Spatially resolved detection of complex ferromagnetic dynamics using optically detected nitrogen-vacancy spins

Spintronic^1,2 and magnonic devices^3–5 are receiving intense scientific attention due to their promise to deliver new technologies that can revolutionize computing and provide greater energy efficiency. In particular, tools for understanding the phenomena such as angular momentum transfer across interfaces,^6–10 spin wave propagation in low dimensional and nanoscale systems,^11,12 domain wall motion,^13–15 microwave (MW)-assisted switching,¹⁶ and relaxation and damping in small structures¹⁷ are needed. There is current interest in materials with more novel magnetic textures than simple ferromagnets, such as skyrmions.¹⁸ 

Nitrogen-vacancy (NV) centers in diamond have emerged as an attractive tool to study the magnetic phenomena at the nanoscale, and they offer a way to convert magnonic signals into optical signals. The NV centers offer a powerful magnetometry tool due to a potent combination of optical and magnetic properties that make the intensity of their photoluminescence (PL) dependent on their spin state. This has allowed detection of just a few resonant nuclear spins and nuclear magnetic resonance imaging with resolutions of tens of nanometers, all under ambient conditions and at room temperature.^19–21 The NV centers have also been used to study the domain wall hopping,²² and the spinwave modes in permalloy.²³ High sensitivity to detect dynamic fields has been achieved by finding the optimal NV centers with long lifetimes and manipulating them (and sometimes the target spins) with intricate microwave and optical pulse sequences.

We have recently demonstrated a new approach²⁴ to detect the ferromagnetic resonance (FMR) using the NV centers in nanodiamonds, whose short spin lifetimes and varied NV-center orientations typically render them unsuitable for conventional optically detected magnetic resonance (ODMR) based magnetometry. In contrast to all other reported approaches to detecting non-NV magnetic resonance signals, our technique requires no excitation at the NV frequency. Rather, the intensity of NV PL responds directly to the magnetic resonance excitation of the system under study, without the need for the intricate pulsed magnetic resonance schemes. Here, we report the extension of this approach to include the detection of several spinwave branches, both dipolar (normalized wave number, kd < 1, where k is the wave number and d is the magnetic film thickness) and dipolar-exchange (1 ≤ kd < 25), as well as dynamics in the multidomain-state. Spectral studies of such complex magnetization dynamics have not been previously reported using the NV centers. We also show that this technique provides spatially resolved information by measuring the dependence of the spectra on the position of the laser spot on the magnetic film.

The sample is a 5 μm thick film of yttrium iron garnet (YIG, Y₃Fe₅O₁₂) epitaxially grown on a (111) oriented gadolinium gallium garnet (GGG) substrate by liquid phase epitaxy. A 400 μm wide, 300 nm thick silver microstrip is lithographically patterned on top of the film as shown in Fig. 1 to apply microwaves (MWs). A small window, 25 μm × 200 μm, is left open in the center of the silver wire to allow optical access to the regions of the samples that experience various MW conditions. The shorted microstrip is driven by an MW generator. A film of nanodiamonds, 50–200 nm in size and containing up to a few thousand NV centers each, is dispersed on top of the sample.

PL is excited in the NV centers using a 520 nm laser, focused down to a <2 μm spot, and is collected by a photodiode. The NV-PL is recorded as a function of a static magnetic field H₀, applied in-plane and perpendicular to the antenna (see Fig. 1), and the frequency, f, of the MW magnetic field H₁. We measure this PL signal at three different positions on the sample as indicated by labels 1, 2, and 3 in Fig. 1. We measure a lock-in signal for both the PL and the reflected MW power (S₁₁) by modulating the amplitude of H₁ at ∼1 kHz. The fractional change of PL (lock-in voltage/DC level) is the primary data of interest and is presented in Fig. 2. (Note: NV lock-in signals are positive for the decreases in NV PL.) This is compared and contrasted to S₁₁ which also changes due to the power absorbed by FMR and other ferromagnetic dynamics. We emphasize that the S₁₁ is averaged over the entire sample while the NV-PL provides local information at the laser spot.

