Introduction

Manipulation of magnetization by spin-orbit torques (SOTs) forms the basis of several promising spintronic technologies such as SOT memory (SOT-MRAM)1,2,3,4,5,6, SOT oscillators7,8,9, neuromorphic computing devices10,11,12,13,14, and SOT-based magnonic logic15,16. Additionally, SOT oscillators serve as a test bed for fundamental studies of strongly nonlinear magnetization dynamics in nanoscale ferromagnets (FMs)17.

The simplest type of SOT oscillator is the spin Hall oscillator (SHO)18,19,20,21,22,23. SHO is based on a bilayer of an FM and a non-magnetic heavy metal (HM), as illustrated in Fig. 1a. A direct electric charge current in the HM layer flowing along the x-axis gives rise to a pure spin current density js along the z-axis (gray dashed arrow) with its magnetic polarization parallel the y-axis (green arrows). Interaction of js with the FM magnetization M gives rise to spin Hall torque τst ~ js opposing the Gilbert damping torque τg. We use the term polarization to refer to the direction of the electron magnetic moment of spin current.

Fig. 1: Spin Hall oscillator dynamics.
figure 1

a Persistent magnetization dynamics in a conventional spin Hall oscillator. Applied direct current Idc leads to spin Hall current js (gray dashed arrow) from heavy metal (HM), which applies spin Hall torque τst (orange arrow) that compensates the Gilbert damping torque τg (dark blue arrow) and drives persistent precession (arrows showing elliptical precession trajectory) of the ferromagnet (FM) magnetization M (red arrow). The spin current is polarized in the plane of the FM film (green arrows), and an external field H is applied to define the precession axis (large black arrow), leading to small-angle precession of magnetization due to the effective field torque τH (turquoise arrow). b Easy-plane spin torque oscillator dynamics. In this geometry, easy-plane magnetic anisotropy is perpendicular to the FM layer plane, and spin Hall current is polarized perpendicular to the easy plane. Spin Hall torque τst pulls M out of the easy plane, and the anisotropy torque τa (turquoise arrow) drives large-amplitude circular magnetization precession around the anisotropy field Ha that is perpendicular to the easy plane.

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When js exceeds a critical value proportional to the FM Gilbert damping parameter α, τst overcomes the damping τg and excites persistent auto-oscillatory elliptical magnetization precession around the equilibrium direction of M. The lowest critical current is observed for M magnetized in the −y-direction by an applied field H.

For easy-plane (EP) magnetic anisotropy coinciding with the FM layer plane, the precession trajectory is elliptical, as shown in Fig. 1a. The precession frequency increases with increasing H and the anisotropy field Ha, and decreases with increasing precession amplitude due to the negative nonlinear frequency shift in this geometry24. The amplitude of precession first increases with increasing js but then saturates at precession cone angles typically not exceeding 20° due to the nonlinear damping mechanism21,25,26. The current-driven auto-oscillations of M generate microwave voltage due to the FM magnetoresistance. The frequency and amplitude of this microwave voltage depend on js, and thus SHOs are electrically tunable microwave signal generators of nanoscale dimensions24.

SHO generators of microwave signals with high output power and low phase noise are desirable for applications10,27. Large-amplitude persistent magnetization dynamics with the precession cone angle of nearly 90° have been predicted for EP FMs upon injection of spin current polarized normal to the easy plane28,29,30. Such type of an EP-SHO with the magnetically easy xz-plane is shown in Fig. 1b. In contrast to the conventional SHO in Fig. 1a, large-amplitude precessional dynamics in EP-SHOs is excited immediately above the critical current28.

The EP-SHO magnetization is tilted out of the EP by the spin Hall torque τst, whereupon it processes with large amplitude around the anisotropy field Ha parallel to the y-axis31. The critical current for these dynamics is defined by a smaller magnetic anisotropy present within the dominant EP anisotropy rather than by the FM Gilbert damping28,29,30. The EP-SHO can operate in zero external magnetic fields, which is desired for many applications. The EP-SHO system is especially attractive for the realization of a magnetic spiking neuron, as has been proposed in several recent theoretical publications32,33,34. The EP-SHO is predicted to generate a large-amplitude sub-nanosecond output voltage pulse in response to an input current pulse exceeding a threshold value. Null output is expected for sub-threshold input pulses. This is the characteristic behavior of a spiking neuron.

