Figure 3: Non-resonant, field-dependent detection of driven spin-wave excitations.

(a) Measurement sequence. The first π/2 pulse prepares an NV spin superposition, which is input into an echo sequence with two π pulses. Synchronized with this sequence, we apply microwave (MW) driving at frequency f during the central 2τ period of free evolution to excite spin-wave excitations in the disc. We read out the final phase ϕ of the NV spin state by measuring the projection on the x and y axis. (b) Experimentally determined effective magnetic field B_eff at NV_B and NV_A as a function of MW-driving frequency f and external static magnetic field B_ext. B_eff is normalized by the square of the drive field measured on-chip using NV_ref. The dashed line is a numerical calculation of the ferromagnetic resonance (FMR) of the disc. For NV_A, the a.c. Stark effect is visible as an enhanced signal in an ∼300-MHz frequency band between the ESR frequency and the dashed-dotted line over the entire magnetic field range. We use the sign of the Stark effect to determine the sign of B_eff in these measurements. Scale bar, 1 μm. (c) Numerically calculated spatial profile of the time-averaged change in the disc’s longitudinal magnetization ΔM_x relative to the saturation magnetization M_S under spatially uniform driving with a 5 G MW field and the associated stray magnetic field ΔB_∥ in the NV-plane, for two MW frequencies close to the FMR f₁=f_FMR−0.1 GHz and f₂=f_FMR−0.3 GHz. We use an external static field B_ext=450 G, corresponding to the highest field used in the measurements in b, at which we expect the disc magnetization to be the most homogeneous and resemblant of the calculated magnetization. (d) Comparison of measured and calculated FMR lineshapes at B_ext=450 G for NV_B and NV_A. The sign, amplitude and width of the lineshapes accurately match the calculations. The 4% difference in frequency presumably results from a difference in the disc’s saturation magnetization and/or fabrication-related imperfections. Error bars represent ±1 standard deviation determined statistically from typically≳100 repetitions of the same measurement.