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. 2025 Jan 22;25(5):1917–1924. doi: 10.1021/acs.nanolett.4c05531

Nanoscale Mapping of Magnetic Auto-Oscillations with a Single Spin Sensor

Toni Hache †,‡,*, Anshu Anshu †, Tetyana Shalomayeva ‡, Gunther Richter §, Rainer Stöhr ‡, Klaus Kern †,∥, Jörg Wrachtrup †,‡,⊥, Aparajita Singha ¶,†,⊥,*
PMCID: PMC11803721  PMID: 39841215

Abstract

graphic file with name nl4c05531_0005.jpg

Spin Hall nano-oscillators convert DC to magnetic auto-oscillations in the microwave regime. Current research on these devices is dedicated to creating next-generation energy-efficient hardware for communication technologies. Despite intensive research on magnetic auto-oscillations within the past decade, the nanoscale mapping of those dynamics remained a challenge. We image the distribution of free-running magnetic auto-oscillations by driving the electron spin resonance transition of a single spin quantum sensor, enabling fast acquisition (100 ms/pixel). With quantitative magnetometry, we experimentally demonstrate for the first time that the auto-oscillation spots are localized at magnetic field minima acting as local potential wells for confining spin-waves. By comparing the magnitudes of the magnetic stray field at these spots, we decipher the different frequencies of the auto-oscillation modes. The insights gained regarding the interaction between auto-oscillation modes and spin-wave potential wells enable advanced engineering of real devices.

Keywords: PL map, auto-oscillation, spin Hall effects, nitrogen-vancancy center, nano-oscillator, nonlinear oscillator

The efficient excitation, manipulation and readout of spin waves is one of the main foci of current research for creating highly energy-efficient hardware for communication technologies.1−9 Large spin-wave amplitudes are achieved in various nano-oscillator devices10−24 via damping compensation resulting in magnetic auto-oscillations. Despite their different geometries, their fundamental principles remain very similar. The interaction of a spin current with a ferromagnetic material generates a spin-transfer or spin–orbit torque compensating the damping.25,26

As the auto-oscillation frequencies typically lie within GHz range, such nano-oscillators are regarded as miniaturized frequency converters with various mechanisms to control the frequency like the dc current, external magnetic field or synchronization to external stimuli.27−32 These aspects render them as attractive candidates for nanoscale microwave voltage and spin wave sources, neuromorphic computing hardware33,34 or localized microwave field generators, for manipulating single spins in quantum technologies.35,36

So far, it has been highly challenging to resolve the spatial distribution of free-running auto-oscillations within single devices. Insight was gained mainly via micromagnetic simulations.37−40 However, the spatially resolved investigation of the spin-wave formation in real devices exposed to imperfections during the fabrication process is an essential step for optimizing these devices toward applications. Here, we map the microwave field generated by the auto-oscillations with a single spin scanning-probe consisting of a nitrogen-vacancy (NV) center with a spatial resolution of <100 nm. Our approach allows us fast, all-optical mapping of distinct auto-oscillation modes. Combining these with additional NV magnetometry measurements41−47 and simulations, we unravel the origin behind the characteristic frequencies of auto-oscillations.

SHNO and Measurement Geometry

We utilize a spin Hall nano-oscillator (SHNO) in order to generate magnetic auto-oscillations. Figure 1(a) shows the schematic of the SHNO device (blue) with a well-defined constriction of d = 750 nm at the center which forms spots with high current densities as shown in Figure 1(b). The spin Hall effect (SHE)48−50 within the Pt layer (Figure 1(c)) generates a pure spin current perpendicular to the applied charge current, resulting in the net injection of spins into the adjacent soft ferromagnetic Ni81F19 layer. The dc current polarity controls the polarization of these spins.12 By aligning them mainly antiparallel to the intrinsic spin polarization of the ferromagnet, a sufficient spin–orbit torque (SOT) is created, and the magnetization is rotated out of its equilibrium direction which is defined by the internal magnetic field in Ni81F19 (Figure 1(d)). This SOT compensates the Gilbert damping torque (GT) resulting in auto-oscillations in the microwave frequency range. In consequence, it is generally believed that auto-oscillations start at spots of small GT and large SOT which are points of low internal magnetic field and large DC density. Both are achieved via forming a constriction. Moreover, local magnetic field minima would form spin-wave potential wells (Figure 1(e)) because auto-oscillations are formed at low frequencies of the dispersion relation in case of in-plane magnetization25 as in our experiment. Therefore, the generated auto-oscillation frequency lies in the spin-wave bandgap of the surrounding material and cannot excite propagating spin waves in neighboring areas.

