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[Yuji Nakagawa](https://orcid.org/0000-0001-7655-5836), [Hirofumi Suto](https://orcid.org/0000-0003-4387-5862), [Yuya Sakuraba](https://orcid.org/0000-0003-4618-9550), Tomoyuki Maeda

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[Determination of coupling state within a spin-torque oscillator using injection locking](https://mdr.nims.go.jp/datasets/0bb81ccb-7bef-4b4e-bc49-7767cbb7d113)

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Determination of coupling state within a spin-torque oscillator using injection lockingcommunications physics ArticleA Nature Portfolio journalhttps://doi.org/10.1038/s42005-025-02469-4Determination of coupling state within aspin-torque oscillator using injectionlockingCheck for updatesYuji Nakagawa 1 , Hirofumi Suto 2, Yuya Sakuraba 2 & Tomoyuki Maeda1Dynamic interactions betweenmagnetizations enable complex operations in spintronic devices, suchas coupled oscillation in spin-torque oscillators (STOs). Here, we report the experimentaldetermination of coupling states in an STO using an analysis method based on injection locking. TheSTO is developed for assisted magnetic recording in hard disk drives and exhibits coupled oscillationof two magnetic layers and oscillation of a single magnetic layer depending on bias current polarities,with the former operation improving recording performance. While conventional spectrummeasurements yield similar peaks for both oscillations, our method clearly distinguishes between thecoupled and single oscillationmodes through resistancemeasurementsbecauseof the insensitivity ofthe coupled oscillation to injection locking, as supported by simulations. Our results demonstrate thatthe injection lockingmethod provides a sensitive probe for examining coupled oscillation states and iswidely applicable to the development of spintronic devices functionalized through dynamic coupling.Nano-magnets integrated into spintronic devices interact with each otherthrough various mechanisms, including spin-polarized currents, spinwaves, and stray fields1–6. While these interactions sometimes pose chal-lenges for device integration, as seen in the increased error rates in densememory cells of magnetoresistive random access memory (MRAM)5, theycan also deliver higher performance and new functionality in other devices,such as spin-torque oscillators (STOs)1–4,6.In STOs, spin-polarized currents provide spin-transfer torque (STT)and induce auto-oscillating precession in oscillation layers. The inter-actions and subsequent coupling between these layers can lead toincreased power and improved coherency for microwave signal generatorfunctions1–3,6–11, as well as focused field distribution for microwavemagnetic field emitter functions4,12–15. Coupling phenomena also playimportant roles in recently proposed neuromorphic computingapplications3,16–21. However, investigating the details of such coupling hasbeen hindered by the nanometer-scale device size and the gigahertz-range oscillation frequency. In previous studies, analysis of couplingstates has mainly relied on simulations9–14 and spectrum measurements,where multiple oscillation peaks arising from different STOs combine asthe operation bias changes, suggesting coupled oscillations1–3.Another notable phenomenon exhibited by STOs is injectionlocking3,19,22–27. Due to their inherent non-linearity, STO oscillation can besynchronized with an external microwave input, such as a microwavemagnetic field or a microwave electrical signal, when the input power issufficient, and the input frequency is close to the STO oscillation fre-quency. Injection locking has been studied in terms of improving oscil-lation characteristics, such as increased output power and reduced phasenoise. Furthermore, a method for analyzing STOs based on injectionlocking has been proposed and demonstrated recently27, in which the DCresistance change of the STO is monitored during locking to an externalmicrowave magnetic field. Because the oscillation frequency in an STO isrelated to the oscillation angle of the magnetization, frequency mod-ification by injection locking changes the average angle between theoscillation layers and adjacent layers, resulting in resistance changethrough the giant magnetoresistance (GMR) effect. This method hasseveral advantages over spectrum measurement, such as classification ofactual and fictitious oscillation signals.The STO analyzed in this study is designed for microwave-assistedmagnetic recording (MAMR), which is one of the next key technologies inhard disk drives (HDDs)13,28. In this application, the STO is fabricated at thetip of thewriter part of theHDDhead.Oscillation layers, referred to as field-generation layers (FGLs), emit a strayfield as amicrowavemagneticfield at afrequency of a few tens of GHz. This microwave field, through ferromag-netic resonance excitation of themediamagnetization, assists the recordingprocess, inwhich the recordingfield from thewriter part switches themediamagnetizations to the desired direction. Implementation of MAMR has1Corporate Laboratory, Toshiba Corporation, Kawasaki, Japan. 