Alex Hamill¹, Tao Qu², Randall H. Victora², Paul A. Crowell^1
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 P_S,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 P_a. We observe an additional threshold power P_osc, above which the splitting induces oscillations in c₀2. 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.

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.

Fig. 2. (a,b) Measured frequency spectra of the oscillations, at various powers P_a relative to P_osc, 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.