Spin-torque oscillation in a magnetic insulator probed by a single-spin sensor

We locally probe the magnetic fields generated by a spin-torque oscillator (STO) in a microbar of ferrimagnetic insulator yttrium-iron-garnet using the spin of a single nitrogen-vacancy (NV) center in diamond. The combined spectral resolution and sensitivity of the NV sensor allows us to resolve multiple spin-wave modes and characterize their damping. When damping is decreased sufficiently via spin injection, the modes auto-oscillate, as indicated by a strongly reduced linewidth, a diverging magnetic power spectral density, and synchronization of the STO frequency to an external microwave source. These results open the way for quantitative, nanoscale mapping of the microwave signals generated by STOs, as well as harnessing STOs as local probes of mesoscopic spin systems.

Figure 1

(a) Schematic illustration of the device: a diamond nanobeam containing a single NV spin is positioned near a hybrid Pt/YIG structure. (b) Scanning electron micrograph of the device (before positioning the diamond nanobeam). (c) NV optical (green) and microwave (red) spin-echo sequence for stray-field magnetometry of spin-wave resonances. A spin-wave (FMR) drive is applied during the central free-precession period. A change in the YIG stray field $\mathrm{\Delta }{B}_{\left|\right|}$ imparts a phase on the NV spin state and is read out via spin-dependent photoluminescence. A free precession time $\tau \approx 5.5\mu \mathrm{s}$ is used for such stray-field magnetometry. (d) Example of YIG spin-wave resonances measured with the pulse sequence in (c), at applied static magnetic field $B_{\mathrm{ext}}=337\mathrm{G}$ aligned with the NV axis. Plotted is the NV-measured stray static magnetic field along the NV axis, $\mathrm{\Delta }{B}_{\left|\right|}$, as a function of the spin-wave drive frequency. The signal is normalized by the square of the drive field $b_1^2$, which is proportional to the spin-wave drive power and is independently measured on-chip using the same NV sensor [20]. Blue dots: data. Red line: double Gaussian fit, yielding $\mathrm{FWHM}=8.5\left(6\right)$ MHz for the dominant mode attributed to the spatially homogeneous ($n=1$) ferromagnetic resonance (FMR) of the YIG bar. (e) Green dots: Magnetic-field ($B_{\mathrm{ext}}$) dependence of the fundamental spin-wave resonance frequency extracted from fits to measurements such as shown in (d). Blue line: fit reveals characteristic Kittel-like behavior of FMR. Black lines: NV transition frequencies corresponding to the $m_s=0\leftrightarrow \pm 1$ transitions. NV-spin manipulation pulses are applied on the $m_s=0\leftrightarrow +1$ transition.

Figure 2

(a) Sketch of the magnetization dynamics of the Pt/YIG device under the influence of a spin current. The electrical current (${\mathbf{J}}_{\mathbf{e}}$) injects a spin current (${\mathbf{J}}_{\mathbf{s}}$) into the YIG, leading to a spin-orbit torque (labeled SOT) that either reduces or enhances magnetic damping depending on the relative orientation between the injected spins and the magnetization M. DT denotes the (intrinsic) damping torque. (b) NV-measured, microwave-driven spin-wave resonance spectra in the YIG as a function of the DC current $I_{\mathrm{dc}}$ through the Pt. [Measurement sequence shown in Fig. 1]. Blue traces: normalized change in YIG stray field $\mathrm{\Delta }{B}_{\left|\right|}/b_1^2$ as a function of microwave driving frequency for $I_{\mathrm{dc}}=5$, 4, 3, 2, 1, 0, −2, −5 mA. Red lines: double Gaussian fit to data. Green dots: center frequency of the fundamental spin-wave mode vs. $I_{\mathrm{dc}}$. Black curve: parabolic fit to green dots. (c) On-resonance $\mathrm{\Delta }{B}_{\left|\right|}$ as a function of microwave driving power $b_1^2$ for different values of $I_{\mathrm{dc}}$. Black, red, and pink dots correspond to $I_{\mathrm{dc}}=4.5$, 4.75, and 5 mA, for which the initial slopes ($d\mathrm{\Delta }{B}_{\left|\right|}/d{b}_1^2$) have no discernable difference. Blue and green squares correspond to $I_{\mathrm{dc}}=3$ and 3.5 mA, for which initial slopes are significantly smaller. (d) Plot of the inverse of the initial slopes, i.e., $d{b}_1^2/d\mathrm{\Delta }{B}_{\left|\right|}$, as a function of $I_{\mathrm{dc}}$. Diagonal and horizontal dashed lines serve as eye guide to illustrate that there exists a current threshold as onset of an auto-oscillating spin torque oscillator (STO).