Fig. 2(a) shows the representative spectra collected as H₀ is swept from −25 mT to +25 mT at 1.8 GHz MW excitation. Shown are the spectra collected by NV-PL at the three positions (left-hand axis) and the S₁₁ (right-hand axis). We note that noise in NV-PL data (as given by the y-channel of the lock-in) is typically smaller than the thickness of the lines used in the graphs. This high signal-to-noise ratio was achieved with 500 ms lock-in time constant and no further averaging. The roughly periodic variation in the NV PL and the MW reflection signal as a function of f is due to the standing wave resonances in the MW circuit that modify the H₁ intensity as a function of f. However, these variations affect neither our analysis nor conclusions.

A striking feature of our approach is the ability to detect a diverse array of excitations of the ferromagnet using the NV PL. Below, we describe these various spinwave excitations whose NV signal intensities are shown in Fig. 2 as a function of H₀ and f. The intensities of these features change between the four spectra due to the varying MW conditions across the sample. We will first describe these features and then discuss their spatial variation.

The peak at $|H0|∼20 mT$ in Fig. 2(a) corresponds to the signal from longitudinal spinwaves (LSW) that propagate along the direction of H₀. The peak itself corresponds to the modes given by the lateral size of the sample, kd ≈ 0 (uniform FMR). The higher field shoulder of this peak is a consequence of the spatial inhomogeneity of H₁ and is associated with higher wave numbers. We associate the second peak (⁠$10<|H0|<14 mT$⁠) with parametrically excited spinwaves from the perpendicular pumping geometry (H₀ ⊥ H₁). We see the largest feature for $|H0|<4 mT$⁠, arising from the unsaturated multi-domain state. Any changes to the PL due to the native NV spin resonances are weak, compared to those due to the ferromagnet, at 1.8 GHz for our polycrystalline nanodiamond powder.

The spinwave excitations discussed above are identified using the field-frequency sweeps shown in Fig. 2. Panels (b)–(d) correspond to NV PL at positions 1, 2, and 3, respectively, and (e) to the changes in S₁₁. The LSW modes with kd ≈ 0 have a dispersion approximately given by the Kittel FMR mode, $f0=γ(H0(H0+4πMs))$⁠. The higher field cutoff for these LSW modes is marked by the curve f_LSW, calculated analytically²⁵ (see the supplementary material²⁶), corresponds to kd = 5. The curves f_⊥ (related to the second peak in panel (a)) and $f‖$ depict the spinwaves generated via first order Suhl instability processes,²⁷ where the spinwaves are excited at f/2. These processes favor the excitation of spinwaves with the lowest damping and group velocity.²⁷ The curve f_⊥ corresponds to the excitation of dipolar-exchange spinwaves by a perpendicular pumping field, $H0⊥H1$⁠, with $kd≈25$ (Ref. 28) and $15°<θ<45°$⁠, where θ is the angle of the spinwave relative to H₀. The curve $f‖$ shows the dynamics driven by parallel pumping,²⁷ $H1||H0$⁠, where an effective excitation takes place for spinwaves with wave numbers on the order of $kd∼0$ and $5 (θ∼90°)$⁠.^29,30 At our MW powers (∼25 mW applied to the sample), the spinwaves can be excited in a broad range of k and θ (Ref. 29–31) due to 3- and 4-magnon scattering processes;^32,33 our data do not allow us to separate the contributions of these processes in the observed PL signal. The signal arising from dynamics in the multi-domain state (H₀ < 4 mT) most likely originates from the resonance modes of individual domains³⁴ as well as the dipolar spinwaves, which have complicated spectra.^35,36

The data in Fig. 2 demonstrate the coupling between the NV centers and the ferromagnet over a broad range of fields and frequencies. A key point is that the native resonances of the NV need not overlap signals arising from the ferromagnet. The NV resonances from the randomly oriented diamonds fall between the extrema of the powder pattern which are shown by green lines. The data in Figs. 2(b)–2(d) also show a pronounced sensitivity of the NV signal to the position of the laser spot on the sample, and clearly contrast with the global S₁₁ data. The NV signal provides information about local magnetic dynamics, as induced by the local H₁ (and the spatially uniform H₀) within the area illuminated by the laser.