2Research Center for Magnetic and Spintronic Materials, National Institute for Materials Science(NIMS), Tsukuba, Japan. e-mail: yuji.nakagawa.d94@mail.toshibaCommunications Physics |            (2026) 9:17 11234567890():,;1234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s42005-025-02469-4&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s42005-025-02469-4&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s42005-025-02469-4&domain=pdfhttp://orcid.org/0000-0001-7655-5836http://orcid.org/0000-0001-7655-5836http://orcid.org/0000-0001-7655-5836http://orcid.org/0000-0001-7655-5836http://orcid.org/0000-0001-7655-5836http://orcid.org/0000-0003-4387-5862http://orcid.org/0000-0003-4387-5862http://orcid.org/0000-0003-4387-5862http://orcid.org/0000-0003-4387-5862http://orcid.org/0000-0003-4387-5862http://orcid.org/0000-0003-4618-9550http://orcid.org/0000-0003-4618-9550http://orcid.org/0000-0003-4618-9550http://orcid.org/0000-0003-4618-9550http://orcid.org/0000-0003-4618-9550mailto:yuji.nakagawa.d94@mail.toshibawww.nature.com/commsphyspartly started14,15,29, and thus STOs have become the second practical spin-tronic device to be used in HDDs, following the magnetoresistive sensorsused in the reader part for decades30.Recently, STO structures with two FGLs have been proposed forMAMR, referred to as dual-FGL STO4,12,14. During oscillation of this typeof STO, the two FGLs are designed to establish an antiferromagneticconfiguration through dipolar coupling. Coupled oscillation of FGLsgenerates a focused field distribution desirable for improving recordingperformance, and more than 20% increase in recording areal density isexpected4. However, conventional spectrum measurements have notrevealed any distinctive features indicating coupled oscillation in dual-FGL STOs fabricated in HDD heads14. Agreement between observedspectrum peaks and micromagnetic simulations has only indirectlysuggested coupled oscillation14. Therefore, an alternative method forcharacterizing the oscillation states is needed.In this study, we demonstrate the determination of the coupledoscillation state in a dual-FGL STO by utilizing injection locking. Asshown in Fig. 1a, b, the STO is fabricated in a state-of-the-art MAMRhead, and the head is placed on a coplanar waveguide (CPW), whichgenerates an external microwave field for injection locking. Firstly, wefound the STO also operates in the opposite bias current direction, inwhich only one FGL oscillates without coupling. This uncoupled oscil-lation cannot be distinguished from the coupled oscillation by conven-tional spectrum measurements because similar oscillation peaks areobserved for both bias current polarities. In contrast, we observed anunambiguous difference in injection locking whereby the resistancechange appears only for the uncoupled oscillation because the sensitivityto the microwave field differs significantly between the two oscillationstates. The absence of the injection locking effect is attributed to Zeemanenergy cancellation in the antiparallel configuration. The proposedanalysis method provides evidence of the coupled oscillation, a key factorfor higher MAMR performance.Structure and operation of HDD head equippedwith STOFigure 1c, d shows the structure of thewriterpart of anHDDhead.Thebasicstructure consists of a coil, a recording pole, and a shield. The coil currentpolarity reflects the information to be recorded (0 or 1) and determines thedirection of the pole magnetization (up or down). The pole is made of highsaturation magnetization materials, such as FeCo-alloy, and its magneticfield transcribes the information onto perpendicularly magnetized grainsfabricated on the disk. The typical pole width at the tip (y-direction inFig. 1c) and write gap (the gap between the pole and shield) are 50 nm and30 nm, respectively. The shield absorbs the magnetic field emanating fromthe side wall of the pole (Hgap) to enable fine recording. The value of μ0Hgapis typically 1.5 T 14.The STOwas fabricated in thewrite gap forMAMR14 by depositing thefollowing four types of layers on the side wall of the pole: FGL (5-nm-thickFeCo-alloy), spin-injection layer (SIL) (2-nm-thick Py), spin sink, and Cuspacer, in the following order: spin sink/SIL1/Cu/FGL1/Cu/SIL2/spin sink/FGL2/Cu. The oscillation of FGL magnetization, which generates a micro-wavemagnetic field, is driven by STT from spin-polarized electrons injectedfrom the SILs and the shield through the Cu spacers. The spin sink layersinclude heavy metals like Ta with short spin-diffusion lengths to block spininjection at the interface. The fabricated STO has a lateral dimension of45 nm in both y- and z-directions.The STO operates in two distinct modes depending on the polarity ofthe bias current (ISTO), which is applied to the STO through the pole andshield (Fig. 1c, d).Themainmodeof operation forMAMRusespositive ISTO(Fig. 1d)14. Starting from the initial state, where all magnetizations arealigned with the Hgap direction, the SIL1 magnetization flips due to STTfrom the reflected spins at the FGL1 interface. This operation is analogous tothat in STT-MRAM, where the magnetization of the recording layer isswitched to the antiparallel state relative to the reference layermagnetization31,32. After the SIL1 reversal, STT from both the transmittedFig. 