Figure 1.

Figure 1

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Measurement overview and electrical characterization of the SHNO device. (a) Sample geometry and schematic representation of the electrical and optical measurements. (b) The simulated dc current density JDC distribution reveals maximum values at the edges of the constriction. (c) A pure spin current generated via SHE in Pt generates a SOT in Ni81F19. This generates magnetic auto-oscillations which generate a microwave field interacting with the single spin sensor. (d) The SOT compensates the GT resulting in auto-oscillations. (e) Local magnetic field minima create spin wave potential wells which confine the auto-oscillations. (f) Top: Auto-oscillation spectra electrically measured as a function of dc currents exhibit the presence of two auto-oscillation modes with characteristic microwave frequencies. Bottom: Integrated auto-oscillation power.

In order to measure the auto-oscillation frequencies in the fabricated samples, all-electrical measurements of the emitted microwave signals are conducted first. These measurements are based on the modulation of the sample resistance via auto-oscillations, affecting the anisotropic magnetoresistance (see Methods and SI 1). In order to achieve sufficient modulation, the magnetization must be rotated partially in the direction of the dc current. However, this is not ideal for the generation of auto-oscillations in these structures, which prefers the dc current to be perpendicular to the magnetization. Hence, only a small tilting of 23° of the external B field is chosen to ensure the generation of auto- oscillations while simultaneously maintaining a sufficient modulation of the resistance. Since the Gilbert damping has to be compensated by a sufficient spin–orbit torque, a characteristic threshold current has to be exceeded before the auto-oscillation state is achieved. As shown in Figure 1(f), this current is reached at about Ithr = 6.5 mA (critical current density ≈ TA/m2) an externally applied magnetic field of 22.75 mT resulting in oscillations at about 3.4 GHz. We observe two oscillation frequencies that decrease with increasing IDC. We attribute this negative frequency shift to several possible effects such as, a) the increased heating of the structure reducing the saturation magnetization, b) the Oersted field that is lowering the effective magnetic field and c) the change of the in-plane magnetization projection during the precession.25 This dc current dependence of the auto-oscillation frequency is an advantageous effect that we use to bring auto-oscillations in resonance to the nitrogen-vacancy (NV) sensor’s spin transition. Notably, no auto-oscillations are observed with reversed polarity of IDC. Due to the symmetry of the spin Hall effect, a reversal of the dc current polarity results in switching of the spin current polarization and the spin–orbit torque. As a result, the damping in the ferromagnet is increased and no auto-oscillations can be excited (see SI 1).

Mapping Magnetic Field Distribution

NV magnetometry is based on the atomic defect in a diamond, where two carbon atoms are replaced by a nitrogen (N) atom and a vacancy (V) forming a color center. The negatively charged NV center has a triplet ground state that is characterized by spin dependent fluorescence intensity. In particular, the mS = 0 state is characterized by significantly higher fluorescence intensity compared to the mS = ± 1 states. The fluorescence readout can be easily modulated when the transition between these mS = 0 and mS = ± 1 states is driven via the microwave signal of appropriate frequency.51