Figure 3

(a) Blue dots show temperature, measured with NV, changes with $I_{\mathrm{dc}}$. (b) Green dots represent center frequencies of fundamental SW mode at different $I_{\mathrm{dc}}$ measured by NV stray-field magnetometry measurements [extracted from Fig. 2]. (c) Normalized effective saturation magnetization ($M_e/M_s$) as a function of $I_{\mathrm{dc}}$: data shown as blue dots are derived from temperature measurements. Data shown as solid green dots are from FMR center frequency measurements without correction to remove impact from Oersted field, while data shown as open green circles are corrected.

Figure 4

(a) NV spin-relaxometry measurement sequence. The NV spin is initialized into ${\mathrm{m}}_{\mathrm{s}}=0$ by a green laser pulse and let to relax for a time τ, after which the spin population is characterized via the spin-dependent PL during a laser readout pulse. Noise that is resonant with an NV transition frequency causes NV spin relaxation. (b) NV spin-relaxometry measurement at $I_{\mathrm{dc}}=5.8\mathrm{mA}$ and $\tau =5\mu \mathrm{s}$. By tuning the magnetic field $B_{\mathrm{ext}}$, the frequency of the $m_s=0\leftrightarrow -1$ transition is swept over three spin-wave (SW) modes in the YIG, whose field-noise causes strong NV spin relaxation and thus dips in the normalized PL signal. (c) Performing the measurement shown in panel (b) for different $I_{\mathrm{dc}}$ yields a 2D plot of PL vs $I_{\mathrm{dc}}$ and $B_{\mathrm{ext}}$ that displays the presence and dispersion of spin-torque oscillators (STOs) in the system. Different delay times τ of 150, 50, 15, 5, and 3 µs are used for the different $I_{\mathrm{dc}}$ ranges of [−5 mA:0 mA], [0.2 mA:1.8 mA], [2 mA:3 mA], [3.2 mA:5 mA], and [5.2 mA:6 mA], respectively. Top horizontal axis shows the $m_s=0\leftrightarrow -1$ transition frequency at corresponding $B_{\mathrm{ext}}$. Blue stars indicate fits of peak centers for the first resonance on the right-hand-side ($\mathrm{ST}{\mathrm{O}}_1$), while red stars are fits of peak centers for the second ($\mathrm{ST}{\mathrm{O}}_2$). These two STOs are also indicated in panel (b). Note that an additional oscillator [data points are orange in color and designated as STO* in panel (b)] appears when $I_{\mathrm{dc}}=5.8\mathrm{mA}$ and persists for higher current. Inset illustrates mode spatial distribution of $\mathrm{ST}{\mathrm{O}}_1$ and $\mathrm{ST}{\mathrm{O}}_2$ along width of Pt/YIG microstructure (W). (d) and (e). Zoomed-in, high-resolution views of (c), where spin-wave modes are observed to approach each other.