1 | Schematic of measurement and STO operations. aHard disk drive (HDD)head supported by a metal arm and placed on a coplanar waveguide (CPW). Thespin-torque oscillator (STO) current (ISTO) and coil current are applied throughHDD leads on the metal arm and electrodes on the side of the HDD head. Amicrowave signal applied to the CPW with a power of PCPW generates a microwavemagnetic field (HCPW). HCPW is injected into the writer part, which is located nearthe edge of the HDD head. b Magnified view of the writer part. An STO with twospin-injection layers (SILs) and two field-generation layers (FGLs) is fabricatedbetween the pole and shield. The STOwidth is 45 nm. c, d Expected STO operationswith negative and positive ISTO, respectively. SIL1 (Py), FGL1 (FeCo), SIL2 (Py), andFGL2 (FeCo) are separated by Cu spacers (light gray) or spin sinks (dark gray). TheCu spacers enable spin-transfer torque (STT) interaction between the magnetiza-tions (purple arrows) of adjacent layers. The coil currentmagnetizes the pole, and themagnetic field from the pole (Hgap) is applied to the STO. With negative ISTO, onlyFGL1 exhibits oscillation (c), while with positive ISTO, both FGL1 and FGL2 oscillatewith antiparallel coupling (d). e STO resistance (RSTO) as a function of ISTO. Thesteps on the negative and positive sides correspond to SIL2 and SIL1 magnetizationreversal, respectively. The vertical dashed lines indicate the ISTO values where dRSTO/dISTO exhibits peaks.https://doi.org/10.1038/s42005-025-02469-4 ArticleCommunications Physics |            (2026) 9:17 2www.nature.com/commsphysspins fromSIL1 and reflected spins at the SIL2 interface work to generate theoscillation (precession) of the FGL1 magnetization. At the same time, STTfrom the reflected spins at the shield interface, where a higher spin-polarization layer (e.g., FeCo-alloy) is attached33, induces the oscillation ofFGL2. This simultaneous oscillation of FGL1 and FGL2 magnetizations isaimed at forming an antiparallel coupling in the in-plane direction via thedipolar field. The resulting localized microwave magnetic field distributionis particularly suitable for MAMR 4,15.This STO should also exhibit an alternative mode of operation withnegative ISTO, where only the FGL1 magnetization is expected to oscillatedue to STT fromSIL1 and SIL2 (Fig. 1c). In contrast to the positive ISTO case,the magnetization reversal occurs in SIL2. The STT from reflected electronsat the FGL2 interface does not affect the shield due to the large volume of theshield, and the FGL1 and shield magnetizations remain in the initial con-figuration. We note that the change in the coil current polarity reverses thedirection and trajectory of the magnetization of all magnetic layers in theSTO, thus maintaining the relationship between the ISTO polarity and theresulting oscillation mode.Figure 1e shows the two-terminal STO resistance (RSTO) as a functionof ISTO. The parabolic behavior arises from Joule heating, which is caused byhigh current density on theorderof 108A/cm2.Additionally, resistance stepsappear both onpositive andnegative ISTOat ±1mA, corresponding toGMReffects due to magnetization reversals of SIL1 and SIL2, respectively.Although another resistance step is expected due to FGL2 magnetizationreversal above+5mA14, we did not use such a large current in this study tominimize damage in the STO.Results and discussionPreparation of the injection-locking measurementTo study the injection locking behavior of STOs to an external micro-wave, we used a CPW, which generates an Oersted magnetic field fromthe signal line upon application of a microwave signal. The CPW wasfabricated on a sapphire substrate by depositing an electrode film withTa(10 nm)/Cu(200 nm)/Ta(10 nm)/Au(100 nm), patterning the film intoa CPW structure with a 3-μm-wide signal line and a 3-μm gap betweenthe signal line and the ground, and depositing an SiO2 non-conductingcoating layer.To precisely position the HDD head above the center of the CPW, weused the reader part of the HDDhead30. The HDD reader utilizes tunnelingmagnetoresistance (TMR) to detect the vertical magnetic field frommagnetic grains on the disk. The TMR reader consists of two magneticlayers separated by an MgO barrier. The magnetization of one magneticlayer is pinned vertically along the z-axis (Fig. 2) via exchange couplingwithan antiferromagnetic material (typically IrMn), while the other layer (thefree layer) has its magnetization biased along the y-axis. Amagnetic fieldHzin the+z or -z direction alters the relative magnetization orientation of thetwo layers, leading to an increase or decrease of TMR, respectively. Thewidth of the TMR reader is less than 20 nm, which is more than two ordersof magnitude smaller than the CPW width.During the positioning, a DC current was applied to the TMR reader,while a low-frequency (1013Hz) AC current (ICPW) of 9.1mAwas appliedto the CPW. The resultingACvoltage (VAC) in the TMR reader, induced bythe CPW’s Oersted field, was measured using a lock-in amplifier. Therelative positionbetween theheadand theCPWwas scannedusing steppingmotors (see Methods for sample alignment details).Figure 2c, d shows the result of the scan. The resistance map (Fig. 2d)clearly reproduces the shape of CPW (Fig. 2e, f). The sign reversal aty = 0 μm and the larger amplitude at x =−50 to 50 μm are consistent withthe magnetic field direction and higher current density in the signal line ofthe CPW, respectively. The y-direction profile of the reader output wasreproduced by simulation assuming a uniform current density in the CPWsignal line, a linear response of the TMR sensor to the magnetic fieldamplitude obtained from Biot–Savart law, and the distance between theHDD head and the CPW of 3 μm (Fig. 2c), where the distance affects thepeak and bottom position ofHz in the y-direction (see also SupplementaryFig. 