First, we use the sensor (sensitivity of <2.3 μT/√Hz) in this mode and scan over the switched off SHNO in order to map the generated stray field which provides an insight into the intrinsic magnetic field distribution. We use an AFM tip consisting of a diamond nanopillar with a single NV center oriented in-plane, as shown in Figure 1(a). This ensures that the external magnetic field is mainly applied along the NV spin with a minor misalignment of about 12.3° without affecting the NV resonances and the fluorescence contrast significantly. At each pixel, the microwave is applied to a stripline and its frequency is swept to determine the resonance frequency of the NV center to calculate the magnetic stray field. The magnetic field component parallel to the NV axis is shown in Figure 2(a). We find areas with a reduced magnetic field at the constriction edges. Furthermore, the scans with higher spatial resolution shown in Figure 2(b) and (c) reveal quantitatively different magnitudes of both field minima. In order to understand the measurements, micromagnetic simulations are conducted to determine the alignment of the magnetic moments inside the SHNO and the effective magnetic field (Figure 2(d)). We find two localized magnetic field minima at the constriction edges which are results of the strong demagnetization field inside the SHNO constriction. As seen in the measurement of the stray field, the mirror symmetry is broken. This is explained by the orientation of the external magnetic field which controls the position of these internal field minima at the constriction edge. The simulated magnetization state is used to calculate the stray field at different heights above the sample. We estimate the distance between NV sensor and sample to about 80 nm by comparing the calculated (shown in Figure 2(e), see also SI 2) with the measured stray field distribution and magnitudes in Figure 2(a). We conclude from this calculation that the minima of the stray field are fingerprints of the local minima of the effective magnetic field inside the SHNO. In order to validate the generally believed formation of auto-oscillations within such field minima and so far studied only via micromagnetic simulations,19,37,40 we now switch on the SHNO and detect the microwave field generated via the auto-oscillations. At this point, it can be expected that the different quantified field magnitudes determine the generation of auto-oscillation modes with distinct frequencies.

Figure 2.

Figure 2

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Magnetic field distribution of the SHNO without dc current. (a) Measurement of the magnetic stray field component parallel to the NV axis depicting localized field minima. (b, c) High-resolution maps revealing characteristic magnetic field magnitudes at each constriction edge. (d) Simulation of the internal field distribution revealing local field minima at the edges of the constriction (circles). (e) Simulated magnetic stray field component along the NV axis at a height of 80 nm above the SHNO revealing localized field minima (circles) as fingerprint of the minima in (d).

NV-Spin Manipulation via SHNO Microwave Field

Recently, the interaction of the microwave field descending from spin waves with spin defects in diamond or silicon carbide was demonstrated.52−65 In order to verify the quality of the auto-oscillation modes as miniaturized MW sources, we now drive the NV sensor on the scanning tip in resonance by only activating the SHNO device. Thereby, no external microwave power but a dc current is applied to the SHNO to generate magnetic auto-oscillations. Due to the precession of the magnetic moments, the dipolar magnetic field is modulated with the frequency of the auto-oscillations in the gigahertz range in close vicinity to the sample. By scanning the diamond AFM tip over the auto-oscillation, the fluorescence intensity of the NV center drops as a function of the generated microwave power only when the SHNO is tuned to provide the desired NV resonance frequency. Therefore, the distribution of the magnetic auto-oscillations can be acquired by simply measuring the fluorescence intensity of the NV sensor. Contrary to a standard spin resonance measurement where excitation frequency or external field sweeps are required, our method is significantly faster as it relies on only our photon collection efficiency (100 ms/pixel).

Since the frequencies of the NV transition and the auto-oscillations depend on the external magnetic field, there is a limited parameter space allowing synchronization of both. Note that the SHNO auto-oscillation frequency can be controlled by the applied dc current. Whereas it only slightly influences the NV sensor due to the change of the Oersted field above the sample. Figure 3(a) depicts the calculated NV resonance frequencies in black, the calculated ferromagnetic resonance (FMR) frequency of a 5 nm thick Ni81F19 thin film in blue, and the measured frequency range of the SHNO device in red. At magnetic fields below Bext = 15 mT, no auto-oscillations are expected due to incomplete alignment of the magnetic moments in the SHNO caused by the shape anisotropy. Due to the demagnetization field within the constriction (Figure 2) and the nonlinear redshift of the auto-oscillations (Figure 1(f)), the auto-oscillations are located at frequencies below the FMR. As a result, a crossing of the auto-oscillation frequency range and the upper NV resonance exists at the used magnetic field of Bext = 22.75 mT. Notably, besides this frequency matching condition, it is imperative to have sufficient microwave power generated by the auto-oscillations at the position of the NV sensor in order to have any interaction between the sensor and our SHNO device.

Figure 3.