Large-amplitude EP persistent dynamics have been theoretically studied in spin-transfer-torque nanopillar devices30,31 but have yet to be explored in SOT devices, such as SHOs. Here we report the experimental realization of a nanowire EP-SHO based on a Pt∣FM bilayer, where FM is a Co∣Ni superlattice35,36,37,38,39,40. The EP-SHO dynamics are achieved via tuning the Co∣Ni perpendicular magnetic anisotropy (PMA) and the magnetic shape anisotropy of the nanowire to manufacture an easy plane defined by the wire axis and the film normal (xz-plane) as shown in Fig. 2a. We present measurements and micromagnetic simulations demonstrating that the microwave power generated by the SHO is maximized when the magnetic easy-plane energy landscape is realized. Our results are relevant for the engineering of scalable, high-power SHOs for wireless communications41, neuromorphic computing12,42,43, room-temperature radio frequency bolometers27, and microwave-assisted magnetic recording44.

Fig. 2: Device schematics and magnetoresistance.
figure 2

a Schematic of easy-plane spin Hall oscillator (EP-SHO) based on a heavy metal (HM=Pt) and a ferromagnetic metal (FM=Co∣Ni superlattice) bilayer nanowire, as well as the Cartesian (x, y, z) and spherical (ϕ, θ) coordinate systems used here. A positive direct charge current in the HM layer + Idc (black dashed arrow) generates a spin Hall current js (gray dashed arrow) flowing in the z-direction with its polarization in the −y-direction (green arrows). Spin current js impinging on the FM applies spin Hall torque τst to magnetization M and pulls it out of the easy xz-plane. The magnetization then precesses about the easy-plane anisotropy field Ha∣∣y as indicated by black arrows. b Scanning electron micrograph of an EP-SHO. The scale bar is 100 nm. c Resistance of the EP-SHO device in b as a function of a 4 kOe (400 mT) magnetic field direction in the xy-plane measured at T = 4.2 K.

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Results

Device geometry and magnetoresistance

Figure 2a shows a schematic of the nanowire EP-SHO device along with the coordinate system used in this article. An applied direct electric current flowing in HM Pt along the length of the nanowire (x-direction) leads to a transverse spin Hall current45 flowing in the z-direction that is polarized in the −y-direction. When injected into the FM, the spin Hall current applies spin Hall torque to the FM magnetization46 and drives auto-oscillatory magnetization dynamics7.

The EP-SHO nanowires studied here were patterned from substrate∣∣seed∣HM∣FM∣cap films deposited by magnetron sputtering (see Methods and Supplementary Note 1). We used Pt (7 nm) for the HM layer and a \({\left[{{{{{{{\rm{Co}}}}}}}}(0.98\,{{{{{{{\rm{nm}}}}}}}})| {{{{{{{\rm{Ni}}}}}}}}(1.46\,{{{{{{{\rm{nm}}}}}}}})\right]}_{2}| {{{{{{{\rm{Co}}}}}}}}(0.98\,{{{{{{{\rm{nm}}}}}}}})\) superlattice as the FM layer. The Co∣Ni superlattice was selected for its large anisotropic magnetoresistance (AMR) and tunability of PMA via the Co and Ni layer thicknesses47. Highly resistive Ta is employed for the seed (3 nm) and capping (4 nm) layers48. Electron beam lithography and Ar+ ion milling were used to define 50 nm wide, 40 μm long nanowires from the film stack. Ta(5 nm)∣Au(40 nm)∣Ta(5 nm) electric leads were attached to the nanowire with the inter-lead gap varying from 50 to 450 nm. The spacing between the leads defines the active region of the nanowire where current density exceeding the critical value for the excitation of auto-oscillations can be achieved. Figure 2b shows a scanning electron micrograph of a typical EP-SHO device.

