Analogs of Rashba-Edelstein effect from density functional theory

Karma Tenzin, Arunesh Roy, Homayoun Jafari, Bruno Banas, Frank T. Cerasoli, Mihir Date, Anooja Jayaraj, Marco Buongiorno Nardelli, and Jagoda Sławińska

Phys. Rev. B 107, 165140 – Published 24 April 2023

Abstract

Studies of structure-property relationships in spintronics are essential for the design of materials that can fill specific roles in devices. For example, materials with low symmetry allow unconventional configurations of charge-to-spin conversion, which can be used to generate efficient spin-orbit torques. Here, we explore the relationship between crystal symmetry and geometry of the Rashba-Edelstein effect (REE) that causes spin accumulation in response to an applied electric current. Based on a symmetry analysis performed for 230 crystallographic space groups, we identify classes of materials that can host conventional or collinear REE. Although transverse spin accumulation is commonly associated with the so-called “Rashba materials”, we show that the presence of specific spin texture does not easily translate to the configuration of REE. More specifically, bulk crystals may simultaneously host different types of spin-orbit fields, depending on the crystallographic point group and the symmetry of the specific $k$ vector, which, averaged over the Brillouin zone, determine the direction and magnitude of the induced spin accumulation. To explore the connection between crystal symmetry, spin texture, and the magnitude of REE, we perform first-principles calculations for representative materials with different symmetries. We believe that our results will be helpful for further computational and experimental studies, as well as the design of spintronics devices.

Received 17 October 2022
Accepted 6 April 2023

DOI:https://doi.org/10.1103/PhysRevB.107.165140

Physics Subject Headings (PhySH)

Fermi surface Spin-orbit coupling Spintronics

Electronic structure Elemental semiconductors Ferroelectrics Semiconductor compounds

Density functional theory Materials modeling Symmetries Symmetries in condensed matter

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Karma Tenzin ^1,2,*, Arunesh Roy ^1,*, Homayoun Jafari ¹, Bruno Banas ¹, Frank T. Cerasoli³, Mihir Date ^1,†, Anooja Jayaraj ⁴, Marco Buongiorno Nardelli ^4,5, and Jagoda Sławińska ^1,‡

¹Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747AG Groningen, Netherlands
²Department of Physical Science, Sherubtse College, Royal University of Bhutan, 42007 Kanglung, Trashigang, Bhutan
³Department of Chemistry, University of California, Davis, Davis, California 95616, USA
⁴Department of Physics, University of North Texas, Denton, Texas 76203, USA
⁵The Santa Fe Institute, Santa Fe, New Mexico 87501, USA

^*These authors contributed equally to this work.
^†Present address: Max Planck Institute of Microstructure Physics, Weinberg 2, 06114 Halle (Saale), Germany.
^‡jagoda.slawinska@rug.nl

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Vol. 107, Iss. 16 — 15 April 2023

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Images

Figure 1
Comparison of conventional and collinear REEs. (a) The left-hand panel shows 2D FS with purely tangential spin texture. They shift from the equilibrium in response to the electric current along $x$ , to induce a net spin accumulation perpendicular to the current. Filled arcs marked in red and blue denote the generated spin imbalance. The right-hand panel shows the conventional REE in the real space. (b) The same for purely radial spin texture. In this case, the induced spin accumulation is parallel to the electric current.
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Figure 2
Geometry, electronic structure, and spin accumulation of ferroelectric GeTe. (a) Schematic view of the crystal structure. (b) Electronic band structure calculated along the $Γ - L - U - X - Γ - Z - U$ line. Note that the band gap is indirect and the VBM lies outside the high-symmetry line. (c) The FS at the energy $E = - 0.27$ eV below the VBM. The color scheme reflects the local band velocity [20]. (d) Left: The spin texture around the $Z$ point showing the star-shaped Fermi contour ( $E = - 0.27$ eV) with a Rashba spin texture. The in-plane ( $S_{x}$ , $S_{y}$ ) components of the spin texture are represented by the arrows and the normal component $S_{z}$ by the color. In this case, the in-plane components correspond to ( $S_{x}, S_{y}$ ) and the normal component to $S_{z}$ . Right: Fermi contour at the BZ edge around the $L$ point showing a Rashba-Dresseslhaus spin texture. (e) Calculated magnitude of the $χ$ tensor as a function of the chemical potential.
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Figure 3
Calculated properties of the monolayer ${In}_{2} {Se}_{3}$ . (a) Side and top view of the crystal structure. (b) Electronic structure calculated along the high-symmetry $k$ lines. The inset shows the magnified region around the VBM. (c) Full 2D-BZ with the constant energy contour for $E = - 130$ meV with respect to the VBM. (d) Zoom-in of the contour with the superimposed in-plane spin texture. ( $S_{x}$ , $S_{y}$ ) components are represented by the arrows. $S_{z}$ is negligible and it is omitted. (e) Calculated $χ_{x y}$ and $χ_{y x}$ as a function of the chemical potential. The volume equivalent was calculated using the effective thickness of ${In}_{2} {Se}_{3}$ equal to 10 Å.
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Figure 4
Structure and electronic properties of the left-handed Te (SG 154). (a) Top view of the crystal structure. (b) Fermi surface at $E = - 30$ meV below the VBM. (c) Band structure of Te shown along the $L - H - A$ path; the Fermi level is set at VBM. (d) Left: Spin texture projected onto the $k_{y} - k_{z}$ plane at $k_{x} = π / a$ with arrows representing the in-plane spin components ( $S_{y}$ , $S_{z}$ ). Right: Projection of the same band onto $k_{x} - k_{y}$ plane at $k_{z} = 0$ . The arrows represent in-plane spin component ( $S_{x}$ , $S_{y}$ ); the normal component is negligible for both planes. (e) Calculated magnitude of the REE as a function of the chemical potential. The component $χ_{x x}$ is omitted as it is equal to $χ_{y y}$ by symmetry.
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Figure 5
Structural, electronic, and spin transport properties of ${Pd}_{4} Se$ . (a) Schematic view of the tetragonal unit cell. (b) Brillouin zone with the high-symmetry $k$ points. (c) Calculated Fermi surface ( $E = E_{F}$ ) consisting of eight nested sheets. (d) Band structure calculated along the high-symmetry lines denoted in (b). (e) Calculated Rashba-Edelstein tensor elements vs chemical potential. (f) Fermi contour ( $E = E_{F}$ ) at the $k_{z} = 0$ plane corresponding to one of the bands visible at the BZ center in (c). The arrows represent ( $S_{x}$ , $S_{y}$ ) components of the spin texture. The negligible component $S_{z}$ is omitted. (g) Same as (f) for one cylindrical band located along the $A - M$ line. (h) Same as (g) but plotted for the $k_{z} = π / c$ plane. Note that (g) and (h) are the projection of the same Fermi contour at different $k_{z}$ ( $M$ and $A$ ).
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