Fig. 2: Detection and simulation of high-order harmonic magnons.

a ODMR spectrum at different bias field. The ODMR at 1.5 mT (solid purple line) corresponds to the cross-section along the dashed purple line in (b), where higher-order harmonic responses are observed under the bias field, indicating strong nonlinear effects. Dashed gray lines: the center of each harmonic peak, corresponding to integer fractions 1/n of ESR frequency f_ESR = 2870 MHz. The ODMR at 9 mT (solid green line) represents the harmonic responses in the saturation magnetization region, indicating that the nonlinear response does not solely originate from domain walls. The depicted resonance peak splitting arises from the magnetic field-induced Zeeman splitting of the NV center’s ESR frequency. b Map of the ODMR signal vs. driving microwave frequency f_pump and magnetic field. Harmonics signals up to the 25th order are detected, with an enlarged image displayed on the right side. c Micromagnetic simulations of different domain configurations, where “one-step” is a single domain wall, “two-step” is a double domain wall, and “multi-step” is multi-domain (see Fig. S8 for details). The lower panels are the simulated spatial distribution of M_z at 2870 MHz of different domain configurations. All models are excited by microwave field at f_pump = 287 MHz. The upper panel shows the spatial average M_z of each model. d MOKE measurement. Hysteresis loop measured by in-plane MOKE measurement. The green arrow: MOKE image (inset) in the saturated magnetization region. The purple arrow: MOKE image (inset) in the abundant domain textures region.