Quantitative imaging of nonlinear spin-wave propagation using diamond quantum sensors

Spin waves propagating in magnetic materials exhibit nonlinear behavior at large amplitudes due to the competition between excitation and relaxation, providing an attractive platform for exploring nonlinear wave dynamics. In particular, spin waves with a nonzero wave number that carry momentum undergo nonlinear relaxation and experience wave number modulation in the nonlinear regime. This nonlinearity has been observed experimentally---for example, in S. R. Lake et al., Phys. Rev. Appl. 17, 034010 (2022)---but a quantitative comparison with theory has not yet been carried out. Here, we image nonlinear spin-wave propagation in two yttrium iron garnet thin films with distinct spin-wave decay rates using a wide-field quantum diamond microscope. We obtain quantitative distributions of spin-wave amplitude and phase as a function of the excitation microwave strength. As a result, we observe a threshold in the spin-wave amplitude beyond which nonlinear effects become evident and confirm that this threshold is consistent with theoretical predictions based on four-magnon scattering for both samples. Moreover, as the amplitude of the spin waves increases, we observe modulation of the wave number across the field of view. We attribute this modulation primarily to a reduction in the saturation magnetization caused by incoherent spin waves generated by multimagnon scattering. Our quantitative measurements provide a pathway for visualizing nonlinear spin-wave dynamics and are crucial for deepening our understanding of the underlying mechanisms.