Long-range spin wave imaging with nitrogen vacancy centers and time resolved magneto-optical measurements Open Access

Spin waves represent collective excitations of the spins in a magnetic material.^1–3 Their quanta are referred to as magnons. In insulating magnetic materials, these quasiparticles carry spin angular momentum and propagate through the material’s magnetic lattice, while avoiding heating associated with charge currents. Their unique properties, including long coherence times and low dissipation,^4–8 as well as frequencies in the giga- to terahertz regime and wavelengths as small as several nanometers,^9–11 render spin waves promising candidates for various applications, such as interference-based, ultrafast, nanoscale magnonic logic circuits, and miniaturized device technologies,^6,8,12–17 particularly in the field of spintronics.^12,18–20

Imaging spin waves with high spatial and temporal resolution is essential for exploiting their potential in technological advancements and understanding their intricate dynamics. Traditional imaging techniques, such as time-resolved magneto-optical Kerr effect (TR-MOKE) microscopy,^21–26 Brillouin light scattering,^27,28 and transmission x-ray microscopy,^29,30 have provided valuable insights into spin wave behavior. However, these methods often have limitations in terms of spatial resolution and sensitivity, particularly when studying spin waves in nanoscale systems or beneath opaque materials, or they need large and expensive facilities for their implementation, as in the case of x-ray microscopy.

In recent years, the emergence of nitrogen-vacancy (NV) centers in diamond as sensitive magnetic field sensors has opened new avenues for spin wave imaging.^31–34 NV centers are point-like defects in the diamond lattice, consisting of a substitutional nitrogen atom adjacent to a vacancy. They exhibit remarkable properties, including high sensitivity to static and fluctuating magnetic fields,^35–38 nanoscale spatial resolution,^39,40 even below opaque materials,⁴¹ and optical addressability.⁴² By using an ensemble of spins instead of a single NV center, the sensitivity can be further enhanced by a scaling of $N$⁠, where N is the number of NV centers.³² However, this enhancement comes at the cost of reduced contrast, which can counteract the improvement in sensitivity to some extent.

In this work, we discuss the use of an ensemble of shallowly implanted NV centers to measure spin waves in a magnetic thin film, in this case the low damping ferrimagnetic insulator yttrium iron garnet (YIG),^7,9 following the seminal work reported by Refs. 40 and 43. We demonstrate how the contrast in the imaged spin wave amplitude can be enhanced, allowing us to image spin waves over a long propagation distance. Furthermore, we phenomenologically model these measurements to explain the observed features in the NV spin wave images. By comparing the spin wave measurements obtained through NV center detection to spin wave imaging acquired with conventional TR-MOKE measurements, we discuss the advantages and limitations of utilizing NV centers for spin wave imaging, as well as the potential of integrating NV center measurements with TR-MOKE imaging into a unified setup.

We excite spin waves in a 200 nm thick YIG film grown by liquid phase epitaxy on a gadolinium gallium garnet substrate by a microwave current sent through a stripline (S1) fabricated onto the YIG surface. The diamond chip is placed on the YIG sample with the NV layer facing toward the magnetic surface, as shown in Fig. 1(a). Additional information on the diamond chip and the sample can be found in  Appendix A. As the spin waves propagate rightward (leftward), they generate a circularly polarized field with handedness that drives the ω₋(ω₊) electron spin resonance (ESR) transition of the NVs, resulting in a spin-dependent photoluminescence (PL) signal.^31,40,44 In Fig. 1(b), the NV photoluminescence signal, obtained via lock-in detection and measured ∼10 µm away from the center of S1, is shown in the dependence of the external magnetic field B_ext and the microwave current frequency. The NV setup is described in detail in  Appendix B. Here, B_ext is applied along S1 at an angle of ϕ = 35° relative to the sample plane, aligning it with one of the four possible orientations of the NV axes. The peaks in the PL signal belong to the ESR transitions in the ground (ω_±, ω_⊥) and excited states (ω_ex), where only the PL signal of NV centers aligned with B_ext results in a linear dependence on B_ext. As the NVs are not only driven by the microwave field of S1 but also by the spin wave stray field B_sw, the ω₋ transitions are enhanced for frequencies above the ferromagnetic resonance (FMR) limit. Due to the handedness of the circularly polarized spin wave stray field, the transitions involving ω₋ (corresponding to spin waves with counterclockwise polarization) are preferentially enhanced when the excitation frequency exceeds the ferromagnetic resonance (FMR) frequency. This occurs because the circular polarization of the stray field aligns with the ω₋ transitions, leading to a stronger coupling in this frequency range.