1). In Fig. 2c, we plotted the experimental result and simulatedHzwithslightly different zero positions in the vertical axis. The offset appearing inthe experiment can be attributed to the contribution from themagneticfieldalong the y-axis. We used the position x = y = 0 μm for the followinginjection locking measurements.Spectrum and injection locking experimentsFigure 3a–c shows the setup and the result of conventional spectrummeasurements. While applying a DC coil current of 50mA, we swept ISTO.The oscillation of the GMR signal at a frequency of fSTO generated by themagnetization oscillation was measured using a spectrum analyzer afterseparating the DC signals using a bias tee and amplifying the signal byaround +50 dB. For these measurements, we used radio frequency (RF)probeswith a bandwidth of 50GHz and directly contactedbareHDDheadsextracted from the production process (Fig. 3a) because the original HDDFig. 2 | Alignment of the HDD head and CPW.a Schematic of the reader part in the hard disk drive(HDD) head, fabricated close to the writer part. Thetunneling magnetoresistance (TMR) reader consistsof an MgO barrier, a pinned layer, and a free layer.b Expected magnetization orientation in the TMRreader depending on the position relative to thecoplanar waveguide (CPW). The free layer magne-tization changes along the direction of the magneticfield generated by the current in the CPW (ICPW),resulting in a change in TMR. c Reader signal (VAC,left axis) and calculated magnetic field in the z-direction (Hz, right axis) during the y-scan atx = 0 μm. VAC is normalized by the maximum valueduring the whole scan in (d). A distance of 3 μm isassumed between the HDD head and the CPW forthe calculation of Hz. Vertical dashed lines indicatethe designed positions of the CPW edges. d Colormap of the reader signal. The vertical pink line atx = 0 corresponds to the scan line in (c). e Opticalmicroscope image of the CPW. f Drawing of theCPW design.https://doi.org/10.1038/s42005-025-02469-4 ArticleCommunications Physics |            (2026) 9:17 3www.nature.com/commsphysleads are incapable of transmitting weak high-frequency signals (seeMethods for spectrum measurement details).Figure 3c shows the spectrum measured with positive ISTO. Weobserved a peak suggesting the coupled oscillation state from fSTO = 19GHzat ISTO =+2mA until 20 GHz at +4mA. This disappearance of the oscil-lation at +4mA is thought to be due to STT imbalance14. In the negativeISTO case (Fig. 3b), a peak is also observable from ISTO =− 2 to−5mAwitha similar frequency to the positive ISTO case, which are expected to originatefrom an isolated FGL1 oscillation. We note that the signals arising from thedifference in oscillation frequencies between FGL and SIL, so-called ficti-tious peaks, were not detected in our experiments and simulations, incontrast to previous studies26,27,34. This may be attributed to the smallerthickness of the SIL in our devices.Figure 3d–f shows the setup and the results of the injection lockingmeasurement. The production-level HDD head and CPW were aligned asdetermined previously (Fig. 2). Using a signal generator, we applied high-frequency signals to the CPW set to a power of PCPW and a frequency offCPW, generating a microwave magnetic field (HCPW) that is injected to theSTO. The signal was generated with a 50% duty with a modulation fre-quency of 1 kHz.ADCcoil current of 50mAand ISTOwere applied throughthe HDD leads (Fig. 3d). The resistance difference between the cases withand without HCPW (ΔRSTO) was monitored with a lock-in amplifier syn-chronizedwith the signal generator at 1 kHz. The 1 kHz signal can be easilymeasured through the HDD leads (see Methods for injection lockingmeasurement details).Figure 3e, f shows the dependence of ΔRSTO on fCPW mapped as afunction of negative and positive ISTO, respectively, using the same HDDhead as in Fig. 3b, c.On the negative bias side, a clear injection locking signalis observed in which ΔRSTO changes from positive to negative as fCPWincreases. This signal appears at the same frequency (19–20 GHz) and in thesame ISTO (−2 to−5 mA) as the signal in Fig. 3b. However, on the positiveISTO side, no injection locking signalwasdetectedat thepositionof the signalobserved in Fig. 3c. This absence of a locking signal for positive ISTOhighlights a clear distinction between the two bias polarities.Figure 4a–d shows the comparison between the results for spectralmeasurement and injection locking measurement at ISTO =+3.0 and−5.0 mA. In thenegative ISTOcase, the frequencyof thepeakobserved in thespectrummeasurement (Fig. 3b)was identical to the center frequency of theinjection locking signal (Fig. 4a). In contrast, as shown in Fig. 4b, theinjection locking signal is not detectable in the positive ISTO case, and onlythe spectrum peak appeared.Injection measurement results at other PCPW values are plotted inFig. 