Fig. 3. NV detection of spinwave instability in the single-magnon NV relaxation regime.

a Microwave absorption during a static magnetic field sweep at 2.2 GHz and +3 dBm microwave power shows a uniform mode FMR absorption signal at 94 Gauss and an absorption shoulder at lower magnetic field, consistent with the model in Fig. 2. b Simultaneously collected NV relaxation is strongest at the lowest field where the instability is driven and is minimal at the uniform mode FMR condition. c Out-of-equilibrium magnons driven by the instability (black) scatter off thermally occupied magnons (red), resulting in product magnons, some of which may be NV-resonant (yellow). An increase in population of NV-resonant magnons increases the dipole field noise at NV frequencies, leading to a change in NV PL. d The four-magnon scattering process redistributes excess magnon population from the driven mode to higher frequencies. e Increasing microwave power shifts the instability shoulder detected by microwave absorption toward lower magnetic field. Curves are vertically shifted from one another for readability. f NV relaxation signal follows the instability shoulder, shifting toward lower magnetic field with increasing microwave power. g Calculated spinwave manifold (gray) and NV center frequency range (green) at 70 Gauss gives the wavevector of the 2.2 GHz instability-driven magnon (2.8 × 10⁶ m⁻¹, black circle) and the range of wavevectors (2.4 × 10⁶ m⁻¹ to 4.2 × 10⁶ m⁻¹, blue region) responsible for NV relaxation. h Calculated wavevector of 2.2 GHz instability-driven spinwave and NV-resonant spinwave wavevector range as a function of magnetic field.