Our experimental arrangement makes possible the excitation of the different dynamic modes of the YIG. At position 1, H₁ is nearly parallel to H₀ (see Fig. 1) and thus induces only a small torque on the YIG magnetization. Therefore, the efficiency of linear excitation is low at this position, but conditions are ideal for parallel pumping, see curve $f‖$ in Fig. 2(b). H₁ is stronger at position 2 (as evidenced by the larger NV ground state resonance) and perpendicular to the film surface and hence to the magnetization; ideal conditions for linear drive of the spinwaves and generated by the strongly non-uniform H₁ at the edge of the microstrip (curves f₀ and f_LSW). However, at our MW power levels the excitation of spinwave via a first order Suhl instability is relatively more dominant for this position, curve $f⊥$ in Fig. 2(c). Finally, at position 3, while most of the features are detectable, they are smaller due to a weaker H₁ resulting from the large separation of this position from the microstrip. The signal here most likely results from a combination of direct excitation by the MWs and by the propagating spinwaves excited at the edges of the microstrip (position 2). The spinwave band, $f⊥$⁠, at position 3 seems to be shifted to higher field (see Fig. 2(a)) and suggests propagating spinwaves. The spinwaves at the center of the band have small group velocity, while the ones at higher field have a larger group velocity and can thus travel the 500 μm to the location of the laser spot where they are detected.

The biggest difference between positions 1 and 2 is in the unsaturated state. Position 1, in the center of the wire, shows the strongest NV signal from the multi-domain state and closely matches the global S₁₁ that is dominated by the region under the wire. This is in contrast to position 2 where the NV signal from the spinwave band and even the uniform FMR mode is larger than the domain-state signal. The intensity of H₁ at position 2 is stronger than at position 1 and cannot explain the relative change of the domain-state signal between the positions. This change is most likely due to the out-of-plane tilted domains³⁷ that arise from the growth-induced anisotropy in these YIG films. The out-of-plane tilted domains are much more effectively excited by the in-plane component of H₁ that exists at position 1 (which being perpendicular to the magnetization can provide a greater torque). Given the significant interest in the various technological uses of domains and domain walls, it should be investigated in further detail. The NV detection may be an ideal way to study the dynamics in domains because of the large response and spatial resolution.

The NV response is sensitive to ferromagnetic dynamics up to fields and frequencies higher than that shown in Fig. 2. The evolution of the ferromagnetic spectrum up to 6.55 GHz and 180 mT, the limit of our current set-up, is shown in Fig. 3. The uniform FMR is indicated by the solid triangular symbols for each frequency. We also see higher field peaks (relative to FMR and indicated by open triangles), which correspond to the LSWs generated by the small, non-uniform perpendicular field at the edges of the 25 μm window in the miscostrip line (see Fig. 1). The k corresponding to these excitations is approximately given by the standing-wave condition, $k≈nπ/W$⁠, where n is an odd number and W is the width of the window. The k are better calculated using formulas from Kalinikos²⁵ (see the supplementary material²⁶) and the peaks correspond to kd = 0.95, 2.2, and 4, with kd increasing with the magnetic field.

At 6.55 GHz (blue line), we see the uniform mode at H₀ = 165 mT. Signals have not been reported at such high fields thus far using magnetometry with nitrogen vacancy centers. Measuring NV signals at higher magnetic field with conventional ODMR can be challenging due to the decay of ODMR contrast with field and due to the ill effects of fields transverse to the NV axis,^38,39 which can exist either due to non-ideality of the experimental alignment or limitations of the measurement geometry. These are especially true in the case of nanodiamonds, where the pulsed ODMR is challenging for ensembles even at modest fields. This highlights the potential versatility of our “off-resonant” modality of detection for the study of magnetic dynamics over a broad range of fields and frequencies.

To conclude, we have shown that the NV centers are sensitive to magnetic dynamics over a broad range of magnetic fields and MW frequencies, and that the NV centers provide localized sensitivity to the magnetic dynamics in the immediate vicinity of the NV detector. These results, combined with the atomic nature of the NV defects, indicate that the NV centers could be used in this “off-resonant” modality to study the ferromagnetic dynamics on the nanoscale and in novel magnetic textures. Domain wall motion is currently a field of intense interest and technological promise.^22,40 The fact that we see such strong signals from the dynamics of this state presents a promising potential avenue for optical read out of domain wall motion and domain dynamics. These results can enhance a recent proposal to use FMR of a ferromagnetic element for amplifying the magnetic resonance signal from a nearby target nuclear spins,⁴¹ and highlight the potential for using spinwave modes in addition to the uniform mode for such a scheme.

Funding for this research was provided primarily by the ARO through award number W911NF-12-1-0587 (NV diamond optical detection and measurement of magnetic signals). We also acknowledge partial support from the Center for Emergent Materials: an NSF MRSEC under award number DMR-1420451 (spin wave dynamics, sample growth, and characterization).