Figure 3

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NV-spin manipulation via SHNO microwave field. (a) The calculated NV resonance (black) at higher frequency overlaps with the SHNO frequency range (red) extracted from Figure 1(f). This auto-oscillation range is located below the calculated thin-film FMR range (blue) as expected for SHNOs in this measurement geometry. (b) NV photoluminescence (PL) drops by 24% when the SHNO is activated by a characteristic positive DC current of IDC = 6.75 mA. The PL reduces only for positive currents for which the SHNO is active. The lowest PL is reached when the SHNO microwave oscillations are in resonance with the NV at 3.33 GHz. The inset shows the position of the NV-AFM tip during the dc sweep. (c) NV photoluminescence (PL) drops by 21% at the second constriction edge when the SHNO is activated by a characteristic positive dc current of IDC = 7.95 mA.

In order to prove this, the diamond tip containing the NV center is brought in contact with the SHNO at the bottom constriction edge, as shown in the inset of Figure 3(b). The dc current is swept stepwise from −9 mA to 9 mA, and the emitted fluorescence is acquired simultaneously. Close to the estimated NV resonance frequency determined from Figure 3(a) the fluorescence intensity decreases strongly and forms a characteristic dip. We attribute this to the fingerprint of a specific NV spin transition (mS = 0 to mS = +1), driven by the microwave field generated by the auto-oscillations inside the SHNO. The minimum is reached at IDC = 6.75 mA which corresponds to a microwave frequency of 3.33 GHz determined from Figure 1(f). The acquired fluorescence for the sweep with the reversed dc current polarity does not show a characteristic dip, which corroborates with the electrical measurement of the auto-oscillations (SI 1). The resonance condition at the second constriction edge (Figure 3(c)) is given for IDC = 7.95 mA. Here, we observed a slight decrease of PL during the variation of the current, which could be caused by nonlinear magnon–magnon interaction generating magnons at the NV resonance. As a next step these current magnitudes are fixed, respectively and lateral scans of the NV tip are conducted in order to acquire the fluorescence output at each pixel. This results in maps showing strong reductions of the fluorescence intensity at positions where the microwave field and, therefore, the auto-oscillation modes are present in the SHNO.

Mapping the Auto-Oscillation Modes

First, a reference map at IDC = 0 mA is obtained, which is subtracted from the maps at nonzero dc currents. As no auto-oscillation are present in this condition, it serves as a background to eliminate any other spurious effects that may also influence the photon count rate. At IDC = 0 mA, only a slight variation in the PL is recorded (compare SI 3), which changes dramatically for the PL maps taken at IDC = 6.75 mA and IDC = 7.95 mA (Figure 4(a), (b)). For 6.75 mA an additional feature appears at the bottom constriction edge, along with a moderate variation at the top edge. For 7.95 mA however, a strong feature appears at the top edge, and the one at the bottom edge almost vanishes. Figures 4(c) and (d) capture these areas in more detail. This behavior is attributed to the two auto-oscillation modes present in this sample. As shown in Figure 1(f), these modes have distinct frequencies, and therefore, different dc currents have to be applied to the SHNO to tune their frequency to the NV transition. Since the second mode has a lower frequency than the first one, a smaller dc current has to be applied to drive the NV resonance. Hence, Mode 2 is located at the bottom edge of the constriction and Mode 1 is located at the top edge. This conclusion is supported by the quantitative measurement of the stray field shown in Figure 2(b) and (c). A smaller stray field is measured at the bottom edge of the constriction caused by the local internal magnetic field minimum which results in a lower auto-oscillation frequency as determined for Mode 2. Both internal field minima form spin-wave potential wells (Figure 1(e)). Due to the spin-wave band gap at low frequencies, the auto-oscillations cannot excite propagating waves in the surrounding area. Therefore, the area of reduced magnetic field at the constriction edges acts as a resonator where high auto-oscillation amplitudes are reached. Additionally, the locally reduced fields result in a smaller Gilbert damping torque which is another contribution for increased precession angles. Due to the formation of two local field minima, a high power and coherent single-mode microwave signal can only be reached if both auto-oscillations can synchronize mutually. This is possible in case of a sufficiently small frequency difference. We note that a variation of temperature in close vicinity of the constriction could potentially influence the PL of the sensor as well. However, thermal effects would show a mirror symmetry with respect to the symmetry axes of the constriction. Thus, we attribute the PL reduction to the interaction with magnetic auto-oscillations only.

