## Introduction

Electron spins associated with nitrogen-vacancy (NV) defects in diamond are magnetic field sensors that provide high spatial resolution and sensitivity at room temperature1,2. They have been used to study nuclear magnetic resonance at the nanoscale3,4, bio-5, paleo-6, and solid-state magnetism7, and electric currents in quantum materials8,9. Most of these applications focus on detecting magnetic fields in the 0–100 megahertz (MHz) frequency range, in which a toolbox of spin-control techniques enables high sensitivity and a tunable detection frequency without requiring a specific electron spin resonance (ESR) frequency1. In contrast, NV-based sensing in the microwave regime [1–100 gigahertz (GHz)] currently relies on tuning the ESR to the frequency of interest using a magnetic bias field10. This bias field changes the properties of e.g., magnetic or superconducting samples under study11,12, for instance by altering their excitation spectrum, which limits its application in materials science. Furthermore, the field must be on the Tesla scale for operation in the 10–100 GHz range13, making the required magnets large and slow to adjust, precluding the small sensor packaging desired for technological applications.

Here, we enable broadband spin-based microwave sensing by interfacing a diamond chip containing a layer of NV sensor spins with a thin-film magnet. The central concept is that the non-linear dynamics of spin waves—the collective spin excitations of the magnetic film14—locally convert a target signal to the NV ESR frequency under the application of a pump field (Fig. 1a, b). We realize a ~1-GHz detection bandwidth at fixed magnetic bias field via four-spin-wave mixing, and microwave detection at multiple GHz above the ESR frequency via difference-frequency generation. The pump-tunable detection frequency enables characterizing the spin-wave band structure despite a multi-GHz detuning and provides insight into the non-linear spin-wave dynamics limiting the conversion process. Furthermore, the converted microwaves are highly coherent, enabling high-fidelity control of the sensor spins via off-resonant drive fields.

## Results

### Sensor platform

Our hybrid diamond-magnet sensor platform consists of an ensemble of near-surface NV spins in a diamond membrane positioned onto a thin film of yttrium iron garnet (YIG)—a magnetic insulator with low spin-wave damping14 (Fig. 1b). A stripline delivers the “two-color” signal and pump microwave fields to the YIG film, in which they excite spin waves at the signal and pump frequencies, fs and fp, respectively. The frequency-converted microwaves at the ESR frequency fNV are detected by measuring the spin-dependent NV photoluminescence under green laser excitation (“Methods” and Fig. 1c). The ESR frequency is fixed by an external magnetic bias field BNV (Fig. 1d).

### Microwave detection via four-spin-wave mixing

Our first detection protocol harnesses degenerate four-spin-wave mixing15,16,17,18,19,20—the magnetic analog of optical four-wave mixing (Fig. 2a). In the quasiparticle picture, this process corresponds to the scattering of two “pump” magnons into a “signal” magnon and an “idler” magnon at frequency $${f}_{{{\mbox{i}}}}=2{f}_{{{\mbox{p}}}}-{f}_{{{\mbox{s}}}}$$. This conversion enables the detection of a microwave signal that is detuned from the ESR frequency, which would be otherwise invisible in the optical response of the NV centers (Fig. 2b). By tuning the frequency of the pump, we enable the detection of signals of specific microwave frequencies (Fig. 2c).

We characterize the bandwidth of the four-wave-mixing detection scheme by measuring the NV photoluminescence contrast as a function of the microwave signal frequency and magnetic bias field. As in Fig. 2b, when the pump field is switched off, we only detect signals resonant with fNV (Fig. 2d). In contrast, when the pump is switched on, a broad band of frequencies becomes detectable (Fig. 2e). The bandwidth Δf of ~1 GHz is limited from below by the ferromagnetic resonance (FMR), the spatially homogenous spin-wave mode below which spin waves cannot be excited in our measurement geometry, and from above by the limited efficiency of our 5-micron-wide stripline to excite high-momentum spin waves. As such, the bandwidth can be extended by using narrower striplines or magnetic coplanar waveguides21.