Figure 5

(a) NV spin relaxation rate (Γ) is measured at the current and magnetic field values indicated by the blue and red stars in Fig. 4, where the spin-torque oscillators (STOs) are resonant with the $m_s=0\leftrightarrow -1$ transition frequency. At each of these current and magnetic field values, we sweep τ, perform an NV spin-relaxometry measurement sequence [Fig. 4], and extract the exponential decay time constant Γ. ${\mathrm{\Gamma }}_{\mathrm{STO}1}$ (red) and ${\mathrm{\Gamma }}_{\mathrm{STO}2}$ (blue) are plotted as a function of $I_{\mathrm{dc}}$. The dramatic order-of-magnitude increase of the relaxation rate above $I_{\mathrm{dc}}\sim 3$ mA indicates spin-torque induced auto-oscillation of the STOs. Inset shows $1/\mathrm{\Gamma }=T_1$ vs $I_{\mathrm{dc}}$ for both STOs. Linear fits at low current ($I_{\mathrm{dc}}<4$ mA) intersect with $T_1=0$ at $I_{th1}=3.5\mathrm{mA}$ and $I_{th2}=4.4\mathrm{mA}$, which we define as the auto-oscillation threshold currents. (b) Measured STO linewidth $\mathrm{\Delta }B$ as a function of $I_{\mathrm{dc}}$ for $\mathrm{ST}{\mathrm{O}}_1$ (blue dots) and $\mathrm{ST}{\mathrm{O}}_2$ (red dots). The vertical axis on the right gives the linewidth in frequency (MHz), calculated from $\mathrm{\Delta }B$ using the Kittel relation at $B_{\mathrm{ext}}\sim 250$ G and $I_{\mathrm{dc}}=0$.

Figure 6

(a) NV spin-relaxometry measurement sequence as in Fig. 4, with added MW drive. For synchronization measurement, $B_{\mathrm{ext}}$ is tuned such that the NV $m_s=0\leftrightarrow -1$ transition coincides with STO resonance. (b) Measured NV photoluminescence (PL) as a function of the MW drive frequency $f_{MW}$, at $I_{\mathrm{dc}}=5.2\mathrm{mA}$, $B_{\mathrm{ext}}=292\mathrm{G}$, and MW drive amplitude $b_1=1.5\mathrm{G}$. When the MW drive is resonant with the NV transition frequency, a dip in the PL is observed because the driving deplete $m_s=0$ population. Over a frequency interval $\mathrm{\Delta }{f}_s$ the STO can be locked to the MW drive and thus detuned from the NV transition, thereby decreasing the NV spin relaxation and correspondingly increasing the measured PL. When the MW drive frequency is detuned beyond the locking interval (i.e., synchronization bandwidth), the STO remains resonant with the NV transition frequency, leading to strong NV-spin relaxation and a corresponding reduced PL. (Appendix pp6 for detailed data analysis.) (c) 2D map of PL vs $f_{MW}$ and MW drive amplitude $b_1$. The synchronization bandwidth increases linearly with $b_1$. $b_1^{\mathrm{th}}$ is the threshold amplitude at which synchronization begins to occur. (d) Synchronization bandwidth vs $b_1$ at different $I_{\mathrm{dc}}$ (4, 5.2, and 5.6 mA).

Figure 7

Pt/YIG hybrid device fabrication processes. (a) $\mathrm{A}{\mathrm{r}}^{+}$ plasma cleaning inside sputter chamber. (b) DC sputtering of 10 nm Pt. Note: this procedure has successfully generated Pt/YIG interfaces showing excellent spin mixing conductance [43]. (c) Coating substrate with PMMA/HSQ/FOX resist stack. (d) E-beam lithography and developing in TMAH to form etching mask. (e) ${\mathrm{O}}_2$ reactive ion etch to remove excessive PMMA and to induce proper undercut. (f) $\mathrm{A}{\mathrm{r}}^{+}$ milling to transfer pattern from the etching mask onto the substrate. (g) Lift-off to remove the resist stack. (h) E-beam patterning of electrical leads and MW driving lines with proper alignment with respect to existing Pt/YIG microstructures.

Figure 8

(a) SEM image of Pt/YIG hybrid shows smooth edge. Throughout the fabrication process, extra care is taken to preserve material quality, e.g., only mild solvents are used. (b) SEM image of an example YIG disc (∼400 nm in diameter), fabricated with the use of high-resolution e-beam resist.