4c, d. At ISTO =−5.0mA, the locking bandwidth increases withincreasing PCPW andHCPW, consistent with the previous study27. The slopeof ΔRSTO with respect to fCPW is independent of PCPW, suggesting thatΔRSTO originates solely from the locking effect to fCPW, where the rela-tionship between fSTO and the oscillation cone angle (the angle between thex-axis and the magnetization) determines ΔRSTO. At ISTO =+3.0mA, noinjection locking signal was observed even at+15 dBm, further confirmingthe absence of this effect for positive ISTO.To investigate the absence of injection locking for positive ISTO inmore detail, we repeated the measurements with PCPW of 15 dBm (Fig. 5)since higher power gives a wider locking range. We found that a lockingsignal exists within a narrow current range between ISTO =+1mA,where the SIL1 reversal occurs, and ISTO =+2mA, where the clearspectrum peak was observed in Fig. 3c. Further increasing ISTO above+2mA results in diminished locking signal. This result indicates thateven with positive ISTO, injection locking can occur after the oscillationappears and before the coupled oscillation becomes stable. After thecoupled oscillation becomes stable at +2mA, the locking signal dimin-ishes because the coupled oscillation is insensitive to injection locking.The locking signals in Fig. 5 mainly consist of negative ΔRSTO values incontrast to the symmetric behavior observed in Fig. 4c. This indicatesthat the locking behavior in the unstable coupled oscillation state withFig. 3 | Experimental setup and results for spectrum and injection lockingmeasurements. a Setup for spectrum measurement. Radio frequency (RF) probescontact the hard disk drive (HDD) head pads directly. A DC coil current and a spin-torque oscillator (STO) current (ISTO) are applied, and the RF signal generated bySTO oscillation is separated by the bias tee andmeasured at a frequency of fSTO withthe spectrum analyzer after amplification. b, c Spectrum measurement results withnegative and positive ISTO, respectively. The intensity is measured from the noisefloor. d Setup for injection locking measurement. Microwave power (PCPW) with afrequency of fCPW is applied to the coplanar waveguide (CPW), generating amicrowave magnetic field (HCPW). The resistance change (ΔRSTO) due to injectionlocking is monitored by the lock-in amplifier connected to the HDD leads, whichalso supplies the coil current and ISTO. e, f Injection locking measurement results atPCPW = 10 dBm with negative and positive ISTO, respectively. The vertical dottedlines in (b, c, e, f) indicate ISTO values for spin-injection layer flipping (sameas Fig. 1e).https://doi.org/10.1038/s42005-025-02469-4 ArticleCommunications Physics |            (2026) 9:17 4www.nature.com/commsphyspositive ISTO is more complicated than that in the single oscillation statewith negative ISTO.Since the injection locking does not occur at a fictitious peakfrequency26, the observed injection locking signal at smaller ISTO in Fig. 5reflects the actual oscillation of FGLs. Therefore, this result supports that thespectrumpeaks at larger ISTO inFig. 3c are also related to actual oscillationofFGLs, because the peaks appear continuously at 19 GHz and atISTO =+2mA (Figs. 3c and 5a) without any anomaly in RSTO (Fig. 1e).Injection locking simulationFor a deeper understanding of the observed injection locking signals, weperformedmicromagnetic simulations12,14. The simulationmodel includes apart of the pole and shield and whole magnetic layers of the STO, with thesame thicknesses as in the experiments. Because Hgap is underestimated inthis model due to the partial head structure, we added a uniform externalDC magnetic field of 0.4 T in the x-direction to align μ0Hgap with thereasonable value of 1.5 T.We applied a uniformmagnetic field oscillating inthe y-direction as HCPW. The magnetization dynamics of each elementfollows the Landau–Lifshitz–Gilbert (LLG) equation with an STT term4,35.Other simulation parameters are listed in Supplementary Table 1.Figure 6a–d shows the simulated STO spectra as a function of fCPW forISTO =−2.6 and+2.0 mA and for severalHCPW values. In the negative ISTOcase (Fig. 6a, c), fSTO was in line with fCPW in the fCPW range from 19.5 to20.5 GHz and 18 to 22 GHz, respectively. Such frequency alignmentaccompanied by an increase in the oscillation amplitude and reduction ofoscillation linewidth is a typical feature of injection locking26,27. The lockingbandwidth increases with increasing HCPW (Fig. 6c), consistent with theexperimental trend in Fig. 4c.For comparison with measurements, we evaluated ΔRSTO values bycalculating the sum of the resistance changes due to the GMR effect at thethree interfaces (SIL1/FGL1, FGL1/SIL2, and FGL2/shield) and taking itsaverage over 80 ns. The resistance change was defined by -cosθ, where θ isthe relative angle between the two magnetization directions across theinterface. The simulated ΔRSTO exhibited