The optically detected magnetic resonance (ODMR) spectrum for this orientation of the external magnetic is shown in Fig. 2(b). By fitting the PL signal with eight Lorentzian functions, we obtain the resonance frequencies for each NV family. Using these values, we calculate the measured parallel $B‖i,m$ and perpendicular $B⊥i,m$ projections of the external magnetic field along each NV axis using Eqs. (C1) and (C2) in  Appendix C. The magnitude of the external field vector is then obtained by $Bmag,i=B‖i,m2+B⊥i,m2$⁠. By averaging these values, we find B_mag = (14.81 ± 0.02) mT.

In addition to the external field B_ext, we then apply a DC current of I_DC = 80 mA through S2, which generates a magnetic DC-field that depends on the NV–S2 distance z₀. The total magnetic field sensed by the NV centers is B_tot = B_ext + B_DC, leading to spatially dependent shifts in the ODMR frequencies. By scanning the sample along the x-axis, we detect and fit the ODMR spectrum at each position x, as shown in Fig. 2(c), where the center of S2 is located at x ≈ 40 µm. Directly above S2, the AC field is strongest, resulting in an enhanced contrast in the ODMR spectrum. From the fits of the measured ODMR spectrum at each position x, we calculate the projections of the total field on the NV axes. The angles θ(x) and ϕ(x) are calculated by minimizing the error between the measured total field amplitudes and the reconstructed total field amplitudes. Thereby, we gain the total field vectors B_tot(x).

The position dependent magnetic DC field is finally obtained by B_DC(x) = B_tot(x) − B_ext. In Fig. 2(d), the x-, y-, and z-components of the obtained DC magnetic field (blue, gray, and red dots) are plotted against the coordinate x. The y-component (gray dots) shows an offset y_off = (0.25 ± 0.01) mT. The green dots show the y-component, when this offset was subtracted. It is possible that the magnet generating the external field has drifted slightly over time, resulting in this field offset. The deviation of B_y from zero in the vicinity of the edges of S2 results from the error of the fitted resonance frequencies in this region. To determine z₀, we subtract the offset from the y-component of the DC field and fit the DC-field components using Eq. (D3) from the supplements. This yields an NV–S2 distance of z₀ = (1.4 ± 0.1) µm. Additional fitting parameters are listed in  Appendix C.

To obtain the phase sensitivity to image individual wavefronts of the spin waves, a second perpendicular reference stripline, S2, isolated from S1 by an insulating SiO₂ layer, is used, as shown in Fig. 1(a). A microwave current that generates an Oersted field B_oe oscillating at the same frequency as B_sw is sent through S2. The superposition of B_oe with the spin wave stray field B_sw results in a standing wave pattern in the total magnetic field that drives the NV ESR with a spatial periodicity equal to the spin wave wavelength.³¹ In Fig. 3(a), the PL signal for a spatial scan over the sample is shown. The x-axis, aligned with S1, is located ∼10 µm away from the center of S1. Furthermore, we scanned over S2, which is aligned with the y-axis, with its center located at x = 40 µm. We find an enhanced contrast in the imaged spin wave amplitude directly above S2. In addition, we observe a 180° phase shift of the wavefronts at the edges of S2 and a light bending of the wavefronts toward the center of S2.

