electron diffraction (VLEED) spin polarimeter [26, 28, 29]. There are two VLEED scattering chambers (i.e., VLEED-B and VLEED-W) mounted at $90^{\circ}$ with respect to each other providing the three components of the SP vector. Once filtered in energy and momentum, the photoelectron beam enters the VLEED scattering chambers through two independent apertures hosted on the DA30 exit plane (black trajectories). VLEED-W measures the SP component along the $x$ -axis, which lays in the sample surface parallel to the analyzer slit. VLEED-B probes the other in-plane component along the $y$ -axis. Both VLEED-W and VLEED-B measure the out-of-plane SP component, allowing cross-normalization of the data. Therefore, the full 3D vectorial SP can be reconstructed.
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Figure 2
(a) $2 H − {NbSe}_{2}$ crystal structure and the Brillouin zone (BZ); the gray area in the BZ marks the $Γ − K − M$ plane probed by 70 eV photon energy, and the colored lines indicate the high-symmetry directions along which we extracted the $E_{B}$ vs $k_{∥}$ ARPES spectra reported in (c). (b) The corresponding Fermi surface acquired with $h ν = 70$ eV linearly horizontal (LH) polarized light. The colored lines mark where the $E_{B}$ vs $k_{∥}$ dispersions have been extracted. (c) Band dispersions $E_{B}$ vs $k_{∥}$ along the high symmetric directions of $2 H − {NbSe}_{2}$ (0001). Panels from left to right: $K^{'} − Γ − K$ (green), $K^{'} − M − K$ (yellow), and $Γ − M$ (pink).
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Figure 3
ARPES and CD-ARPES spectra of the ${NbSe}_{2}$ electronic bands measured at 70 eV photon energy along the $K − Γ − K^{'}$ high-symmetry direction. (a) Circular polarization right (CPR) and (b) circular polarization left (CPL). Parts (c) and (d) reports the sum ( $CPR + CPL$ ) and the circular dichroic ARPES spectrum, respectively. The experimental geometry is sketched in panels (e) and (f) for the CPR-CPL light polarization, respectively.
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Figure 4
ARPES, CD-ARPES, and SARPES spectra of the spin-polarized pockets along the $K − M − K^{'}$ high-symmetry direction. The ARPES data were acquired at $h ν = 25$ eV. (a) Sum spectra ( $CPR + CPL$ ). (b) Circular dichroic ARPES spectrum. (c) SARPES data measured along the out-of-plane spin component with 25 eV linearly polarized light. (d) Sketch of the Brillouin zone and of the spin-polarized pockets under investigation. The green line marks the direction along which the measurements were performed. The brown rectangles in panels (a) and (b) indicate the corresponding area where the SARPES map in (c) was acquired.
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Figure 5
ARPES, circular dichroic ARPES (CD-ARPES), and SARPES measured along the $Γ − K^{'}$ direction at different photon energies: (a) 25 eV, (b) 33 eV, and (c) 44 eV. The ARPES and SARPES data were measured with linearly horizontal polarized light. The colored arrows on the ARPES and CD-ARPES spectra mark the $k_{x}$ momenta where the spin texture has been probed. Top row reports the ARPES and CD-ARPES spectra, middle panels show the spin-filtered EDCs and the corresponding out-of-plane SP values. Bottom row reports the CD signal obtained from the CD-ARPES at the same $k_{∥}$ value where the SARPES was performed.
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Physical Review B

covering condensed matter and materials physics

Measuring spin-polarized electronic states of quantum materials: $2 H - {NbSe}_{2}$

Chiara Bigi, Federico Mazzola, Jun Fujii, Ivana Vobornik, Giancarlo Panaccione, and Giorgio Rossi

Phys. Rev. B 103, 245142 – Published 25 June 2021

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Physical Review B

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Measuring spin-polarized electronic states of quantum materials: 2H−NbSe2

Chiara Bigi, Federico Mazzola, Jun Fujii, Ivana Vobornik, Giancarlo Panaccione, and Giorgio Rossi

Phys. Rev. B 103, 245142 – Published 25 June 2021

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Measuring spin-polarized electronic states of quantum materials: $2 H - {NbSe}_{2}$