a decrease (increase) at fre-quencies lower (higher) than the intrinsic fSTO and reproduced the experi-mental result. Additionally, the bottom figure in Fig. 6e shows the averagedphase of FGL1 magnetization relative to HCPW. The phase also showedpositive (negative) shift in the lower (higher) side of fCPW compared to fSTO.The phasewas zero on average out of the locking regime of fCPWbecause themagnetization oscillation andHCPWwere uncorrelatedwithout locking.Wenote that the relative phase of the injection locking is different from that offerromagnetic resonance, where 90 degrees is obtained at the resonant peak.In contrast to the negative ISTO case, no locking behavior was observedin the positive ISTO simulations with HCPW= 2.0 mT (Fig. 6b), which cor-responds to the same amplitude as in Fig. 6c. However, with a much largeramplitude of 40.0 mT, locking did occur as shown in Fig. 6d, f. The lockingrange is small considering the large HCPW value of 40.0mT, and the fre-quencydependenceofΔRSTO is reversed compared to thenegative ISTO case.In the bottom figure in Fig. 6f, we plotted the phase of the FGL2 magneti-zation relative toHCPW atHCPW = 40.0 mT, as well as the phase of FGL1 forvarious HCPW values (0.5–40.0mT) in the positive ISTO case. The relativephasewasnon-zero at the locking center and shows antisymmetric behaviorbetween FGL1 and FGL2 magnetizations. Furthermore, the relative phasesof FGL1 andFGL2magnetizationswere swapped at some calculation points(fCPW = 19.6 and 20.3 GHz), indicating a more complicated dynamicsduring the locking as discussed later.Figure 6g, h is the time-domain plots of the oscillation behavior of theFGLs during injection locking in the negative and positive ISTO cases at thecenter frequency of the locking, 20.4 and 19.9 GHz, respectively. Withnegative ISTO, the FGL1 oscillation was locked in phase withHCPW (Fig. 6g).FGL2 magnetization also oscillated slightly in the same phase as HCPW.However, with positive ISTO,HCPW lies between FGL1 and FGL2 oscillationsFig. 4 | Comparisons between spectrum andinjection locking measurement results.a, b Spectrum intensity (Top) and resistance change(ΔRSTO) due to injection locking for PCPW = 10 dBm(Bottom) as functions of fSTO (Top) and fCPW(Bottom) at ISTO =−5.0 (a) and+3.0 mA (b), wherePCPW, fSTO, fCPW and ISTO are the microwave powerapplied to the coplanar waveguide (CPW), theoscillation frequency of the spin-torque oscillator(STO), the microwave frequency applied to theCPW, and the STO current, respectively.c, d Injection locking result at ISTO =−5.0 and+3.0 mA, respectively, with various PCPW (0, 5, 10,15 dBm). The vertical dashed lines in a (Bottom),b (Bottom), c, and d indicate the peak positions inthe spectra (a (Top) and b (Top)).https://doi.org/10.1038/s42005-025-02469-4 ArticleCommunications Physics |            (2026) 9:17 5www.nature.com/commsphys(Fig. 6h). As summarized in the bottom figures of Fig. 6f, the relative phaseswere slightly smaller than 90 degrees, indicating that the FGL1 and FGL2magnetizations were canted from the antiparallel configuration.The simulation results can explain why the coupled state is insensitiveto injection locking. As shown in Fig. 6g, when only a single FGL is oscil-lating (negative ISTO), the system can minimize its Zeeman energy bysynchronizing its phase withHCPW. Although the STO needs to change itsoscillation frequency to align fCPW, the locked state is energetically preferred.However, in the case of coupled oscillation case (positive ISTO), there is atrade-off betweenFGL1 andFGL2 in terms ofZeeman energyminimization.Although each FGL prefers to align with HCPW, it is prevented by theirantiferromagnetic coupling.OnlywhenHCPW is sufficiently strong canbothFGLs approachHCPW symmetrically and form a canted configuration. Theorder of crossing my = 0 can be either of FGL1-HCPW-FGL2 (Fig. 6h) andFGL2-HCPW-FGL1. Because both configurations are stable, the latter con-figurationwasoccasionally observedduring the simulation (fCPW = 19.6 and20.3 GHz in Fig. 6f (Bottom)).Based on the estimated distance of 3 μm between the HDD head andthe CPW(Fig. 2c and Supplementary Fig. 1), we can also estimate theHCPWgenerated for each PCPW in the experiment. Assuming no signal loss in theCPW and RF cables between the CPW and signal generator, the values ofμ0HCPW are 0.25, 0.45, 0.80, and 1.42 mT for PCPW = 0, 5, 10, and 15 dBm,respectively. Although there is a difference in the locking range between theexperiment (0.3 GHz at PCPW = 15 dBm) and the simulation (2 GHz atμ0HCPW = 1.42 mT), this discrepancy is partly attributable to signal loss inthe CPW at frequencies around fCPW = 20GHz.We discuss the relationship between the sign of ΔRSTO and fCPW.Because the injection locking leads to resistance change at the threeinterfaces (SIL1/FGL1, FGL1/SIL2, and FGL2/shield), the interpretation ofΔRSTO is not straightforward. In the negative ISTO case, only FGL1 isoscillating, and the first two interfaces are responsible for the ΔRSTOchange. Injection locking in STO generally modulates the oscillation coneangle, which increases with higher fSTO and fCPW than the original fSTO(see Fig. 1e in ref. 27). In the negative ISTO with higher fSTO, since SIL1and SIL2 are