In the following, we compare our NV measurements to TR-MOKE measurements in the Damon–Eshbach (DE) configuration,⁴⁵ where the external field is applied in the YIG thin film plane along S1. TR-MOKE measurements involve synchronizing the rf excitation and optical probing pulses. A fixed phase relationship between excitation and probing is established to capture a stationary rastered image of the dynamic out-of-plane component. To achieve this synchronization, typically a pulsed Ti:Sa-laser with a repetition rate f_rep = 80 MHz is employed, while the excitation frequency f_ex of the spin waves fulfills f_ex = n · f_rep, with n being an integer. However, for a direct comparison between NV and TR-MOKE imaging, this frequency limitation presents a disadvantage. NV centers permit the detection of spin waves within a narrow frequency range, limiting the number of comparative images that can be captured. To overcome this constraint in TR-MOKE, we employ super-Nyquist sampling MOKE.⁴⁶ In that case, we can tune the rf excitation to any intermediate frequency f_ex = n · f_rep + ɛ, where ɛ is a rational number. Demodulating the Kerr signal at the frequency ɛ enables direct extraction of the real and imaginary components of the magnetic rf-susceptibility, thereby providing phase-resolved measurements of the spin precession.⁴⁶ See  Appendix B for further information concerning the MOKE setup. The lock-in detected Kerr signal S_Kerr is then normalized to the topographic signal S_Topo to gain an enhanced contrast in the measured spin wavefronts. Figure 3(c) shows a TR-MOKE measurement of propagating spin waves. As it is not possible to image spin waves propagating beneath S2 with TR-MOKE, the measurement is taken far away from S2. In  Appendix F, we additionally show spin wave measurements with different wavelengths.

To extract the spin wave dispersion from both measurement techniques, we adjust the external static magnetic field B_ext such that the spin wave frequency coincides with the ω₋ NV ESR frequencies. The mathematical equations to calculate the dispersion are given in  Appendix E. This allows us to probe spin waves with varying wavelength, detectable by both measurement techniques. In the NV measurements, the field is applied along S1 and one of the NV quantization axes. The NV measurements were only taken above 23 mT because the external magnetic field was applied using a permanent magnet mounted on a linear translation stage. Due to the limited movement range of the stage, fields below 23 mT could not be achieved without employing a different magnet setup. Given that the external field is always less than 30 mT, significantly smaller than the saturation magnetization of YIG μ₀M_S ≈ 185 mT, the static magnetization of the YIG film tilts only slightly out of plane, at an angle B sin(ϕ)/(μ₀M_S) ≤ 5.3°.³¹ Hence, a direct comparison between the NV measurements and the in-plane MOKE measurements is feasible. In addition, in  Appendix G, we demonstrate that within this range of magnetic fields, MOKE measurements in the DE configuration and with the field applied along the NV axis yield consistent wavelengths within the error margin. To facilitate a direct comparison of the measured wavelengths, we transpose the in-plane fields of the TR-MOKE measurements into the direction of the NV center axis. In Fig. 4, the theoretical dispersion curve (red line), alongside the fitted wavelength of the NV measurement (blue dots) and the MOKE measurements (green dots), is shown, which are in good agreement with each other.  Appendix H provides information about the fit model. This consistency demonstrates the reliability and equivalence of the two measurement techniques.

