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Degenerate and nondegenerate parametric excitation in yttrium iron garnet nanostructures

H. Merbouche, P. Che, T. Srivastava, N. Beaulieu, J. Ben Youssef, M. Muñoz, M. d’Aquino, C. Serpico, G. de Loubens, P. Bortolotti, A. Anane, S.O. Demokritov, and V.E. Demidov

Phys. Rev. Applied 21, 064041 – Published 17 June 2024

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Abstract

We study experimentally the processes of parametric excitation in microscopic magnetically saturated disks of nanometer-thick yttrium iron garnet. We show that, depending on the relative orientation of the parametric pumping field and the static magnetization, excitation of either degenerate or nondegenerate magnon pairs is possible. In the latter case, which is particularly important for applications associated with the realization of computation in the reciprocal space, a single-frequency pumping can generate pairs of magnons whose frequencies correspond to different eigenmodes of the disk. We show that, depending on the size of the disk and the modes involved, the frequency difference in a pair can vary in the range 0.1–0.8 GHz. We demonstrate that in this system, one can easily realize a practically important situation where several magnon pairs share the same mode. We also observe the simultaneous generation of up to six different modes using a fixed-frequency monochromatic pumping. Our experimental findings are supported by numerical calculations that allow us to unambiguously identify the excited modes. Our results open new possibilities for the implementation of reciprocal-space computing.

Received 20 June 2023
Revised 7 February 2024
Accepted 17 May 2024

DOI:https://doi.org/10.1103/PhysRevApplied.21.064041

Physics Subject Headings (PhySH)

Magnetization dynamics Micromagnetism Spin waves

Magnetic thin films

Brillouin scattering & spectroscopy Micromagnetic modeling

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

H. Merbouche ^1,*, P. Che ², T. Srivastava ³, N. Beaulieu ⁴, J. Ben Youssef ⁴, M. Muñoz ⁵, M. d’Aquino ⁶, C. Serpico⁶, G. de Loubens ³, P. Bortolotti ², A. Anane ², S.O. Demokritov ¹, and V.E. Demidov ¹

¹Institute for Applied Physics, University of Muenster, Münster, Germany
²Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, Palaiseau, France
³SPEC, CEA, CNRS, Université Paris-Saclay, Gif-sur-Yvette, France
⁴LabSTICC, UMR 6285 CNRS, Université de Bretagne Occidentale, Brest, France
⁵Instituto de Tecnologías Físicas y de la Información (CSIC), Madrid, Spain
⁶Department of Electrical Engineering and ICT, University of Naples Federico II, Naples, Italy

^*Corresponding author: [email protected]

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Vol. 21, Iss. 6 — June 2024

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Figure 1
(a) Experimental setup. YIG disks with a thickness 52 nm and a diameter of 0.5, 1, and 2 µm are excited by a dynamic field h_rf created with the use of a 4-µm-wide antenna. The static magnetic field H₀ is applied either parallel or transverse to the dynamic field. Insets show electron-microscope images of the disks taken before the antenna was fabricated. (b) Characterization of the eigenmode spectrum of a 0.5-µm disk. The graph shows the intensity of the dynamic magnetization as a function of the excitation frequency under conditions of direct linear excitation (φ = 90°) with P = 0.2 mW at H₀= 20 mT. Arrows mark the frequencies of the detected resonant peaks. Vertical lines mark the calculated frequencies of the eigenmodes. The calculated spatial profiles of the modes are shown close to the corresponding lines. These profiles present the absolute value of the out-of-plane component of the dynamic magnetization.
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Figure 2
(a) Representative BLS spectrum of parametrically excited magnetic oscillations recorded at pumping frequency f_p= 3.28 GHz and pumping power P = 2 mW. (b) BLS spectra measured for pumping frequency f_p ranging from 2.4 to 4.8 GHz combined in a linear-scale color map. Color interpolation is used to improve readability. (c) Power dependences of the intensity of the modes labeled “A,” “B,” and “C” in (b). (d) Temporal dependences of the modes labeled “B” and “D” in (b) measured at P = 10 mW. The data were obtained at H₀= 20 mT and φ = 0° (parallel-pumping geometry) on the D = 0.5 µm disk.
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Figure 3
(a) Representative BLS spectrum of parametrically excited magnetic oscillations recorded at pumping frequency f_p= 3.48 GHz and pumping power P = 5 mW. (b) BLS spectra measured for pumping frequency f_p ranging from 2.8 to 4.8 GHz combined in a linear-scale color map. Color interpolation is used to improve readability. Vertical lines mark the experimentally detected frequencies of the eigenmodes. Labeling of the modes is based on a comparison of measured and calculated frequencies, as discussed in the text. (c) Power dependences of the intensity of the modes labeled “A1” and “A2” in (b). (d) Temporal dependences of the modes labeled “A1,” “A2,” and “B” in (b) measured at P = 10 mW. The data were obtained at H₀= 20 mT and φ = 90° (transverse-pumping geometry) on the D = 0.5 µm disk.
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Figure 4
(a),(b) BLS spectra measured for pumping frequency f_p ranging from 2.8 to 4.8 GHz combined in a linear-scale color map. Color interpolation is used to improve readability. (a) D = 1 µm and (b) D = 2 µm. “A”, “B” and “C” indicate the 3 pairs of modes excited for a pumping frequency f_p of 3.46, 3.92 and 4.46 GHz respectively. Vertical dashed lines in (a) mark the frequencies of the modes common for pairs A, B, and C. (c) BLS spectrum recorded for the 2-µm disk at f_p= 3.48 GHz, as marked by an arrow in (b). The data were obtained at P = 5 mW, H₀= 20 mT, and φ = 90° (transverse-pumping geometry).
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Physical Review Applied

Degenerate and nondegenerate parametric excitation in yttrium iron garnet nanostructures

H. Merbouche, P. Che, T. Srivastava, N. Beaulieu, J. Ben Youssef, M. Muñoz, M. d’Aquino, C. Serpico, G. de Loubens, P. Bortolotti, A. Anane, S.O. Demokritov, and V.E. Demidov

Phys. Rev. Applied 21, 064041 – Published 17 June 2024

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