In this article, we study and compare two types of SHOs: the standard SHO (S-SHO), similar to that shown in Fig. 1a, and the EP-SHO. In the S-SHO configuration, moderate-amplitude auto-oscillatory dynamics are driven by the antidamping spin Hall torque around the effective magnetic field often dominated by the applied field H.

The maximum antidamping spin Hall torque efficiency in this configuration is achieved for a saturating field H applied parallel to the direction of the spin Hall current polarization (along the y-axis: θ = 90°, ϕH = 90°)49. However, the maximum efficiency of converting magnetization oscillations to resistance oscillations due to AMR oscillations is achieved at ϕ = 45°. For this reason, the external field is usually applied at an angle between ϕH = 45° and ϕH = 90° as a compromise50.

In the EP-SHO configuration, the applied field H is nearly zero, and the energy landscape is dominated by internal fields: shape anisotropy and PMA. The goal is to artificially manufacture an EP in the xz-plane, such that spin Hall current from the Pt underlayer is polarized orthogonal to the EP. In this case, the spin Hall torque pushes the magnetization out of the EP, where it precesses about the effective EP field, as shown in Fig. 2a.

Magnetic shape anisotropy for a nanowire of rectangular cross section can be approximately described via demagnetization fields along the three principal axes: \({H}_{{{{{{{{{\rm{D}}}}}}}}}_{{{{{{{{\rm{x}}}}}}}}}}=-4\pi {D}_{{{{{{{{\rm{x}}}}}}}}}{M}_{{{{{{{{\rm{x}}}}}}}}},{H}_{{{{{{{{{\rm{D}}}}}}}}}_{{{{{{{{\rm{y}}}}}}}}}}=-4\pi {D}_{{{{{{{{\rm{y}}}}}}}}}{M}_{{{{{{{{\rm{y}}}}}}}}}\), and \({H}_{{{{{{{{{\rm{D}}}}}}}}}_{{{{{{{{\rm{z}}}}}}}}}}=-4\pi {D}_{{{{{{{{\rm{z}}}}}}}}}{M}_{{{{{{{{\rm{z}}}}}}}}}\), where Di are the demagnetization factors and Mi are the magnetization components in the i = x, y, z-directions. The saturation magnetization of the Co∣Ni superlattice is estimated from thickness dependent FMR measurements to be Ms ≈ 997 emu cm−3 (997 kA m−1) (Supplementary Note 2). The demagnetization factors for the Co∣Ni nanowire used here can are calculated using analytical expressions51: Dx = 1.4 × 10−4, Dy = 0.121, and Dz = 0.879. Upon patterning the nanowire, the y-axis becomes a hard magnetic axis with a maximum demagnetization field of \({H}_{{{{{{{{{\rm{D}}}}}}}}}_{{{{{{{{\rm{y}}}}}}}}}}=1.52\) kOe (\({\mu }_{0}{H}_{{{{{{{{{\rm{D}}}}}}}}}_{{{{{{{{\rm{y}}}}}}}}}}=152\) mT), while the x-axis has a maximum demagnetization field of only a few Oe. The demagnetization field in the direction perpendicular-to-the-film plane is \({H}_{{{{{{{{{\rm{D}}}}}}}}}_{{{{{{{{\rm{z}}}}}}}}}}=11.0\) kOe (\({\mu }_{0}{H}_{{{{{{{{{\rm{D}}}}}}}}}_{{{{{{{{\rm{z}}}}}}}}}}=1.10\) T). The PMA field HPMA is always in the opposite direction as \({H}_{{{{{{{{{\rm{D}}}}}}}}}_{{{{{{{{\rm{z}}}}}}}}}}\); therefore to achieve an easy xz-plane, we require the \({H}_{{{{{{{{\rm{PMA}}}}}}}}}={H}_{{{{{{{{{\rm{D}}}}}}}}}_{{{{{{{{\rm{z}}}}}}}}}}=11.0\) kOe (μ0HPMA = 1.10 T) in order to compensate the demagnetization field along the z-axis.