Figure 4.

Figure 4

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Localization of the auto-oscillation modes (a), (b) PL map at IDC = 6.75 mA (IDC = 7.95 mA) when auto-oscillation Mode 2 (Mode 1) is in resonance with the NV at the bottom constriction edge (upper constriction edge). For both dc currents, only one of the modes is in resonance with the NV and the second one off-resonance, respectively. (c, d) Finer PL map at the interaction area of Mode 2 (Mode 1) revealing two lobes. (e) Micromagnetic simulation of the auto-oscillation power localized at the constriction edge. (f, g) Microwave field in-plane (out-of-plane) component being perpendicular to the NV axis. (h) Microwave field interacting with the NV revealing two lobes as seen in the experiment. (i) Total microwave field (microwave fields are calculated at a height of 80 nm above the SHNO).

Interestingly, the PL maps shown in Figure 4(c) and (d) reveal two lobes within the area of NV-SHNO interaction which is a result of the generated microwave field of the auto-oscillations. In order to understand this shape, micromagnetic simulations are conducted. As shown in Figure 4(e), the strongest auto-oscillation intensity is formed at the constriction edge, which is in agreement with our experimental observation. This data was used to calculate the microwave power at a height of 80 nm above the SHNO. Figure 4(f) and (g) show the in-plane and the out-of-plane components of this microwave field, respectively, which are both perpendicular to the NV axis. Surprisingly, the strongest microwave field is not generated above the maximum of the auto-oscillation power. Additionally, the out-of-plane component has two microwave power maxima. We attribute these behaviors to the elliptical precession cone of the magnetic moments in this thin film sample (see SI 4). Figure 4(h) shows the combination of the perpendicular components to the microwave field, which interacts with the NV. There, two maxima are visible, which form lobes similar to the feature seen in the measurement. The simulation allows us to conclude that the spot of highest auto-oscillation intensity is located between these two lobes and the constriction edge. For comparison, the total microwave power is shown in Figure 4(i), which does not show the two lobes. Hence, the lobes are seen due to the selective interaction of the NV with the three-dimensional microwave field.

To the best of our knowledge, this is the first nanoscale imaging of the magnetization dynamics in a ferromagnetic metal utilizing a near-surface single NV-center. Furthermore, we demonstrate that such nano-oscillator devices produce a strongly localized microwave field, which might be attractive as a miniaturized microwave source for specific quantum technologies where a propagating or global microwave field may not be preferred. The combination of nanoscale resolution and quantitative magnetometry demonstrated in this work uniquely determines the magnetic field distribution of a real auto-oscillator device. Quantum sensing of the microwave field generated by the auto-oscillations revealed their position at two separated local minima of the magnetic field. This confinement is explained by the formation of spin wave potential wells due to the local lowering of the spin-wave band gap, which prohibits propagating spin waves. The quantitative measurement revealed the distinct stray magnetic field magnitudes at these potential wells explaining the formation of two auto-oscillation modes with specific frequencies. The asymmetry of the auto-oscillation spots with respect to the sample symmetry is caused by the position of these potential wells controlled by the external magnetic field (SI 5). This proves the importance of local field minima for the formation of auto-oscillations instead of being defined by the areas of largest antidamping only. This work opens up new possibilities with more profound insights about how to control multimode auto-oscillations in real devices where the coherence and output power are currently limited. Our work and further investigations to reveal dynamical properties of such devices will pave the way to design new SHNO or auto-oscillator devices with engineered internal magnetic field distributions.

Methods

SHNO Fabrication

The shapes of the SHNO and the electrical contacts were fabricated using electron-beam lithography. The metallic layers of SHNO were deposited using magnetron-sputtering. The bottom Ta layer is used as the seed layer and the top one for oxidation protection. The gold for the electrical contacts was deposited by using thermal evaporation. A 5 nm thick Cr layer was used as the adhesion layer below the 100 nm thick Au layer.