In conclusion, the utilization of NV centers presents several advantages in the measurement of spin waves. Their high resolution capabilities can extend beyond the diffraction limit,^{37,39,47–52} potentially enabling more precise characterization of spin wave phenomena. Moreover, their ability to measure through opaque materials offers unique opportunities for non-invasive investigations.^41,53 In addition, NV centers exhibit remarkable sensitivity to magnetic fields,^37,54,55 enhancing their utility in detecting subtle magnetic variations. However, it is worth noting some limitations of NV centers, including the lack of time resolution and the requirement of a standing wave for effectively imaging wavefronts. In addition, NV centers are limited to probing only spin waves at the NV ESR frequencies. In comparison, Kerr microscopy offers high time resolution and the flexibility to probe a wide range of frequencies. However, TR-MOKE cannot image spin waves through opaque materials thicker than the skin depth, and the spatial resolution is ultimately limited by diffraction. To overcome these limitations and harness the complementary strengths of both techniques, we propose a combined approach. By integrating NV center measurements with Kerr microscopy, one can benefit from high-resolution imaging, non-invasive probing through opaque materials, high sensitivity to magnetic fields, high time resolution, and flexibility in probing frequencies. This integrated approach promises to advance the capability to probe spin wave dynamics and enable new insights into the field.

This work was supported by the Bayerisches Staatsministerium für Wissenschaft und Kunst through project IQ-Sense via the Munich Quantum Valley (MQV) and by the DFG via the Munich Center for Quantum Science and Technology (MCQST) under Germany’s Excellence Strategy EXC-2111 (Project No. 390814868).

The authors have no conflicts to disclose.

Carolina Lüthi: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Lukas Colombo: Validation (equal); Writing – review & editing (equal). Franz Vilsmeier: Validation (equal); Writing – review & editing (equal). Christian Back: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

We use a type IIa single-crystal diamond of size 0.5 mm × 0.5 mm × 100 µm grown by chemical vapor deposition, with nitrogen content $<$1 ppm, surface roughness $<$2 nm Ra, and (100)-orientation (Applied Diamond). It was implanted with¹⁵ N⁺ ions at an energy of 4 keV, a dose of 1.2 × 10¹³ ions /cm², and a tilt angle of 7° (performed by CuttingEdge Ions), resulting in an implantation depth of 6 nm. Following this, it underwent annealing in a vacuum environment of ∼10⁻⁶ mbar. The annealing process involved a 45-min ramp to 900 °C, followed by 3 h at 900 ± 10 °C and a 2 h ramp to room temperature. To remove the graphitic layer that formed during the annealing, it was acid cleaned for 4 h by a boiling three-acid mix consisting of 3 ml sulfuric acid (H₂SO₄), 3 ml nitric acid (HNO₃), and 3 ml perchloric acid (HClO₄). After thoroughly cleaning both the YIG substrate and the diamond membrane in isopropanol and acetone using an ultrasonic bath, the diamond membrane was carefully placed on the YIG sample using tweezers. To ensure proper alignment of the NV center orientation, which lies in the plane parallel to the sides of the diamond, the placement process was conducted under a microscope. A small droplet of isopropanol was applied to the YIG surface to aid adhesion. The diamond membrane was gently positioned on the droplet and softly pressed onto the surface with tweezers to ensure close contact. The tweezers were released once the isopropanol had fully evaporated, as observed through the microscope. This evaporation step improved the adhesion between the diamond membrane and the YIG substrate, ensuring a stable placement.

We use a 200 nm thick YIG thin film grown on a gadolinium gallium garnet substrate via liquid phase epitaxy. The thin film possesses a saturation magnetization of μ₀M_S = 0.185 mT and an exchange stiffness of $Aex=3.7⋅10−12Jm$⁠, as determined from a fit to the dispersion measured by the NV centers. To excite spin waves, stripline S1 with a width of 5 µm was fabricated on top of the YIG film by optical lithography and electron beam evaporation of Ti(5 nm)/Au(100 nm). A second stripline, S2, of Ti(5 nm)/Au(200 nm) with width 30 µm as well as a 150 µm thick SiO₂ layer were fabricated on top of S1 by optical lithography and electron beam evaporation.

