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### Ferromagnetic resonance assisted NV spin rotation

We first discuss the measurement system and device structure as illustrated in Fig. 1a. A 10-μm-wide and 50-μm-long YIG/Pt strip was fabricated by standard photolithography and ion mill etching processes from a Gd_{3}Ga_{5}O_{12} (substrate)/YIG (20 nm)/Pt (10 nm) film. A diamond nanobeam^{27} containing individually addressable NV centers was transferred onto the surface of the YIG/Pt strip to establish nanoscale proximity between NV spins and the studied samples (see Supplementary Note 1). The diamond nanobeams used in this work have a shape of an equilateral triangular prism with approximate dimensions of 500 nm × 500 m × 10 μm, which are fabricated following a top-down etching and an angle-etching procedure^{27}. A 500-nm-thick on-chip Au stripline was fabricated next to the YIG/Pt strip, delivering microwave currents to manipulate the NV spin state and to excite ferromagnetic resonance (FMR) of the YIG strip. We employed a scanning confocal microscope to optically locate NV centers. A photoluminescence (PL) image shown in Fig. 1b provides an overview of the device structure, where an NV center (NV_{1}) is positioned on top of the YIG/Pt strip, demonstrating the single-spin addressability. We first performed optically detected magnetic resonance (ODMR) measurements to examine the NV electron spin resonance (ESR) and the FMR of the patterned YIG strip. A green laser was applied to constantly initialize the NV spin to the *m*_{s} = 0 state, and the emitted PL was monitored via a single-photon detector. An external magnetic field *B*_{ext} was applied along the NV-axis, with an angle of 60° relative to the z-axis as illustrated in Fig. 1a. Figure 1c shows the normalized PL intensity as a function of the microwave frequency (f) and the external magnetic field *B*_{ext}. The straight line denoted by (f_ -) results from the expected decrease in NV fluorescence of NV ESR transition in the electronic ground state: (f_ -) = 2.87 (- gamma B_{{mathrm{ext}}}/2{uppi}), where (gamma) is the gyromagnetic ratio. The other two straight lines denoted by (f_{{mathrm{e}} pm }) result from the NV ESR at the optically excited state: (f!_{{mathrm{e}} pm }) = 1.42 ± (gamma B_{{mathrm{ext}}}/2{uppi}). The NV fluorescence also decreases when (f) matches the FMR frequency (f_{{mathrm{FMR}}}) of the YIG strip as shown by the curved dash line below (f_{{mathrm{e}} + }). This NV-based off-resonant detection of spin wave modes in a proximal ferromagnet is attributed to multi-magnon scattering processes, giving rise to enhanced magnon densities at the NV ESR frequencies^{28,29,30}.

Next we performed NV Rabi oscillation measurements to characterize the coherent spin rotation rate (f_{{mathrm{Rabi}}}) of NV_{1}. When a microwave magnetic field with NV ESR frequencies (f_ pm) is applied at the NV site, the NV spin will periodically oscillate between two different states, i.e. *m*_{s} = 0 and *m*_{s} = 1 or *m*_{s} = 0 and *m*_{s} = −1, in the rotation frame, which is referred to as Rabi oscillations^{31}. Here, (f_ pm) characterizes NV ESR frequencies corresponding to the spin transition between *m*_{s} = 0 and *m*_{s} = ±1 states. The coherent spin rotation rate (f_{{mathrm{Rabi}}}) is proportional to the amplitude of the local microwave field that is perpendicular to the NV-axis^{30,32}. Figure 1d, e show the measured PL intensity of NV_{1} as a function of the microwave duration time *t* at two different NV ESR frequencies. When (f_ -) is detuned from (f_{{mathrm{FMR}}}) by 50 MHz, the measured PL spectrum slowly oscillates with a characteristic (f_{{mathrm{Rabi}}}) of 0.8 MHz, from which the local microwave field (h_{{mathrm{rf}}}) generated by the Au stripline is estimated to be 0.5 Oe. Notably, when (f_ – = f_{{mathrm{FMR}}}), the NV PL spectrum exhibits a significantly accelerated oscillation behavior with an enhancement of (f_{{mathrm{Rabi}}}) from 0.8 to 9 MHz. This one order of magnitude enhancement of the NV coherent spin rotation rate results from a larger oscillating stray field (h_{{mathrm{FMR}}}) generated by the quasi-uniform precession of the YIG magnetization, which amplifies the effective microwave magnetic field experienced by the NV spin (see Supplementary Note 2).