Electrical Measurements

A direct current source was used to supply the direct current. It was passed through a bias tee, a microwave probe and impedance-matched electrical contacts to the SHNO. The auto-oscillations generate a microwave signal IMW via the anisotropic magneto-resistance within the Ni81F19 layer. This signal is transmitted through the microwave probe and passes the bias tee through the high frequency output. Three low-noise microwave-amplifiers amplify the signal by about 58 dB before the signal is acquired by a spectrum analyzer.

NV Quantum Sensing

We used a commercially available diamond tip (Qzabre, Q5) with a single NV in in-plane orientation (110 cut) in order to minimize components of the external magnetic field perpendicular to the NV axis. We use this sensor in two different measurement modes. 1) Spatially resolved NV spin resonance: In order to determine stray magnetic field at each pixel above the sample quantitatively, the SHNO was switched off, and the microwave was applied to a separate stripline at various frequencies. At the resonance frequency, the fluorescence intensity of the NV dropped, and this frequency was used to calculate the magnetic field component parallel to the NV axis. 2) Spatially resolved auto-oscillation detection: The external microwave is switched off. The microwave field is generated by the auto-oscillations within the SHNO which causes the NV spin transition. During the lateral scan, the NV fluorescence would drop only at pixels that are in close vicinity to the auto-oscillations. Therefore, the locations of auto-oscillations are revealed relatively fast compared to other established methods because only the fluorescence intensity has to be acquired once at each pixel (100 ms/pixel).

Micromagnetic Simulations

First, SHNO was modeled in COMSOL Multiphysics. The dc current density in the Pt layer and the resulting Oersted field within the Ni81F19 layer were simulated using the conductivities σPt = 3.1 MS/m and σNi81F19 = 1 MS/m. The shape, dc current density, and Oersted field were exported and used as input for the micromagnetic simulations. Mumax366 was used to study the relaxed magnetization state and the time-evolution of the dynamic magnetization in the SHNO. An external field of 22.75 mT is applied under 23° as shown in Figure 1(a). The saturation magnetization, exchange stiffness and Gilbert damping parameter were set to Msat = 630 kA/m, Aex = 10 pJ/m and α = 0.02. A polarization factor of P = 0.16 was used to convert the imported current density to the spin-current density. The orientation of the spin-current polarization is perpendicular to the current density in each pixel of the simulation. A simulation area of 2000 × 2000 × 5 nm around the constriction was discretized in 512 × 512 × 1 points. A time window of 200 ns was simulated with 50 ps time steps. The FFT revealed the auto-oscillation frequency. The spatial distribution of this auto-oscillation intensity was plotted in Figure 4(e). In order to achieve two distinct auto-oscillation frequencies as in the experiment, a small asymmetry was introduced between both constriction edges (see SI 6).

Microwave Field Calculations

The spatial distribution of the dynamic magnetization from the micromagnetic simulations was used to calculate the stray magnetic field at 80 nm (distance to the NV sensor) above the SHNO for each time step. The FFT revealed the dynamic three-dimensional microwave magnetic field at the NV position caused by the auto-oscillations. Figure 4(f)-(i) shows the squared magnitudes being proportional to the generated microwave power.

Acknowledgments

A.S. gratefully acknowledges an IQST-YR grant from the Center for Integrated Quantum Science and Technology supported by funding from the Carl Zeiss Foundation and an Emmy Noether grant from the Deutsche Forschungsgemeinschaft (project no. 504973613). J.W. acknowledges: BMBF via project QCOMP, the EU via project AMADEUS and the DFG via GRK2642. We gratefully acknowledge Frank Thiele from the Central Scientific Facility Materials at the Max Planck Institut for Intelligent Systems (Stuttgart) for the thin film deposition.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.4c05531.

  • Additional experimental details, simulations, details about data evaluation, supplementary figures (PDF)

Author Contributions

T.H. and A.S. envisioned and designed the experiment. T.H. and A.A. built the electrical measurement setup. T.H. fabricated the SHNO devices. T.H. and A.A. performed electrical characterization of the SHNO devices. T.H. conducted the NV measurements, performed the micromagnetic simulations as well as microwave field calculations. T.H. and A.S. prepared the manuscript with contributions from all coauthors.

Open access funded by Max Planck Society.

The authors declare no competing financial interest.

Supplementary Material

nl4c05531_si_001.pdf (4MB, pdf)

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