At 14 dBm signal and pump power, consecutive mixing processes generate higher-order idler modes at discrete and equally spaced frequencies (Fig. 2f). Motivated by the success of their optical counterparts in high-precision spectrometry22, such “spin-wave frequency combs” are of great interest because of potential applications in microwave metrology20,23,24. We use the spin-wave comb to realize sensitivity to multiple microwave frequencies by detecting the n-th order idler frequency,

$${f}_{i}^{(n)}=\left(n+1\right){f}_{{{{{\rm{p}}}}}}-n{f}_{{{{{\rm{s}}}}}}$$
(1)

when it is resonant with the ESR frequency (Fig. 2f, upper inset). An increasing number of idler modes appears with increasing drive power (Supplementary Fig. 3), such that at large powers we resolve up to the n = 10th idler order (Fig. 2f, bottom inset). The shift of the idler frequency is amplified by the integer n over the shift of the signal frequency (Eq. 1), leading to a 1/n decrease in the linewidth of the NV ESR response24 (Fig. 2f) and a correspondingly enhanced ability to resolve closely spaced signal frequencies.

### Coherent spin control via four-spin-wave mixing

In addition to enabling off-resonant quantum sensing, the idlers also provide a resource for off-resonant control of spin- or other quantum systems. The resolving of the NV’s 3-MHz hyperfine splitting in the idler-driven ESR spectrum (Fig. 3a) evidences the high coherence of the microwave field emitted by the idler spin wave, implying that the linewidth is determined by the drive rather than the spin-wave damping24. This allows driving coherent NV spin rotations (Rabi oscillations) by pulsing the pump with varying duration τ (Fig. 3b).

Remarkably, these Rabi oscillations respond to externally applied microwaves that are detuned by hundreds of MHz from the ESR frequency (Fig. 3c). Such magnon-mediated, off-resonant Rabi control is a new instrument in the toolbox of spin-manipulation techniques, providing universal off-resonant quantum control with potential applications in quantum information processing. The idler-driven Rabi frequency exceeds the signal-induced AC Stark shift25 by about an order of magnitude for the same off-resonant signal power (Supplementary Fig. 4). The decrease of the Rabi frequency with increasing detuning δf (Fig. 3c) is the combined result of a reduced spin-wave excitation efficiency at higher frequency, because the stripline is less efficient in exciting spin waves with short wavelengths (Supplementary Note 2), and a reduced spin-wave scattering strength due to the increasing momentum mismatch between signal and pump spin waves17,18,19.

Since the Rabi frequency depends linearly on the idler amplitude11, it provides insight into the magnetization dynamics in the film. As expected, the idler amplitude initially grows with increasing signal and pump power15,20, but then reaches a maximum and starts to decrease (Fig. 3d). We attribute the decrease to Suhl instabilities of the second type16: Both signal and pump modes decay into a pair of high-momentum magnons beyond a certain threshold amplitude, which drains energy from the idler mode. This interpretation is supported by a model of the four-wave interactions between the dominant two idler modes, the signal and pump modes, and the two pairs of high-momentum “Suhl” magnons (Supplementary Figs. 5 and 6). The intermode coupling is induced by exchange and dipolar interactions, as well as crystalline anisotropy, and follows from the leading-order terms in the Holstein-Primakoff expansion17. Based on the interacting eight-mode Hamiltonian we compute the steady-state dynamics of the idler mode as a function of pump and signal power (Fig. 3e, Supplementary Note 4), which qualitatively reproduces the observed power dependence in Fig. 3d.

### Microwave detection via difference-frequency generation

Our second detection protocol relies on difference-frequency generation, which enables down-conversion of GHz signals to MHz frequencies accessible to established quantum sensing techniques1. The difference frequency is generated by the longitudinal component of the magnetization under the driving of two spin waves of different frequencies26 (Fig. 4a, Supplementary Note 5). In contrast to the four-wave mixing protocol, the converted frequency does not have to lie within the spin-wave band. By tuning the ESR frequency into resonance with the difference frequency (Fig. 4b), we detect microwave signals that are detuned by several gigahertz when $${f}_{{{\mbox{p}}}}-{f}_{{{\mbox{s}}}}=\pm {f}_{{{\mbox{NV}}}}$$ (Fig. 4c). Alternatively, AC magnetometry protocols can provide difference-frequency detection with enhanced sensitivity at arbitrary bias fields1. We only observe ESR contrast when both fs and fp are above the FMR (Fig. 4d), confirming that the conversion is mediated by spin waves in the YIG. We anticipate the conversion process can also be applied in other magnetic materials to characterize high-frequency magnetic band structures that would otherwise be out of reach for NV magnetometry (Supplementary Note 6). Similar to Fig. 2e, the conversion is limited by the spin-wave excitation efficiency, which explains the observation of the largest ESR contrast for long-wavelength spin waves (i.e., just above the FMR).