### Electrical control of NV spin rotation

To achieve electrical control of the coherent NV spin rotation rate, we further employed the SOT generated by the Pt layer to vary the amplitude of the oscillating stray field (h_{{mathrm{FMR}}}) generated by the resonant YIG strip. Figure 2a illustrates the optical, microwave, and electrical measurement sequence. A 3-μs-long green laser pulse was first applied to initialize the NV spin to the *m*_{s} = 0 state. A microwave pulse at a frequency (f_ -) was applied to induce an *m*_{s} = 0 ↔ −1 transition. To minimize the current-induced Joule heat, an electric current sequence synchronized with the microwave pulse was applied in the Pt layer. Last, a second green laser pulse was applied to measure the spin-dependent PL of the NV center and re-initialize the NV spin for the next measurement sequence. The time duration of the microwave (electrical) pulses systematically varies from zero to a few hundred nanoseconds in order to detect a time-dependent variation of the NV PL intensity. Figure 2b shows the Rabi oscillation spectrum of NV_{1} measured at three different electric current densities *J*_{c} when (f_ – = f_{{mathrm{FMR}}}). Without applying an electric current, (f_{{mathrm{Rabi}}}) is measured to be 9 MHz, exhibiting a significant enhancement in comparison to the off-FMR condition as discussed above. When *J*_{c} = −1 × 10^{11} A/m^{2}, we observed a faster oscillation behavior of the measured PL spectrum with an enhanced (f_{{mathrm{Rabi}}}) = 11 MHz. When *J*_{c} = 1 × 10^{11} A/m^{2}, the NV spin exhibits a slower oscillation behavior with a reduced (f_{{mathrm{Rabi}}}) of 7 MHz. To further illustrate the electrical tuning and amplification effect at the YIG FMR condition, Fig. 2c plots the normalized NV Rabi frequency ((f_{{mathrm{Rabi}}}/sqrt P)) as a function of (f_ – – f_{{mathrm{FMR}}}) when *J*_{c} = 0 and ±1 × 10^{11} A/m^{2}. Note that the variation of the input microwave power *P* needs to be normalized to characterize the driving efficiency of NV spin rotation (see Supplementary Note 3). Figure 2d plots (f_{{mathrm{Rabi}}}/sqrt P) measured at (f_ – = f_{{mathrm{FMR}}}) as a function of the electric current density. In general, (f_{{mathrm{Rabi}}}/sqrt P) follows a quasi-linear dependence on *J*_{c} and exhibits ~±23% variation when *J*_{c} = ±1 × 10^{11} A/m^{2}.

The electrically tunable (f_{{mathrm{Rabi}}}) results from the SOT-induced variation of the local microwave magnetic field at the NV site. When an electric current flows through the Pt layer, a spin current *J*_{s} is generated by the spin Hall effect^{33}. Due to the interfacial scattering process, *J*_{s} will transport across the YIG/Pt interface and thereby exerts a damping-like spin-transfer torque (tau {boldsymbol{ = m}} times ({boldsymbol{m}} times {boldsymbol{s}})) on the YIG magnetization. Here, ({boldsymbol{m}}) is the magnetization of the YIG pattern and ({boldsymbol{s}}) is the spin polarization of the injected spin currents. Depending on the polarity of the electric current, the magnitude of ** τ** effectively increases or decreases the precessional cone angle ({Theta}) of the YIG magnetization, leading to a variation of the amplitude of the oscillating stray field (h_{{mathrm{FMR}}}) as follows: (h_{{mathrm{FMR}}})(propto)(M_{mathrm{s}}) sin({Theta}). According to the SOT model, the electric current density dependence of ({Theta}) is given by

^{24,25}:

$$f_{{mathrm{Rabi}}}/sqrt P propto {Theta} = frac{{h_{{mathrm{rf}}}}}{{{Delta} H_0 + frac{{2pi f_{{mathrm{FMR}}}}}{gamma }(alpha + frac{{{mathrm{sin}},varphi }}{{left( {B_{{mathrm{ext}}} ,+, 2pi M_{{mathrm{eff}}}} right)mu _0M_{mathrm{s}}t_{{mathrm{YIG}}}}}frac{{kappa theta _{{mathrm{SH}}}hbar J_{mathrm{c}}}}{{2e}})}}$$

(1)

where Δ*H*_{0} is the film inhomogeneity contribution to the FMR linewidth, μ_{0} is the free-space permeability, (hbar) is the reduced Planck constant, (alpha), (M_{{mathrm{eff}}}), (M_{mathrm{s}}), and (t_{{mathrm{YIG}}}) correspond to the intrinsic magnetic damping, effective demagnetizing field, saturation magnetization, and thickness of the YIG strip, respectively. (varphi) characterizes the angle between the in-plane projection of the YIG magnetization and the applied electric current, (kappa) characterizes the spin transport efficiency at the YIG/Pt interface^{25}, and (theta _{{mathrm{SH}}}) is the spin Hall angle of the Pt layer. Taking (theta _{{mathrm{SH}}}) = 0.07^{33}, (kappa) = 0.25 with other known material parameters (({Delta} H_0) = 6.3 Oe, (alpha) = 0.001, and *M*_{s} = (M_{{mathrm{eff}}}) = 1.31 × 10^{5} A/m), the blue curve in Fig. 2d plots the current density dependence of (f_{{mathrm{Rabi}}}/sqrt P) predicted by the SOT-model, which is in excellent agreement with our experimental results.