The setup used for the NV center measurements is an in-house built confocal microscope. The NV centers were optically excited by a 515 nm laser (iBeam smart-S 515-S, Toptica), which was focused to a diffraction-limited spot by an objective with a numerical aperture of 0.9 and a magnification of 63. Before the objective, a polarizer in combination with a λ/2-plate was used to rotate the polarization of the laser light, maximizing the contrast in the ω_±. The NV PL was gathered by the same objective, separated from the excitation light by a dichroic short pass mirror (cutoff wavelength 600 nm, Edmund Optics) and a long-pass filter (cut-on wavelength 590 nm). Microwaves for driving the NVs and spin waves were generated using a microwave generator (N5183A MXG, Agilent) at 0 dBm output power. To simultaneously send a microwave current through the pair of striplines S1 and S2 depicted in Fig. 1(a), the microwave excitation was divided using a power combiner (ZFRSC-123-S+, Mini-Circuits). To measure the PL signal with a lock-in amplifier, the microwave signal was modulated by a coaxial switch (139-ZASWA-2-50DRA, Mini-Circuits) at a frequency of 1.742 kHz. The PL photons were collected by an avalanche photodiode and, after passing a voltage amplifier, measured by the lock-in amplifier. Thereby, the microwave excitation of the NV centers and the spin waves was modulated, allowing the lock-in amplifier to isolate the dynamic component of the photoluminescence (PL) signal from the background signal. As the lock-in amplifier is designed to detect only variations caused by the modulated microwave signal, the static background PL signal (PL₀) is not detected. Consequently, we do not normalize the signal by PL₀. Each data point was measured for 1 s at the third filter order. To gain an improved signal, each column in Fig. 3(a) was measured five times and averaged. All measurements were conducted at room temperature.

The TR-MOKE measurements utilized a custom-built confocal microscope. A pulsed 800 nm Ti:Sa-laser was employed, which was first attenuated and polarized using a half-wave plate and a polarizer capable of handling the high optical power densities produced by the laser. The beam then passed through a pellicle beam splitter with 92% transmission. A Wollaston prism splits the returning beam into two linearly polarized components, each directed toward a differential detector with two photodiodes. To keep the repetition rate of the laser constant, the laser’s cavity length was actively adjusted to match the repetition rate to a global frequency reference. This adjustment was facilitated by a control loop incorporating a photodiode detecting generated pulses and mixed with the reference signal to produce a down-converted signal for use by a phase-locked loop and a proportional-integral-derivative controller. The reference signal, derived from a 10 MHz rubidium atomic clock, underwent frequency multiplication to achieve the desired 80 MHz value. The 10 MHz reference signal was also utilized for an arbitrary waveform generator producing MW signals at 20 dBm output power sent to the sample’s stripline S1 [Fig. 1(a)]. The output of the lock-in, which is the differential signal generated by the rotation in polarization and obtained by taking the difference of the outputs of the detectors, is referred to as the Kerr signal S_Kerr, while the summed signal of the two photodiodes is referred to as the topographic signal S_Topo. Each data point was measured for 1 s at the third filter order.

In Table I, the expected and fitted parameters for the DC magnetic field, obtained using Eq. (D3), are presented. Here, I_DC denotes the DC current through S2, x₀ represents the offset of the center of S2 from x = 0, w is the width of the microstrip line, and z₀ is the unknown distance between the NV centers and the YIG surface. We find a good agreement between these values.

Figures 5 and 6 provide additional images of the observed spin wave wavefronts, captured by the NV setup and the TR-MOKE setup respectively, under various external fields, resulting in different excitation frequencies and wavelengths.

In Fig. 7, the spin wave dispersion (for spin waves excited at the ω₋ transition frequency of the NVs) extracted for the case where the external magnetic field is applied in the DE configuration (green dots) and along S1 at an angle of ϕ = 35° relative to the sample plane, aligning it with one of the four possible NV center axis directions (blue dots), is plotted against the theory curve (red line). The deviation in the fitted wavelengths arises from errors in the magnetic field calibration, which was done separately for the DE and NV configurations. However, within the bounds of this error, the measurements closely match the expected theoretical curve, demonstrating the negligible effect of the perpendicular component of the external field with respect to the thin film plane.