Figure 9

SOT and its dependence on the relative orientation between injected spins and bias field. (a) Assuming the DC current ${\mathbf{J}}_{\mathbf{e}}$ is along the long direction of the device ($x$ axis), a spin current is sent along the vertical, $z$ direction. The injected spins are necessarily oriented along the short direction ($y$ axis) of the device. Therefore, the ideal orientation of the bias field $B_{\mathrm{ext}}$ is along the $y$ direction, as then the YIG magnetization $\mathbf{M}$ (in the absence of excitation) is parallel to the orientation of the injected spins $\mathbf{s}$. This leads to the maximal spin-orbit torque (SOT) available. The SOT can act either along or against the damping torque (DT), depending on the orientation of injected spins, which is set by the direction of the DC current. (b) Orientation of the NV, and hence ${\mathbf{B}}_{\mathrm{ext}}$, employed in single-spin sensing in this work ($\mathrm{N}{\mathrm{V}}_a$). The projection of ${\mathbf{B}}_{\mathrm{ext}}$ on the $y$ axis is $\sim 0.72|{\mathbf{B}}_{\mathrm{ext}}|$. (c) Orientation of another NV ($\mathrm{N}{\mathrm{V}}_b$) present in the nanobeam. The projection of the corresponding ${\mathbf{B}}_{\mathrm{ext}}$ on the $y$ axis is $\sim 0.08|{\mathbf{B}}_{\mathrm{ext}}|$. (d) Influence of $I_{\mathrm{dc}}$ on SW linewidth measured via NV spin-relaxometry [similar to those shown in main text Fig. 5] but now with $\mathrm{N}{\mathrm{V}}_b$.

Figure 10

Determination of saturation magnetization ($M_s$). (a) NV spin-relaxometry measurements at $I_{\mathrm{dc}}=0$ on $m_s=0\leftrightarrow -1$ transition over a wide range of $B_{\mathrm{ext}}$ (red dots on gray vertical plane). The bottom plane of the figure including green dots showing center frequency of the fundamental SW mode, a blue trace showing a fit to the green dots, and black line indicating the NV $m_s=0\leftrightarrow -1$ transition, is reproduced from main text Fig. 1. The strongest NV spin-relaxometry resonance dip at $I_{\mathrm{dc}}=0$ corresponds to the crossing point of the NV $m_s=0\leftrightarrow -1$ transition and the fundamental mode of the Pt/YIG microstructure at $B_{\mathrm{ext}}=245$ Gauss and $f=2.18$ GHz. (b) To validate our analytical formalism to calculate $M_s$, a micromagnetic simulation (OOMMF) is performed at $B_{\mathrm{ext}}=245$ Gauss with different values of $M_s$. Simulation results (black dots) match very well with analytical calculation (blue line). Red dashed line corresponds to the frequency of the fundamental mode ($f=2.18$ GHz) and the crossing point between this red dashed line and blue line determines the saturation magnetization $M_s$ used throughout this work.

Figure 11

SW mode designation and micromagnetic simulation (OOMMF). (a) This figure is reproduced from main text Fig. 4 with SW mode labeled as $M_1$, $M_2$,…, $M_5$. (b) OOMMF simulation along with NV spin-relaxometry data [line cut from (a)] at $I_{\mathrm{dc}}=0$. Vertical plane (gray color shaded) can be projected onto the NV $m_s=0\leftrightarrow -1$ transition frequency (black diagonal line on the bottom plane). Relaxometry data (red points) and fit (blue line) are in this vertical plane; and the resonance dip can thus be projected onto the NV transition frequency connected via color-coded dashed lines (with the same color as the label of the corresponding mode). Green solid line is OOMMF simulation at bias field of 245 G (along NV axis). Resonance peaks (bulk mode $n=1$, 2, 3; edge modes $n^{\prime }=1$, 2) are visible in simulation. Solid color-coded lines on the bottom plane show well-recognized correspondence between simulated resonance peaks and resonance dips measured with NV spin-relaxometry.

