Anatomy of spin-wave-driven magnetic texture motion via magnonic torques

Hanxu Ai (艾もぐさ寒かん旭あさひ) and Jin Lan (兰金)

Phys. Rev. B 107, 054441 – Published 28 February 2023

Abstract

The interplay between spin waves and magnetic texture represents the information exchange between the fast and slow dynamical parts of magnetic systems. Here we formulate a set of magnonic torques acting on background magnetic texture, by extracting time-invariant information from the fast precessing spin waves. Under the frame of magnonic torques, we use theoretical formulations and micromagnetic simulations to investigate the spin-wave-driven domain wall motion in two typical symmetry-breaking situations: the rotational symmetry broken by the Dzyaloshinskii-Moriya interaction and the translational symmetry broken by magnetic damping. The torque-based microscopic analyses provide compact yet quantitative tools to reinterpret the magnetic texture dynamics induced by spin waves, beyond the conventional framework of global momentum conservation.

Received 23 November 2022
Revised 29 January 2023
Accepted 14 February 2023

DOI:https://doi.org/10.1103/PhysRevB.107.054441

Physics Subject Headings (PhySH)

Domain walls Dzyaloshinskii-Moriya interaction Magnetic texture Magnons Spin current Spin transfer torque Spin waves Spin-orbit torque

Thiele equation

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Hanxu Ai (艾もぐさ寒かん旭あさひ) and Jin Lan (兰金)^*

Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin 300354, China and Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparing Technology, Tianjin University, Tianjin 300354, China

^*Corresponding author: lanjin@tju.edu.cn

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Issue

Vol. 107, Iss. 5 — 1 February 2023

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Images

Figure 1
Schematics of the domain wall dynamics induced by (a) spin waves, (b) the equivalent magnonic torques, and (c) magnonic forces. In (a) and (b), the red arrows depict the domain wall magnetizations, and all magnetizations are united in a magnetic Bloch sphere. For (a) the red circles represent the precessing spin waves, and for (b) the green/orange/purple/blue arrows represent the corresponding magnonic torques. In (c), the arrows depict the magnonic/internal forces (see Appendix pp2 for definitions) in the left/right panels at three selected times. The black dots plot the time evolution of the domain wall in parametric space ${X, Φ ふぁい}$ , and the red dots depict the three observation points.
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Figure 2
Spin-wave-driven domain wall motion under (a) $D \neq 0$ , $α あるふぁ = 0$ and (b) $D = 0$ , $α あるふぁ \neq 0$ . In (a), the upper panel plots the time evolution of domain wall position under a set of different DM strengths $D$ , and the lower panel plots the scaling factor $η いーた$ as function of DM strength. In (b), the upper panel plots the time evolution of domain wall position under a set of magnetic dampings $α あるふぁ$ , the lower panel plots the domain wall velocity $V$ for a relatively long time. For all plots, the dots/solid lines are extracted from micromagnetic simulations based on the original LLG equation (1) and the magnonic torques (11), and the dashed lines are based on Eq. (12). The spin wave is excited at $x_{0} = - 300 nm$ with excitation frequency $f = 10 GHz$ and spin wave density ${ρ ろー}_{0} = 0.02$ .
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Figure 3
Time evolution of (a) domain wall velocity $V$ and (b) angle $Φ ふぁい$ under $D = 0.6 \times 10^{- 3} A$ and $α あるふぁ = 0.05$ . The dots are for wave-based analysis using Eq. (1), the solid lines are for torque-based analysis using Eq. (11), and dashed lines are for force-based analysis using Eq. (12), respectively.
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Figure 4
Transmission probability of the spin wave across the domain wall under different DM strengths. The black/red/blue lines represent different DM strengths, and the gray shaded area denotes the frequency range below the gap.
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Figure 5
Modification of magnetic profile by magnonic DM torque in (a) a uniform domain and (b) a domain wall. The gray solid line is for total magnetization $m^{y}$ extracted from wave-based simulations, and all other lines (dots) are for the static magnetization $m_{0}^{y}$ . The blue dots are from wave-based simulations, the blue solid line is from torque-based simulations, and the red dashed line is from theoretical equations (D3) and (D4). In all simulations and calculations, the DM strength is $D = 0.9 \times 10^{- 3} A$ and the magnetic damping is $α あるふぁ = 0.05$ . The spin wave density is ${ρ ろー}_{0} = 9 \times 10^{- 3}$ at the excitation point $x = 0 nm$ , and all magnetic data are taken after a relaxation time of $t = 3 ns$ .
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