### Control of NV spin rotation by propagating spin wave modes

So far, we have demonstrated the electrical control of coherent spin rotation of an NV single spin by the quasi-FMR spin wave mode of a proximal ferromagnet. Next, we further extend the measurement platform to a more general scenario, where propagating spin waves with specific wavevectors and group velocities are involved. Figure 3a shows the schematic of the device structure, where an Au coplanar waveguide (CPW) and an insulating SiO_{x} spacer are fabricated on a patterned 80-μm-wide and 300-μm-long YIG (100 nm)/Pt (10 nm) waveguide. The width of the signal and ground lines of the CPW and the center-to-center separation between them are 1.5 and 3.15 μm, respectively, and the long-axis of the CPW is perpendicular to the YIG waveguide as shown by the scanning electron microscope image of Fig. 3b. A diamond nanobeam containing an individual NV center (NV_{2}) was transferred on top of the Pt layer with a distance of ~5.5 μm to the center of signal line. An external magnetic field *B*_{ext} was applied along the long-axis of the CPW to excite the Damon-Eschbach surface spin wave mode^{34} at the YIG/Pt interface. The propagating nature of the excited spin wave has been experimentally confirmed by the measurements of microwave transmission between the two CPWs (see Supplementary Note 4). Figure 3c plots the characteristic wavevector spectrum. The well-defined excitation peaks are determined by the spatial distribution of the microwave fields generated by the CPW (see Supplementary Note 5)^{35}. Figure 3d shows the ODMR map measured by the NV spin sensor, where up to four propagating surface spin wave modes with distinct wavevectors: *k*_{1}, *k*_{2}, *k*_{3}, and *k*_{4} emerge. The field dispersion curves of these spin wave modes follow the theoretical prediction as shown by the white dash lines (see Supplementary Note 5) and cross with the NV ESR frequency (f_ -) between 2.1 and 2.6 GHz.

To illustrate the amplification effect of the propagating spin waves on the NV spin rotation rate, the red curve in Fig. 4a shows (f_{{mathrm{Rabi}}}/sqrt P) measured as a function of (f_ -). Remarkably, (f_{{mathrm{Rabi}}}/sqrt P) reaches the peak values of 15531, 16509, 5774, and 1977 MHz/(sqrt {{mathrm{mW}}}) when (f_ -) meets the resonant condition of the *k*_{1}, *k*_{2}, *k*_{3}, and *k*_{4} spin wave modes, respectively. As a comparison, the gray curve shows (f_{{mathrm{Rabi}}}/sqrt P) measured in the high magnetic field regime where (f_ -) stays far away from the resonant frequencies of the series of spin wave modes as illustrated in the inset of Fig. 4a. At the off-resonant condition, (f_{{mathrm{Rabi}}}/sqrt P) follows an average value of 120 MHz/(sqrt {{mathrm{mW}}}). The enhancement ratio of (f_{{mathrm{Rabi}}}/sqrt P) reaches 129, 138, 48, and 17 at the resonant condition of *k*_{1}, *k*_{2}, *k*_{3}, and *k*_{4} spin wave modes, respectively, in quantitative agreement with the theoretical calculations^{36} (see Supplementary Note 2). We notice that the enhancement of (f_{{mathrm{Rabi}}}/sqrt P) decreases with increasing wavevector, which is attributable to a reduced microwave excitation efficiency of the higher order propagating spin wave modes^{37}. Similar to the quasi-FMR spin wave mode, we also employ spin currents generated by the Pt layer as a tuning knob to electrically control the NV spin rotation rate. Figure 4b plots the variation of (f_{{mathrm{Rabi}}}/sqrt P) as a function of *J*_{c} at the resonant condition of the *k*_{1} and *k*_{2} spin wave modes. The normalized NV Rabi frequencies exhibit a systematic variation on the magnitude of *J*_{c}, in agreement with the SOT model predicted by Eq. (1). The reduced electrical tunability of NV spin rotation rate results from a much larger thickness of the YIG film as well as the higher resonant frequencies and wave vector of the propagating spin wave modes^{38}. In addition to the surface spin wave modes, we also observed the similar behaviors for back volume spin wave modes when the external magnetic field is parallel to the short-axis of the CPWs, confirming the universality of the coupling between NV spins and the propagating magnons (see Supplementary Note 6).

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