Nonlocal Stimulation of Three-Magnon Splitting in a Magnetic Vortex

L. Körber, K. Schultheiss, T. Hula, R. Verba, J. Fassbender, A. Kákay, and H. Schultheiss

Phys. Rev. Lett. 125, 207203 – Published 12 November 2020

Abstract

We present a combined numerical, theoretical, and experimental study on stimulated three-magnon splitting in a magnetic disk in the vortex state. Our micromagnetic simulations and Brillouin-light-scattering results confirm that three-magnon splitting can be triggered even below threshold by exciting one of the secondary modes by magnons propagating in a waveguide next to the disk. The experiments show that stimulation is possible over an extended range of excitation powers and a wide range of frequencies around the eigenfrequencies of the secondary modes. Rate-equation calculations predict an instantaneous response to stimulation and the possibility to prematurely trigger three-magnon splitting even above threshold in a sustainable manner. These predictions are confirmed experimentally using time-resolved Brillouin-light-scattering measurements and are in a good qualitative agreement with the theoretical results. We believe that the controllable mechanism of stimulated three-magnon splitting could provide a possibility to utilize magnon-based nonlinear networks as hardware for neuromorphic computing.

Received 27 May 2020
Accepted 5 October 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.207203

Physics Subject Headings (PhySH)

Dipolar interaction Ferromagnetism Magnetic vortices Magnetization dynamics Spin dynamics Spin waves

Nonlinear waves

Brillouin scattering & spectroscopy Micromagnetic modeling

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

L. Körber ^1,2,*, K. Schultheiss ^1,†, T. Hula^1,3, R. Verba⁴, J. Fassbender^1,2, A. Kákay¹, and H. Schultheiss ^1,2

¹Helmholtz-Zentrum Dresden - Rossendorf, Institut für Ionenstrahlphysik und Materialforschung, D-01328 Dresden, Germany
²Fakultät Physik, Technische Universität Dresden, D-01062 Dresden, Germany
³Institut für Physik, Technische Universität Chemnitz, D-09126 Chemnitz, Germany
⁴Institute of Magnetism, Kyiv 03142, Ukraine

^*l.koerber@hzdr.de
^†k.schultheiss@hzdr.de

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Vol. 125, Iss. 20 — 13 November 2020

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Images

Figure 1
(a) Experimental realization (left) and simulation model (right) of the vortex-state permalloy disk and of the longitudinally magnetized $2 μ m$ wide waveguide. The experimental image has been acquired using scanning electron microscopy. An $Ω$ -shaped antenna is used to excite the disk with a rf field $b_{D}$ at frequency $f_{D}$ . Additionally, a strip-line antenna is used to excite magnons in the waveguide with a rf field $b_{WG}$ at frequency $f_{WG}$ . (b) Dispersion of the vortex disk calculated using micromagnetic simulations. Exemplary scattering channels for three different excitation frequencies are marked on the dispersion. The hatched rectangular region represents an approximate frequency and wave-vector interval in which the waveguide can efficiently excite magnons in the disk. (c) Numerically obtained spatial profiles of the magnons taking part in a 3MS channel: the directly excited radial mode with frequency $f_{D}$ and the secondary azimuthal modes with $f_{+}$ and $f_{-}$ .
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Figure 2
Spectra of the vortex disk obtained by micromagnetic simulations and $μ BLS$ experiments for three cases: (a) exciting only the disk below threshold at frequency $f_{D}$ , (b) exciting only the waveguide at frequency $f_{+}$ , and (c) both combined, showing an additional signal at $f_{-}$ . (d) Mode profiles obtained from the simulation in (c).
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Figure 3
(a) BLS spectra of the disk when excited below threshold at frequency $f_{D}$ and the excitation frequency in the waveguide $f_{WG}$ is varied. The response at $f_{-}$ corresponds to the lower duplet, as a result of stimulated 3MS. In (b), the BLS response is extracted by integrating over a frequency interval around the respective frequencies when the disk is excited at $f_{D} = 7.2 GHz$ below threshold and the excitation power in the waveguide is varied at constant frequency $f_{WG} = f_{+} = 4.46 GHz$ . Arrows indicate the corresponding logarithmic intensity axis.
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Figure 4
Temporal evolution of the spin-wave intensities obtained by nonlinear spin-wave (SW) theory and TR $μ BLS$ , respectively. The time frames when the rf fields are turned on are marked by the boxes on top of the axes. In (a) and (b), only the radial mode at $f_{D}$ is excited below threshold. In (c) and (d), an additional rf field is applied at $f_{+}$ in the waveguide, showing a successful stimulation of the mode at $f_{-}$ . Panels (e) and (f) show spontaneous 3MS above threshold, whereas (g) and (h) show a shortening of the parametric time delay by applying a rf pulse at $f_{+}$ in the waveguide. The ratio between the intensity levels of different modes in the experiments deviates from the theoretical calculation, likely due to the spatial dependence of the duplets which form standing waves. Since TR $μ BLS$ measurements are time-consuming they were only performed at one position on the disk. Different scales were used for theory and experiments to highlight the feedback on the directly excited mode from theory, but also to show the small signals of TR $μ BLS$ .
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