non-flipped and flipped, respectively (Fig. 1c), the anglebetween SIL1 and FGL1 increases, and SIL2 and FGL1 decreases at thesame time, leading to a cancellation of ΔRSTO. Nevertheless, distinctnegative ΔRSTO signals were observed in higher fCPW sides, and as well aspositive ΔRSTO signals on the lower fCPW sides (Figs. 4c and 6e), whichindicates that the FGL1/SIL2 interface is more dominant than the SIL1/FGL1 interface. Our simulation results suggest that this asymmetry arisesbecause the out-of-plane component of magnetization is larger in theflipped SIL2, while the non-flipped SIL1 has a larger in-plane componentand can exhibit oscillation12. In the experiment, the non-symmetricity ofGMR response, where GMR is more sensitive to changes in the relativemagnetization angle around 180 degrees than around 0 degrees36, mayfurther contribute to this antisymmetric behavior between the SIL1/FGL1and FGL1/SIL2 interfaces.With positive ISTO (Fig. 1d), SIL1 is flipped, and its interface is moreinfluential onΔRSTO than the non-flipped SIL2 interface. Because the sign ofΔRSTO is determined by the flipping, the contribution to ΔRSTO from SIL1/FGL1 and FGL1/SIL2 interfaces leads to the same ΔRSTO-fCPW relationshipas in the negative ISTO case. However, the resistance change at the shield/FGL2 interface,where the shieldmagnetization is non-flipped, is addedwiththe same sign as theFGL1/SIL2 interface andovercome that at theFGL1/SIL2interface. Therefore, the frequency dependence of ΔRSTO is reversed com-pared to the negative ISTO case. However, this reversed behavior is notaccessible in the experiment due to limitations on the achievable PCPW.Finally, we comment on other advanced techniques for analyzingnanoscale magnetization dynamics. As described in the introductory section,superimposing a microwave electrical signal on a bias current is another wayto induce injection locking in STOs3,22–24. In this type of injection locking, theoscillating STT synchronizes with the magnetization oscillation. However,because multiple spin injections occur at the three interfaces: SIL1/FGL1,FGL1/SIL2, and FGL2/shield, the oscillating STT cannot be clearly defined inthe dual-FGL STO. Even if oscillation state dependence on sensitivity tocurrent-based injection locking can be observed, the interpretation will becomplicated. In contrast, injection locking by microwave magnetic fieldsensures that both FGLs experience the same microwave field, allowing forelucidation of their coupling state, as discussed from the viewpoint of Zee-man energy minimization. In addition, microwave electrical signal injectionrequires high-frequency-compatible lead designs, which are unnecessary forapplications like MAMR. On the other hand, the microwave magnetic fieldcan be injected without such design constraints, and injection locking can bedetected by measuring ΔRSTO.Recently, combining current-based injection locking with opticaldetection of magnetization was proposed for analyzing a coupling state ofmultiple oscillators separated by a few hundred nanometers in the in-planedirection of the thinfilms6,37.While thismethod offers the advantage of real-space imaging, its spatial resolution limited by the wavelength of light isinsufficient for dual-FGL STOs, where the two FGLs are separated by only afew nanometers in the stacking direction of the thin films. Onlysynchrotron-based x-ray magnetic circular dichroism (XMCD) offers bothspatial and temporal resolutions compatible with the size and frequency ofSTOs38–40. Additionally, to combine themicrowave field injectionwith theseimaging techniques, a CPW must be placed while keeping the deviceaccessible by light or x-ray, whereas our resistance-based detection can beeasily implemented by attaching a CPW to the surface of the devices.ConclusionsIn conclusion, we have developed a method for detecting the couplingstate in STOs by utilizing injection locking with an external microwaveFig. 5 | Injection locking measurement resultswith a larger PCPW. aMapping of resistance change(ΔRSTO) due to injection locking at PCPW = 15 dBmwith fCPW and positive ISTO sweeping, where PCPW,fCPW and ISTO are the microwave power applied tothe coplanar waveguide (CPW), the microwavefrequency applied to the CPW, and the spin-torqueoscillator (STO) current, respectively. The verticaldashed line indicates the ISTO value for spin-injection layer flipping (same as Fig. 1e). b Injectionlocking result at PCPW = 15 dBm and ISTO from 1.0to 2.0 mA. The plots are shifted vertically by 1 mΩfor clarity.https://doi.org/10.1038/s42005-025-02469-4 ArticleCommunications Physics |            (2026) 9:17 6www.nature.com/commsphysmagnetic field. We demonstrated this technique on an STO fabricatedin a state-of-the-art HDD head. While conventional spectrum mea-surement cannot differentiate the oscillation states, yielding similarresults for different bias polarities, our injection locking measurementclearly distinguished between single, coupled, and unstable coupledoscillation states and confirmed the designed coupled oscillation in theSTO, which offers improved oscillation properties and a broader areaof applications. Our method utilizes resistance measurement and anexternal CPW as a microwave field