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Engineering spin-orbit effects and Berry curvature by deposition of a monolayer of Eu on WSe2

Johanna P. Carbone, Dongwook Go, Yuriy Mokrousov, Gustav Bihlmayer, and Stefan Blügel
Phys. Rev. B 106, 064401 – Published 1 August 2022
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  • INTRODUCTION
  • RESULTS
  • DISCUSSION
  • CONCLUSION
  • ACKNOWLEDGMENTS
    • Supplemental Material
    References

    Abstract

    Motivated by recent progress in two-dimensional (2D) spintronics, we present a monolayer of Eu deposited on 1H−WSe2 as a promising platform for engineering spin-orbit effects and Berry curvature. By first-principles calculations based on density functional theory, we show that Eu/WSe2 exhibits intriguing properties such as high magnetic anisotropy, valley-dependent polarization of spin and orbital angular momenta, and Rashba textures. These originate from magnetic and spin-orbit proximity effects at the interface and the interplay between localized 4f magnetic moments of Eu and mobile charge carriers of Eu and WSe2. The analysis of the magnetic properties reveal a ferromagnetic configuration with an out-of-plane easy axis of the magnetization, which favor a pronounced anomalous Hall effect in the proposed system. Thus, we promote 4f rare-earth metals deposited on top of a transition-metal dichalcogenides as a promising platform for 2D spintronics.

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    • Received 5 April 2022
    • Revised 27 June 2022
    • Accepted 20 July 2022

    DOI:https://doi.org/10.1103/PhysRevB.106.064401

    ©2022 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Anomalous Hall effectMagnetic anisotropyMagnetismSpin-orbit coupling
    1. Physical Systems
    2-dimensional systemsRare-earth magnetic materials
    1. Techniques
    Density functional theoryWannier function methods
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Johanna P. Carbone1,2,*, Dongwook Go1,3, Yuriy Mokrousov1,3, Gustav Bihlmayer1, and Stefan Blügel1

    • 1Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
    • 2Physics Department, RWTH-Aachen University, 52062 Aachen, Germany
    • 3Institute of Physics, Johannes Gutenberg University Mainz, 55099 Mainz, Germany

    • *j.carbone@fz-juelich.de

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    Issue

    Vol. 106, Iss. 6 — 1 August 2022

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    Images

    • Figure 1
      Figure 1

      Structure of the 1×1 unit cell of Eu (purple spheres) monolayer deposited on top of the W atom (gray spheres) of a single layer of WSe2. Se atoms are indicated by yellow spheres.

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    • Figure 2
      Figure 2

      (a) Contribution to the local DOS of the f and d electrons of Eu. The total DOS (TDOS) is shown as gray shaded area. (b) Contribution to the local DOS of the s,p,d electrons of Eu, d electrons of W, and p electrons of Se. Both DOS in panels (a) and (b) have been calculated without SOC. (c) Band structure of Eu/WSe2 calculated with DFT+U (blue dashed line represents the majority channel and red dashed line represents the minority channel) and with DFT+U+SOC (black solid line). (d) First Brillouin zone with high-symmetry points.

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    • Figure 3
      Figure 3

      (a) Magnetic anisotropy energy curve: the total energy of the system plotted vs the polar angle θ of the magnetization measured from the z axis. (b) The energy of the spin-spiral states of a flat spiral, i.e., with cone angle β=π/2, computed for the values of the q vector along the Γ−K−M path, presented with respect to the ferromagnetic ground state at the Γ point.

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    • Figure 4
      Figure 4

      Spin and orbital texture in k space at the Fermi surface. (a) Expectation value for the out-of-plane component of the orbital angular momentum at the Fermi surface 〈Lz〉FS. (b) Magnitude of the expectation value of the in-plane component of the orbital angular momentum 〈Lxy〉FS=〈Lx〉FS2+〈Ly〉FS2. Analogously, the z component and the magnitude of the in-plane component for the spin expectation value at the Fermi surface are shown in panels (c) and (d), respectively. 〈Lz〉FS>(<)0 and 〈Sz〉FS>(<)0 [color blue (red)] correspond to the angular-momentum direction (anti)parallel to the spin of Eu-4f electrons.

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    • Figure 5
      Figure 5

      (a) Band structure around the Fermi energy with color scale indicating the value of the Berry curvature Ωnk. (b) Berry curvature summed over all occupied states along the k path Γ−K−M−K′−Γ.

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    • Figure 6
      Figure 6

      Anomalous Hall conductivity as a function of the Fermi level.

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    • Figure 7
      Figure 7

      Comparison of the electronic structure of Eu monolayer on WSe2 monolayer for two simulation cells: (a) 1×1 unit cell (high coverage of Eu) and (b) 3×3 unit cell (low coverage of Eu). The corresponding band structures determined neglecting SOC are shown in panels (c) and (d), where blue and red lines indicate majority and minority states, respectively.

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