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 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.

💡 Research Summary

In this work the authors demonstrate quantitative imaging of nonlinear spin‑wave propagation in two yttrium‑iron‑garnet (YIG) thin films using a wide‑field quantum diamond microscope (QDM) based on ensembles of nitrogen‑vacancy (NV) centers. The experimental platform consists of a (111)‑oriented high‑purity diamond chip bearing a shallow NV layer (~30 nm below the surface) that is bonded to the magnetic film with a sub‑micron gap (≈860 nm). Two YIG samples are investigated: YIG‑A, a 54 nm sputtered film with relatively high damping, and YIG‑B, a 109 nm liquid‑phase‑epitaxy (LPE) film with lower damping. A coplanar stripline deposited on each film launches surface spin waves when driven by a microwave source; the static magnetic field (B₀ = 25.17 mT) is applied in‑plane along the stripline, ensuring that the excited Damon‑Eshbach modes propagate perpendicular to B₀.

NV centers are optically pumped with a 515 nm laser and their red fluorescence is imaged on an sCMOS camera. By measuring the Rabi oscillation frequency of the NV spin transition (m_s = 0 ↔ −1) at each pixel, the local circularly‑polarized microwave magnetic field B_mw is extracted. Because the NV resonance frequency (≈2.166 GHz) lies on the spin‑wave dispersion curve, the measured B_mw contains contributions from the spin‑wave field B_sw and from the stripline field B_strip. The authors model the measured field as

B_mw(x) = q B_sw² + 2 B_sw B_strip cos