source, eliminating the need forhigh-frequency output detection or integration of a CPW, which areoften incompatible with device structures. Therefore, our methodoffers a versatile and broadly applicable approach for detecting oscil-lations and studying coupling effects in both laboratory- andproduction-level spintronic devices.Fig. 6 | Simulation results of injection locking.a–d Spectrum intensity mapping during injectionlocking at (ISTO, μ0HCPW) = (−2.6 mA, 0.5 mT) (a),(2.0 mA, 2.0 mT) (b), (−2.6 mA, 2.0 mT) (c), and(2.0 mA, 40.0 mT) (d), where ISTO and HCPW is thespin-torque oscillator (STO) current and themicrowave magnetic field oscillating in the y-direction, respectively. The bottom and vertical axesare the oscillation frequencies of HCPW (fCPW) andthe STO (fSTO), respectively. e, f Resistance change(ΔRSTO) due to injection locking (Top) and oscilla-tion phase of the first field-generation layer (FGL1)relative to HCPW (Bottom) during injection lockingat ISTO =−2.6 (e) and +2.0 mA (f). Results atμ0HCPW = 0.5–2.0 mT are plotted in both (e) and (f).The results for μ0HCPW = 40.0 mT and the phase ofFGL2 are added to (f). Vertical dotted lines indicatethe frequencies used for (g) and (h). g, h Time-domain plots of themagnetization in the y-direction(my) andHCPW at ISTO =−2.6 mA (g) and+2.0 mA(h). fCPW was set to the center of the locking band-width for each case.my andHCPW were normalized.https://doi.org/10.1038/s42005-025-02469-4 ArticleCommunications Physics |            (2026) 9:17 7www.nature.com/commsphysMethodsSample alignmentThe CPW was mounted on a 6-axis (x, y, z, θx, θy, and θz) positionercontrolled by stepping motors with a resolution of 50 nm in x- and y-directions (Kohzu precision YA07A-R202). First, we roughly aligned theCPW to theHDDhead using CCD cameras. For fine positioning, we used aTMR sensor fabricated in the HDD head, as described in the main text.During the scan in the x-y plane, we applied a 1013Hz sinusoidal voltage tothe CPW from a function generator (NF corporation WF1946) and a DCcurrent to the TMR sensor from a DC current source (Keithley 6221)through the HDD leads. A lock-in amplifier (NF corporation LI5640)measured the output voltage.SpectrummeasurementFor the spectrum measurement, we contacted the electrode pads ofthe HDD head directly, using RF probes applicable up to 50 GHz.ISTO and the coil current are supplied by DC current sources(Keithley 6221 and Keysight B2961A, respectively). After separatingthe RF signals using a bias tee (Keysight 11612B), we amplified thesignal using two RF amplifiers (B&Z Technologies BZP140UD1X2 onthe bias tee side and Keysight 83050A on the spectrum analyzer side).The total gain was around 50 dB. A resolution bandwidth of 1 MHzwas used as a measurement parameter of the spectrum analyzer(Keysight N9030A). We subtracted the noise floor as background,which is the spectra at ISTO = 0 mA.Injection locking measurementAfter the sample alignment, the DC current sources for ISTO and the coilcurrentwere connected to theHDDhead through theHDD leads.A lock-inamplifier (NF corporation LI5640) is also connected to the ISTO line. From asignal generator (Keysight E8257D with a high output power option), RFsignalswere applied to theCPWwith apulsemodulationwith amodulationfrequency of 1 kHz at a 50% duty cycle. The lock-in amplifier measured thevoltage (resistance) difference in the STO betweenwith and without the RFsignals, while sweeping the frequency of the RF signals (fCPW) in 0.05 GHzsteps at a rate of 0.1 s per point.Data availabilityThe related data are available from the corresponding author on reasonablerequest.Received: 26 June 2025; Accepted: 15 December 2025;References1. Kaka, S. et al. Mutual phase-locking of microwave spin torque nano-oscillators. Nature 437, 389–392 (2005).2. Mancoff, F. 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All authorsdiscussed the results and wrote the manuscript.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s42005-025-02469-4.Correspondence and requests for materials should be addressed toYuji Nakagawa.Peer review information Communications Physics thanks HimanshuFulara, Pranaba Muduli and the other, anonymous, reviewer(s) for theircontribution to the peer review of this work. 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To view a copy of thislicence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2025https://doi.org/10.1038/s42005-025-02469-4 ArticleCommunications Physics |            (2026) 9:17 9https://doi.org/10.1109/IEDM19574.2021.9720691https://doi.org/10.1109/IEDM19574.2021.9720691https://doi.org/10.1109/IEDM19574.2021.9720691https://doi.org/10.1038/s42005-025-02469-4http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/www.nature.com/commsphys Determination of coupling state within a spin-torque oscillator using injection locking Structure and operation of HDD head equipped with STO Results and discussion Preparation of the injection-locking measurement Spectrum and injection locking experiments Injection locking simulation Conclusions Methods Sample alignment Spectrum measurement Injection locking measurement Data availability References Acknowledgements Author contributions Competing interests Additional information