Spin orbit torque nano-oscillators by dipole field-localized spin wave modes

Spin Hall effect (SHE)-spin torque can drive magnetic auto-oscillations or excite propagating spin waves Divinskiy et al. (2018); Fulara et al. (2019); Demidov et al. (2020); Evelt et al. (2018); Fulara et al. (2020) in a ferromagnet Demidov et al. (2012); Liu et al. (2012); Collet et al. (2016), potentially enabling a dc current-tunable microwave source Kiselev et al. (2003); Shao et al. (2021), neuromorphic computing Dieny et al. (2020); Zahedinejad et al. (2020) and spin orbit torque magnonics Divinskiy et al. (2018); Fulara et al. (2019); Demidov et al. (2020); Evelt et al. (2018); Fulara et al. (2020). However, nonlinear magnon scattering can degrade the quality of spin-Hall oscillators broadening linewidth, and hampering the achievement of auto-oscillation Collet et al. (2016); Duan et al. (2014); Barsukov et al. (2019). A ferromagnetic film with spatially extended dimensions harbors a large number of degenerate spin wave modes which can enable nonlinear magnon scattering that redistributes energy between modes, hampering coherent oscillation of a desired mode Duan et al. (2014); Demidov et al. (2011, 2017). These adverse effects can be reduced either by avoiding the degeneracy Divinskiy et al. (2017); Demidov et al. (2012) e.g. via spatial localization or by suppressing the nonlinear mode coupling Divinskiy et al. (2019); Evelt et al. (2018). Spatial localization in, e.g., nanoconstrictions and planar nano-gap contacts Demidov et al. (2012, 2014, 2015a); Liu et al. (2013); Demidov et al. (2015b); Haidar et al. (2019); Awad et al. (2017); Sato et al. (2019); Hache et al. (2020); Spicer et al. (2018); Zahedinejad et al. (2018); Dvornik et al. (2018) produces discrete modes whose frequencies lie below the spin wave dispersion for the extended sample thus reducing scattering channels Demidov et al. (2012); Duan et al. (2014); Fulara et al. (2020) and enabling auto-oscillation. Alternative to geometrical confinement, a localized region of reduced internal magnetic field generated by the dipole field of a nearby micromagnetic particle confines the spin wave modes in a nanoscale magnetic field well Adur et al. (2014); Chia et al. (2012); Lee et al. (2010); Zhang et al. (2017) thus enabling auto-oscillation. Dipole-field localized modes offer advantages as spin-Hall oscillators Zhang et al. (2017): First, in contrast to most geometrically confined oscillator modes, our field confinement offers in-situ tunability. In particular, the lateral confinement and field well depth are tunable by particle parameters—size, moment, particle-sample separation—the latter of which can be altered in-operando, and is continuously controllable if the particle is mounted on a cantilever whose height is variable. This provides an in-situ tunability of the magnon spectrum and mode separations, and hence tuning of nonlinear magnon scattering to control performance of the oscillators. Second, these dipole-field localized modes are confined by magnetic field rather than by sample boundaries thus avoiding artifacts from fabrication imperfection, so they can provide cleaner confinement.

Here, we demonstrate spin-Hall auto-oscillations of localized spin wave modes spatially confined by the magnetic dipole field of a nearby Ni particle above a Py/Pt stripe. Multiple well-resolved localized modes are driven into narrow-linewidth, large-amplitude auto-oscillations persistent up to room temperature (RT). The auto-oscillating localized modes exhibit a minimum linewidth of 5 MHz at 80 K which increases to 18 MHz at RT. We observe a linewidth for the first localized mode that is approximately proportional to temperature and primarily limited by thermal fluctuations. This high quality oscillator with its in-operando tunability of spatial confinement provides a powerful tool for systematic study of the fundamental aspects of spin-Hall oscillators, including the impact of multi-mode interactions, for advancing the future oscillators.

