Alex Hamill1, Tao Qu2, Randall H. Victora2, Paul A. Crowell1 
1School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota, United States,
2Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, Minnesota, United States 
**Abstract Body** The FMR magnon population (hereafter defined as the FMR amplitude c0) can become unstable when driven by microwave power Pa greater than a threshold power PS,such that it undergoes three-magnon splitting to two magnons c±k of half the frequency and equal and opposite wavevectors [1]. We employ time-resolved homodyning spectroscopy to examine this instability over five orders of magnitude in microwave power Pa. We observe an additional threshold power Posc, above which the splitting induces oscillations in c0[2]. At
high powers, we find that these oscillations induce 180° phase shifts in FMR. Our model predicts these phase shifts and that, similarly, the half-frequency magnons undergo 90° phase
shifts. Notably, we find that these phase shifts correspond to reversals in the three-magnon scattering direction between splitting and confluence (see Fig. 1a,b). The scattering direction is found to be determined by |Ψ0|, the absolute phase between FMR and its three-magnon scattering term. These reversals generate pronounced oscillations of the FMR amplitude after turning off the microwave excitation (see Fig. 1b,d). We also observe broadening in the frequency spectra of the oscillations (see Fig. 2a,b). From our micromagnetic simulations, we find that this corresponds to higher-order scattering processes that vary with FMR frequency (see Fig. 2c,d). These findings shed light on the relationship between three-magnon splitting and confluence, the role of phase dynamics in magnon scattering, and the higher-order magnon scattering processes at high microwave powers. 
**References** 
[1] H. Suhl, J. Phys. Chem. Solids, Vol. 1, pp. 209-227 (1957)
[2] T. Qu†, A. Hamill†, R. H. Victora, and P. A. Crowell, arXiv:2204.11969 (2022) 
The Minnesota Supercomputing Institute (MSI) provided resources that contributed to the
research results reported within this abstract. The authors acknowledge support by SMART, a
center funded by nCORE, a SRC program sponsored by NIST. The authors also acknowledge
support by DARPA under Grant W911NF-17-1-0100, MINT at Minnesota, and the NSF
XSEDE through Allocation No. TG-ECS200001. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/2cd20e06470fac11a685d745715202a5.png) 
Fig. 1. (a,b) Numerical solutions of the magnon amplitudes c0 and ck during and after microwave excitation. Color-coding corresponds to |Ψ0|. (c,d) Corresponding experimental data of c0, showing the power dependence of the oscillations and scattering reversals. Data is normalized to the turn-on peak at 46 dB. 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/e93ab1523191603144783a3632406752.png) 
Fig. 2. (a,b) Measured frequency spectra of the oscillations, at various powers Pa relative to Posc, for FMR frequencies of 1.5 GHz (left column) and 2.5 GHz (right column). (c,d) the
corresponding simulated magnon amplitudes at powers below and above the onset of broadening, showing the different higher-order scattering processes at 1.5 GHz and 2.5 GHz.

Scattering Reversals and Higher Order Interactions in Three

In magnetic thin films, large excitation amplitudes can lead to the onset of the first order Suhl instability, where the driven uniform mode undergoes three magnon scattering to two modes of half the frequency and equal and opposite wavevectors. Although experimental studies of the steady-state behavior are established, a comprehensive study of the nonequilibrium behavior over a large range of excitation powers is lacking. We have developed an experimental technique for sensitive detection of the time evolution of the FMR amplitude over five orders of magnitude in power, which provides a highly comprehensive understanding of the three-magnon scattering process. Applying this technique to patterned 3μm thick YIG thin films, we observe strong agreement with our results from micromagnetic simulations of the Suhl instability. We have developed a semianalytical model to explain the three magnon scattering process. This model shows quantitative agreement with experiment and simulation, including a predicted additional regime corresponding to power-dependent nonlinear oscillatory behavior on the order of 50 MHz. Additional observed effects will also be discussed. This work was supported by SMART, a center funded by nCORE, a SRC program sponsored by NIST, DARPA under Grant W911NF-17-0100, MINT at Minnesota, and the NSF XSEDE through Allocation No. TG-ECS200001. We acknowledge the use of MSI resources.

![](https://assets.underline.io/uploads/markdown_image/1/image/1206326856094257491a60e9c5fd8367.jpg)

Time-resolved Nonlinear Magnetization Dynamics in YIG Thin Films

Time-resolved Nonlinear Magnetization Dynamics in YIG Thin Films

GOD: Magnetization Dynamics IV

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Scattering Reversals and Higher Order Interactions in Three

Time-resolved Nonlinear Magnetization Dynamics in YIG Thin Films

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