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

Abstract

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 non-zero wavenumber that carry momentum undergo nonlinear relaxation and experience wavenumber 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 wavenumber across the field of view. We attribute this modulation primarily to a reduction in the saturation magnetization caused by incoherent spin waves generated by multi-magnon scattering. Our quantitative measurements provide a pathway for visualizing nonlinear spin-wave dynamics and are crucial for deepening our understanding of the underlying mechanisms.

Figures (6)

• Figure 1: (a) Schematic of the experiment. (b) Dispersion relation of the surface spin waves for YIG-A at an external magnetic field $B_{0} = 25.17 \, \mathrm{mT}$. The horizontal dashed line corresponds to the resonance frequency of the NV spin. (c) Two-dimensional image of the microwave amplitude at an external magnetic field $B_{0} = 25.17 \, \mathrm{mT}$ and input microwave power $P_{\mathrm{mw}} = 11 \, \mathrm{dBm}$ for YIG-A. (d) One-dimensional microwave amplitude distribution $B_{\mathrm{mw}}(x)$ for the data in (c).
• Figure 2: (a) One-dimensional microwave amplitude distribution $B_{\mathrm{mw}}(x)$ obtained at five different input microwave powers from $P_{\mathrm{mw}} = 11 \, \mathrm{dBm}$ to $25 \, \mathrm{dBm}$ for YIG-A. The triangular markers with error bars represent experimental data, and the solid black lines correspond to the fitting results. (b) Comparison of $B_{\mathrm{mw}}(x)$ for data between large input microwave power ($P_{\mathrm{mw}} = 25 \, \mathrm{dBm}$) and small input microwave power ($P_{\mathrm{mw}} = 11 \, \mathrm{dBm}$) for YIG-A. (c) Microwave amplitude and (d) Wavenumber distribution from the spin waves for each input microwave power calculated from the fitting results for YIG-A.
• Figure 3: (a) Calculated spin-wave amplitude distribution $m_{x}(x)$ for each input microwave power for YIG-A. (b) Heatmap of the spin-wave amplitude distribution as a function of the input microwave amplitude. (c)(d) Dependence of the spin-wave amplitude on input microwave amplitude (c) at $x = 4 \, \mathrm{\mu m}$ and (d) at $x = 13 \, \mathrm{\mu m}$.
• Figure 4: (a)(b) Schematic of the reduction of the static magnetization along the $y$-axis, (a) considering contributions from all spin waves. (b) considering only contributions from excited coherent spin waves. (c) Static magnetization distribution obtained by converting the wavenumber distribution for YIG-A. (d) Estimation of the static magnetization distribution considering only contributions from the excited coherent spin waves for YIG-A.
• Figure 5: (a) Input microwave power dependence of the one-dimensional microwave amplitude distribution $B_{\mathrm{mw}}(x)$ obtained for YIG-B. The triangular markers with error bars represent experimental data, and the solid black lines correspond to the fitting results. (b) Comparison of $B_{\mathrm{mw}}(x)$ for data with large input microwave power ($P_{\mathrm{mw}} = 22 \, \mathrm{dBm}$) and data with small input microwave power ($P_{\mathrm{mw}} = 6 \, \mathrm{dBm}$) for YIG-B. (c) Microwave amplitude and (d) Wavenumber distribution from the spin waves for each input microwave power calculated from the fitting results for YIG-B.