Py (5 nm)/ Pt (5 nm) films are deposited on an undoped-Si substrate by e-beam evaporation. The Py/Pt strips are defined with e-beam lithography using Cr as a hard mask Duan (2013) for ion milling. A Ti/Ag/Au coplanar stripline (CPS) is fabricated on the Py/Pt strip via photolithography. Figure 1(a) shows a scanning electron microscopy image of our device. 3 $\mu\rm m$-width strips provide tapered transitions to the 700 nm $\times$ 1 $\mu\rm m$ region of interest in the center where current density is much higher. This geometry reduces heating and contact resistance. A 150 nm-thick $\text{Al}_{2}\text{O}_{3}$ spacer deposited on the device defines its separation from a 1 $\mu\rm m$ Ni particle located on top, in the center of the active region, with $\pm$ 200 nm accuracy in the strip width direction [see supplement for further details]. We measured two nominally identical devices labeled as Device #1 and Device #2. They show similar results with minimal device-to-device variation [see supplement]. We report measurements performed at temperatures from 80 K to RT with an external field $H_{\text{ext}}$ applied in the film plane at an angle $105^{\circ}$ with respect to the orientation of the current flow along the length of the strip. As depicted in Figure 1(b), the spin Hall effect D’Yakonov and Perel’ (1971); Hirsch (1999) in Pt converts a charge current density $J_{C}$ into a spin current density $J_{S}$, which exerts an anti-damping spin torque $\tau_{\text{ST}}$ Berger (1996); Slonczewski (1996) on the Py magnetization. We apply dc charge currents exceeding the critical current needed to fully compensate the damping and excite the auto-oscillation. The microwave power emitted by the device is detected via anisotropic magnetoresistance (AMR) effect, and measured by a low-noise amplifier and spectrum analyzer Duan et al. (2014); Thadani (2009).

We use a nearby micromagnetic particle to introduce a spatially localized minimum in the internal static field—a field well—in the sample Adur et al. (2014); Chia et al. (2012); Lee et al. (2010); Zhang et al. (2017). The lowest-frequency spin wave modes at the bottom of the well are discrete localized modes (LM) whose frequencies lie well below the spin wave continuum. In addition, a large number of spin wave modes, both sample-confined modes and highest-order localized modes with high mode densities, reside at the top of the field-well at much higher frequencies. The depth of the field-well, typically several hundreds of Gauss, determines the spectral separation between lowest-lying localized modes and the high density higher-frequency modes. The spatial confinement provided by the field-well determines the spectral separations between the various discrete localized modes. The four lowest-frequency localized modes are localized width modes LM1 ($n$ = 1, $m$ = 1), LM2 ($n$ = 2, $m$ = 1), a localized length mode LM3 ($n$ = 1, $m$ = 2), and a localized width mode LM4 ($n$ = 3, $m$ = 1) Zhang et al. (2017). Figure 1(c) shows micromagnetic simulated mode profiles of the lowest-four localized modes in the 700 nm $\times$ 1 $\mu\rm m$ active region. The mode area of LM1 is about 350 nm $\times$ 600 nm.

In summary, a new type of spin-Hall oscillator that is spatially confined by a localizing magnetic field is demonstrated. We observe multiple dipole field-localized spin wave modes driven into auto-oscillation by spin-Hall torque. These localized modes oscillators exhibit good properties: narrow-linewidth, large-amplitude and persistence up to RT. The auto-oscillating localized modes exhibit a linewidth of 5 MHz at 80 K which increases to 18 MHz at RT. We observe that the linewidth of the first localized mode is approximately proportional to temperature, limited dominantly by thermal fluctuations. These results indicate a clean oscillator system which provides opportunity to study auto-oscillators in their intrinsic regime. The concurrence of good properties, proportionality to temperature and field-localization demonstrates the advantages of field-localization method.

For future applications, the dipole-field localization provides an alternative confining mechanism that can assist further studies and help resolve issues in spin-Hall auto-oscillators, e.g. their spatial self-broadening Demidov et al. (2016). In addition, the demonstrated unique strength of localized modes spin-Hall oscillator here can be expanded by putting the particle on a cantilever to scan the localized mode oscillator ($x$ and $y$ directions) and tune well spatial confinement and depth ($z$-direction). We observed signals with sufficiently strong signal-noise-ratio that allows the strip to be widened to a few microns for imaging. Spatial confinement studies tuned by varying cantilever tip-sample separation can reveal the impact of multi-mode interactions on spin-orbit torque auto-oscillation. Finally, the particle-confined localized modes oscillator combined with spatial-scannability can be utilized to study synchronization Awad et al. (2017) and interactions between spatially separate auto-oscillators by varying their lateral separation.

