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  • Letter
  • Open Access

Hidden interplay of current-induced spin and orbital torques in bulk Fe3GeTe2

Tom G. Saunderson, Dongwook Go, Stefan Blügel, Mathias Kläui, and Yuriy Mokrousov
Phys. Rev. Research 4, L042022 – Published 7 November 2022
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    Abstract

    Low crystal symmetry of magnetic van der Waals materials naturally promotes spin-orbital complexity unachievable in common magnetic materials used for spin-orbit torque switching. Here, using first-principles methods, we demonstrate that an interplay of spin and orbital degrees of freedom has a profound impact on spin-orbit torques in the prototypical van der Waals ferromagnet Fe3GeTe2. While we show that bulk Fe3GeTe2 hosts strong “hidden” current-induced torques harvested by each of its layers, we uncover that their origin alternates between the conventional spin flux torque and the so-called orbital torque as the magnetization direction is varied. A drastic difference in the behavior of the two types of torques results in a nontrivial evolution of switching properties with doping. Our findings promote the design of nonequilibrium orbital properties as the guiding mechanism for crafting the properties of spin-orbit torques in layered van der Waals materials.

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    • Received 19 May 2022
    • Accepted 5 September 2022

    DOI:https://doi.org/10.1103/PhysRevResearch.4.L042022

    Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

    Published by the American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Electrical generation of spin carriersMagnetismMagnetization dynamicsSpin currentSpin-orbit couplingSpin-orbit torque
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Tom G. Saunderson1,2,*, Dongwook Go1,2, Stefan Blügel2, Mathias Kläui1,3, and Yuriy Mokrousov1,2

    • 1Institute of Physics, Johannes Gutenberg University, 55099 Mainz, Germany
    • 2Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
    • 3Centre for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, 7491 Trondheim, Norway

    • *tsaunder@uni-mainz.de

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    Vol. 4, Iss. 4 — November - December 2022

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    • Figure 1
      Figure 1

      A schematic illustration for current-induced torques in Fe3GeTe2 (FGT) with (a) an out-of-plane and (b) in-plane magnetization. In both instances the current direction is along the x axis. The crystal structure of Fe3GeTe2, consisting of two individual layers, A and B, is displayed on the left. The direction of the magnetization at angle θ with the z axis is marked with MA and MB for each layer. The current-induced torques on each layer are opposite, so that the overall torque is vanishing. While for out-of-plane FGT, the magnetic torque is mainly driven by the flow of the spin angular momentum between layers [marked with arrows in (a)], the magnetic torque is dominated by prominent orbital accumulation for in-plane FGT [marked with arrows in (b)].

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    • Figure 2
      Figure 2

      Angular dependence of current-induced torque and the spin and orbital contributions in FGT. (a) The θ component of the antidamping current-induced torque on the magnetization (TMθ, black triangles), the spin contribution (Φθ, red dashed square), and the orbital contribution (TSOθ, blue dashed circle) for single-layer FGT as a function of θ. (b) Same as in (a) for the torkance projected onto the A layer in bulk FGT. (c) The y component of the current-induced orbital (Ly, blue dashed circle) and spin (Sy, red dashed square) moment summed over Fe atoms in the A layer of bulk FGT as a function of the angle θ.

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    • Figure 3
      Figure 3

      Properties of the current-induced torque and orbital angular momentum of the A layer of Fe3GeTe2 for the magnetization angle of θ=30∘ [(a), (c), (e), (g)] and θ=90∘ [(b), (d), (f), (h)]. In (a) and (b) the plotted band structure is superimposed with the colored circles whose color and size represent the expectation value of the total torkance TM,nkθ. Similarly, in (c) and (d) it is the y component of the current-induced orbital angular momentum Ly,nk which is represented with the circles. Additionally, the k-space distribution of Ly,k for the two angles is shown in (g) and (h). (e) and (f) display the total integrated (Tθ, solid line), flux (Φθ, red dashed line), and orbital (TSOθ, blue dashed line) torkance as a function of band filling for(e) θ=30∘ and (f) θ=90∘, where E=0 represents the true Fermi energy of FGT. The prominent current-induced orbital angular momentum and orbital torque for the in-plane magnetization is evident.

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