## Discussion

We demonstrated magnon-mediated, spin-based sensing of microwave magnetic fields over a gigahertz bandwidth at fixed magnetic bias field. The frequency of the pump determines the detection frequency, with a detection range that is limited only by the frequencies at which spin waves can be excited efficiently. The coherent nature of the frequency conversion enables coherent manipulation of solid-state spins via off-resonant drive fields, as demonstrated here for spins in diamond. This coherence allows combining with advanced spin-manipulation protocols such as heterodyne or dressed-state sensing27,28,29 to further enhance the detection capabilities, and opens the way for applications in hybrid quantum technologies30. Wide-field readout of NV centers in a larger sensing volume would enhance the microwave sensitivity, which is ultimately limited by thermal spin-wave noise. We envision the detection of free-space microwaves using on-chip microwave-to-spin-wave transducers31 such as stripline resonators, and the characterization of local microwave generators such as spin-torque oscillators by combining with a suitable magnetic material32 and applying a pump field. Imaging of the spatial magnetization dynamics generated by spin-wave mixing using scanning-NV magnetometry could provide insight into the spin-wave dispersion and interactions with nanoscale sensitivity2. The demonstrated hybrid diamond-magnet sensor platform enables broadband microwave characterization without requiring large magnetic bias fields and opens the way for probing high-frequency magnetic spectra of new materials, such as van-der-Waals magnets.

## Methods

### Experimental setup

The NV photoluminescence is read out using a confocal microscope described in ref. 11. The NV-YIG chip and its fabrication were described in ref. 33. It consists of a 2 × 2 × 0.05-mm3 diamond membrane with an estimated near-surface NV density of 103/μm2 placed on top of a 235-nm-thick YIG film grown using liquid phase epitaxy on a 500-μm-thick GGG substrate (Matesy GmbH). The diamond-YIG separation distance is ~2 μm, limited by small particles (such as dust) between the diamond and the YIG surfaces. The signal and pump microwaves are generated by two Rohde & Schwarz microwave sources (SGS100A), combined by a Mini-Circuits power combiner (ZFRSC-123-S+, total loss: ~ −10 dB) and amplified by an AR amplifier (30S1G6, amplification: ~44 dB). All measurements were performed at room temperature.

### NV microwave magnetometry

The four NV-center families are sensitive to microwave magnetic fields at their electron spin resonance (ESR) frequencies, which are determined by the magnetic bias field BNV via the NV spin Hamiltonian $$H=D{S}_{z}^{2}+\gamma {{{{{{\bf{B}}}}}}}_{{{\mbox{NV}}}}\cdot {{{{{\bf{S}}}}}}$$, with D = 2.87 $${{\mbox{GHz}}}$$ the zero-field splitting, γ = 28 $${{\mbox{GHz}}}/{{\mbox{T}}}\,$$ the electron gyromagnetic ratio and $${S}_{i\in \{x,y,z\}}$$ the ith spin-1 Pauli matrix. In this work, we align the field along one of the NV orientations, such that this “on-axis” family has $$|0\rangle \leftrightarrow|\pm 1\rangle$$ ESR frequencies given by $$D\pm \gamma {B}_{{{\mbox{NV}}}}$$ (with $${B}_{{{\mbox{NV}}}}=|{{{{{{\bf{B}}}}}}}_{{{\mbox{NV}}}}|$$). For the other three “off-axis” families, the bias field is equally misaligned by ~71° due to crystal symmetry, leading to the ESR frequency plotted in Fig. 4b (labeled “Off-axis”). The photoluminescence dips were recorded using continuous-wave microwaves and non-resonant optical excitation at 515 nm. For the Rabi oscillations, we first initialize the NV spin in the $$|0\rangle$$-state via a ~1-μs green laser pulse, then we drive the spin using an idler pulse and finally we read out the NV photons in the first 300–400 ns of a second laser pulse.

### Data processing

The data presented in Figs. 2f and 4d are normalized by the median of each row and column (Supplementary Fig. 2).