Supplementary Information
Spin orbit torque nano-oscillators by dipole field-localized spin wave modes

Device #1 and Device #2 are patterned on the same substrate with the same dimensions. The particles are carefully selected such that their sizes are very close. As shown in the scanning electron microscope (SEM) images in Figure S1, the particle size of Device #1 is 907 nm $\times$ 837 nm, while the particle size of Device #2 is 917 nm in diameter. The particle-sample separation can be controlled accurately using thin film deposition and atomic force microscopy (AFM) thickness calibration. Figure S2 shows the auto-oscillation results of Device #1. The first localized mode reaches minimum FWHM linewidth of 20 MHz at RT, and 5 MHz at 80 K. The maximum power is 0.23 pW at RT, and 5.1 pW at 80 K. By comparing Figure S2 with Figure 2 (main text), the experimental results from two devices closely resemble each other with minimal device-to-device variation regarding mode structures and oscillator property of minimum linewidth. The spectral separations between localized modes are about the same. There are only two slight differences. First, the resonance frequencies of the localized modes in Device #1 are 0.4 GHz smaller than the frequencies in Device #2. This is due to the slightly larger moment of particle in Device #1. Second, the bias currents in Device #1 are 0.3 $\sim$ 0.5 mA higher than currents in Device #2, and could be due to the slight device-to-device variations. Such closely resembling results support that the localized modes confined by particle-field are away from sample edges, and has avoided variations from the fabrication edge imperfections.

Figure S4 shows the full spectrum with larger frequency range at 700 G, which gives information on which modes are excited in auto-oscillations. The group of the modes at frequency below 6.4 GHz are from localized modes. It is empty from 6.4 to 8.5 GHz, and then there are two high-frequency peaks. The frequencies of the two high-frequency peaks are twice the frequency of the two localized modes, denoted by markers, and therefore are second harmonics of those localized modes. The empty frequency region corresponds to the resonance conditions of the sample-confined modes (SCM). There are signals around those resonance conditions in ST-FMR spectra, but not in auto-oscillation spectra. This result can also be seen by comparing the ST-FMR result in Fig. 3(a) in main text and the auto-oscillation color map at 500 G in Fig. S3(a). Such results are reasonable because there are very high mode densities around those resonance conditions, with both sample-confined modes and higher-order localized modes. The degeneracies between a large number of modes and nonlinear four magnon scattering between multiple modes cause no modes into auto-oscillations.

We measured bare 700 nm $\times$ 1 $\mu\rm m$ Py/Pt stripe without particle as supplementary measurements. The modes in a sub-micron stripe are bulk modes including quasi-uniform mode (QM), backward volume width modes at higher-field side of QM Duan et al. (2015), and surface modes at lower-field side of QM. Figure S7(a) shows ST-FMR spectra with increasing currents at 80 K, at $f$ = 6 GHz. We observed one main peak from quasi-uniform mode, and several smaller peaks from high-$k$ bulk modes. By comparing these spectra with spectra of Device #1 with a particle in Figure 3(a) (main text), it is clear that qualitatively different modes are excited from those different spectra. The Mode A and Mode B peaks become very sharp at high currents, and will be onset for auto-oscillation first, as shown in auto-oscillation color maps at $H_{\text{ext}}$ = 580 G in Figure S7(b) and 700 G in Figure S7(c). Modes A, B, C and D are labeled in both ST-FMR and auto-oscillation spectra, correspondingly.

To glue the Ni particle to the center of the sample, we use optical microscope with micro-manipulators (Alessi REL-3200). A sharp glass tip, made by using a laser-based glass puller (Sutter Instrument P-2000) is inserted in the micro-manipulator. We put a drop of G1 epoxy, 1um-diameter Ni spherical particles (SkySpring Nanomaterials, Inc.) and our sample on a glass slide. We dip glass tip a few microns in to the epoxy to pick up a small droplet and put it on the sample. We then find a desired magnetic particle under the microscope and use another glass tip to pick it up with electrostatic forces. After putting the particle to the center of the sample, the exact position can be further adjusted by the glass tip from different directions. The device is then stored in $\text{N}_{2}$ box to avoid oxidization before the epoxy is cured. This gluing method is modified from a procedure from Ref. Herman (2011).

In the measurements, the soft Ni particle aligns with the external field, with its dipole field anti-align with the external field, creating a spatial field well.