Atomistic Modeling of Spin and Electron Dynamics in Two-Dimensional Magnets Switched by Two-Dimensional Topological Insulators

Sabyasachi Tiwari, Maarten L. Van de Put, Kristiaan Temst, William G. Vandenberghe, and Bart Sorée

Phys. Rev. Applied 19, 014040 – Published 12 January 2023

Abstract

To design fast memory devices, we need material combinations that can facilitate fast read and write operations. We present a heterostructure comprising a two-dimensional (2D) magnet and a 2D topological insulator (TI) as a viable option for designing fast memory devices. We theoretically model the spin-charge dynamics between 2D magnets and 2D TIs. Using the adiabatic approximation, we combine the nonequilibrium Green’s function method for spin-dependent electron transport and a time-quantified Monte Carlo method for simulating magnetization dynamics. We show that it is possible to switch a magnetic domain of a ferromagnet using the spin torque from spin-polarized edge states of a 2D TI. We show further that the switching of 2D magnets by TIs is strongly dependent on the interface exchange ( $J_{int}$ ), and an optimal interface exchange, is required for efficient switching. Finally, we compare experimentally grown Cr compounds and show that Cr compounds with higher anisotropy (such as $Cr I_{3}$ ) result in a lower switching speed but a more stable magnetic order.

Received 1 April 2022
Revised 10 October 2022
Accepted 21 November 2022

DOI:https://doi.org/10.1103/PhysRevApplied.19.014040

Physics Subject Headings (PhySH)

Ballistic transport Spin polarization

2-dimensional systems Devices for digital logic, storage & processing Ferromagnets Magnetic multilayers Topological insulators

Methods in magnetism

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Sabyasachi Tiwari ^1,2,3, Maarten L. Van de Put^1,3, Kristiaan Temst⁴, William G. Vandenberghe^1,*, and Bart Sorée ^3,5,6,†

¹Department of Materials Science and Engineering, The University of Texas at Dallas, 800 W Campbell Road, Richardson, Texas 75080, USA
²Department of Materials Engineering, KU Leuven, Kasteelpark Arenberg 44, Leuven 3001, Belgium
³Imec, Kapeldreef 75, Heverlee 3001, Belgium
⁴Quantum Solid State Physics, Department of Physics and Astronomy, KU Leuven, Celestijnenlaan 200 D, Leuven B-3001, Belgium
⁵Department of Electrical Engineering, KU Leuven, Kasteelpark Arenberg 10, Leuven 3001, Belgium
⁶Department of Physics, University of Antwerp, Groenenborgerlaan 171, Antwerp 2020, Belgium

^*william.vandenberghe@utdallas.edu
^†bart.soree@imec.be

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Vol. 19, Iss. 1 — January 2023

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Images

Figure 1
Choice of spin in a MC step using the TQMC method. The spin $S_{1}$ shows the initial spin state, which can take a value within a radius $R$ , with the spin state ranging between $S_{1}$ and $S_{2}$ (illustrated by the black circle). The spin state $S_{2}$ shows an intermediate spin state that can take a value within the radius $R$ (illustrated in blue), with the spin state switching from $S_{2}$ to $S_{3}$ . The radius $R$ is determined by the Gilbert damping.
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Figure 2
Interface between a 2D TI and a layered magnet. Electrons are injected from the contacts (illustrated by the blue arrow below the right contact) at time $t + Δ t$ . The flowing electrons carry a small magnetic moment (illustrated by the small blue arrows), exerting a torque due to the electronic magnetic configuration $m (t + Δ t)$ on the interfaced magnet, with magnetic configuration $M (t + Δ t)$ (illustrated by the red arrows).
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Figure 3
(a) Device configuration studied for TI-FM switching. The 2D TI is contacted with a drain and a source contact, and a voltage ( $V_{D S}$ ) is applied between the contacts. (b) Magnetization of the 2D FM as a function of time. (b.1) The bias is applied at $t = 0$ ns and switched to 100 meV from $- 100$ meV at $0.25$ ns. (b.2) The magnetization of the 2D FM in the $z$ direction ( $S_{z}$ ) switches its direction (from $3 μ_{B}$ to $- 3 μ_{B}$ ). (b.3) Induced magnetization in the 2D TI.
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Figure 4
Magnetic configuration [ $M (t)$ ] of the FM (upper three panels) and the electronic spin configuration [ $m (t)$ ] of the TI (lower three panels) at $t = 0.23$ , $0.27$ , and $0.41$ ns when the voltage pulse is switched at $t = 0.25$ ns. The atomic structure of the FM is shown superimposed on the magnetic configuration of the TI.
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Figure 5
(a) Applied $V_{D S}$ (a.1) and the magnetization of the top 2D FM for $α = 0.02, 0.03, 0.04, 0.05$ (a.2). (b) Applied $V_{D S}$ and the magnetization of the top 2D FM for interface interaction strengths $J_{int} = 5, 25, 50, 100, 150$ meV (b.2). (c) Transition time for the applied pulse in (b.1) as a function of $J_{int}$ . (d) Magnetization at $t = 0.45$ ns for $J_{int} = 25$ and $150$ meV. The upper two panels show the magnetization of the 2D FM in the $z$ direction ( $S_{z} / | M |$ ), and the lower two panels show the induced magnetization in the 2D TI ( $m_{z}$ ).
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Figure 6
(a) Transition time as a function of nearest-neighbor anisotropy $Δ_{NN}$ . We perform the same sweep of $Δ_{NN}$ for ten different starting configurations. The solid line shows the median, and the shaded region shows the 25th–75th percentile. (b) Comparison of switching in $Cr I_{3}$ , $Cr B r_{3}$ , $Cr C l_{3}$ , and $Cr Ge T e_{3}$ . (b.1) Applied $V_{D S}$ ; (b.2) magnetization ( $S_{z} / | M |$ ) for $Cr I_{3}$ , $Cr B r_{3}$ , $Cr C l_{3}$ , and $Cr Ge T e_{3}$ . We use an interface exchange $J_{int} = 25$ meV, and $α = 0.005$ .
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