Figure 12

Micromagnetic simulation (OOMMF) of SW spectrum and spatial magnetization profiles for different eigenmodes. (a) OOMMF simulated spectrum (performed at 245 G bias field along NV axis). Vertical axis represents spatially averaged magnetic susceptibility (imaginary part), $\langle {\chi }^{″}\rangle$. (b) and (c) At $f=2.08$ and 2.14 GHz, map of simulated local susceptibility (imaginary part),${\chi }^{″}$, shows an edge mode localized at the corner of YIG microstructure. (d)–(f) At $f=2.18$, 2.26, and 2.36 GHz, map of simulated local susceptibility (imaginary part),${\chi }^{″}$, shows bulk mode sustained over entire YIG microstructur(e) with mode order $n=1$, 2, 3 respectively. All spatial mode profile maps use the same color scale (right bottom color bar).

Figure 13

Estimate of mode hybridization coupling strength. (a) Measured NV upper transition frequencies at 337 G as a function of DC current. The data is fit to a quadratic function (as well as smaller linear and constant terms). (b) NV spin-relaxometry data [from Fig. 4] plotted at the plane of $f_{\mathrm{NV}}\left(B,I_{\mathrm{dc}}\right)$. (c) Frequency value associated with each mode center ($B_{1,2},I_{\mathrm{dc}}$) from (b). (d) Dispersion at a fixed field ($B=284.54\mathrm{G}$) as a function of the DC current.

Figure 14

$\mathrm{ST}{\mathrm{O}}_1$ synchronization test to understand $I_{\mathrm{dc}}$ range of auto-oscillation and extract synchronization frequency interval. (a) NV PL vs field sweep [similar measurements as in main text Fig. 4] at $I_{\mathrm{dc}}=4\mathrm{mA}$ to find mode resonance as indicated by blue arrow. (b) At $I_{\mathrm{dc}}=4\mathrm{mA}$ and $B_{\mathrm{ext}}=270\mathrm{G}$ (mode resonance matching NV transition frequency), we perform 2D sweeping of the MW driving frequency and amplitude and simultaneously record the corresponding NV PL signal. This measurement is the same as that performed in Fig. 6. Here the 2D plot color bar corresponds to the PL level shaded by gray color shown in (a) and a dashed arrow is used to illustrate such correspondence. (c) and (e) show the same field sweep as in a but at different values of $I_{\mathrm{dc}}:5.2$ and 5.6 mA, respectively. (d) and (f) show a similar 2D plot but with different values of both $I_{\mathrm{dc}}:5.2$ and 5.6 mA and $B_{\mathrm{ext}}=292$ and 302.6 G.

Figure 15

Characterization of $\mathrm{ST}{\mathrm{O}}_2$ by testing synchronization to external MW signals. (a) NV PL vs field sweep at $I_{\mathrm{dc}}=5.1\mathrm{mA}$ to find center frequency of free running $\mathrm{ST}{\mathrm{O}}_2$, as indicated by red arrow. (b) At $I_{\mathrm{dc}}=5.1\mathrm{mA}$ and $B_{\mathrm{ext}}=273.4\mathrm{G}$, we perform 2D sweeping of the MW driving frequency and amplitude, and simultaneously record the corresponding NV PL signal. 2D plot color bar corresponds to the PL level covered by the gray shaded region shown in (a) and a dashed arrow is used to illustrate such correspondence. (c) Similar measurement as in (a) but at $I_{\mathrm{dc}}=5.8\mathrm{mA}$, and mode resonance takes place at $B_{\mathrm{ext}}=294\mathrm{G}$. (d) At $I_{\mathrm{dc}}=5.8\mathrm{mA}$, and $B_{\mathrm{ext}}=294\mathrm{G}$, we perform synchronization test measurements. No discernible signal contrast is observed.

Figure 16

Coexistence of STOs and their competing synchronization to external MW source. (a) At $I_{\mathrm{dc}}=5.2\mathrm{mA}$, NV PL vs field sweep shows two resonance peaks, which correspond to $\mathrm{ST}{\mathrm{O}}_2$ (lower field) hence higher frequency) and $\mathrm{ST}{\mathrm{O}}_1$. (b) At $I_{\mathrm{dc}}=5.2\mathrm{mA}$ and $B_{\mathrm{ext}}=292\mathrm{G}$, synchronization test shows a parameter space area with an interesting signal feature surrounded by dashed yellow triangle.