To characterize the HPMA in the magnetic multilayers used here, we made broadband ferromagnetic resonance measurements (FMR)52 prior to patterning of the multilayers into the nanowire devices. Using these measurements, we adjusted the Co and Ni layer thicknesses such that the sum of Pt∣Co and Co∣Ni interfacial PMA contributions at room temperature is less than, but nearly compensates the demagnetization field in the z-direction, as described in Supplementary Note 2. Furthermore, we find the PMA of the multilayer increases by 12% upon cooling from 295 K to 4.2 K as discussed in the Supplementary Note 3. For this reason, the equilibrium direction of magnetization in our nanowire devices at 4.2 K is along the z-axis. However, this uniaxial anisotropy is small and the dominant anisotropy is the easy-xz-plane anisotropy. Furthermore, this small z-axis uniaxial anisotropy can then be continuously tuned by temperature from easy-z-axis to easy-x-axis, achieving perfect easy-xz-plane anisotropy at the transition temperature. In this work, we tune the temperature via Joule heating by the applied direct current.

In this article, we report measurements of a SHO device with an active region length l = 145 nm made at T = 4.2 K. This device was chosen because its impedance is similar to that of our 50 Ω microwave circuitry. Figure 2c shows the resistance of the EP-SHO device as a function of in-plane angle ϕH (θH = 90∘) of applied magnetic field H = 4 kOe (μ0H = 400 mT) and a small probe current of Idc = 0.1 mA. From measurements of a similar device, we find the magnetoresistance to be due to both AMR and spin Hall magnetoresistance (SMR)53,54 with approximately equal contributions.

Microwave emission experiment

The auto-oscillatory magnetization dynamics in SHO devices are excited by spin Hall torque55 from a direct current Idc exceeding a critical value Ic. These magnetization auto-oscillations give rise to the device resistance oscillations due to AMR and SMR with the amplitude δRac and to a microwave voltage with the amplitude Vac ~ IdcδRac56.

We first study the S-SHO configuration shown in Fig. 1a achieved by the application of a large magnetic field H = 2.2 kOe (μ0H = 220 mT) in the plane of the sample at ϕH = 68°, θH = 90 °. Figure 3a shows power spectral density (PSD) measured in this S-SHO configuration as a function of Idc. The dynamics show a blue frequency shift with increasing Idc above the critical current Ic = 1 mA. The observed blue frequency shift is a nonlinear effect expected for the case of a saturating magnetic field applied perpendicular to the easy plane24,57. Figure 3c shows the total integrated microwave power P generated by the SHO as a function of Idc. The integrated power versus Idc is non-monotonic and peaks at P = 74 pW near Idc ≈ 2.15 mA. All values of microwave power given in this article are those delivered to a standard 50 Ω load.

Fig. 3: Microwave signal emission.
figure 3

Power spectral density (PSD) of microwave signal generated as a function of applied direct current Idc for the a high-field standard spin Hall oscillator (S-SHO) configuration and b low-field easy-plane spin Hall oscillator (EP-SHO) configuration. The lowest energy mode and its second and third harmonics are labeled m1, m2, and m3, respectively. Results from corresponding micromagnetic simulations (see Fig. 3b) are shown as gray curve. Integrated power for the c S-SHO and d EP-SHO. The amplitude of resistance oscillations for the e S-SHO and f EP-SHO. ϕH and θH indicate the angle of applied field H following the coordinate system shown in Fig. 2a.

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We next measure the same device in a nearly zero external magnetic field—a configuration allowing us to achieve the EP-SHO regime of operation. In the EP-SHO configuration, the energy landscape is dominated by PMA and the shape anisotropy fields. Figure 3b shows measured PSD as a function of Idc for H = 140 Oe (μ0H = 14 mT) and \(\left({\phi }_{{{{{{{{\rm{H}}}}}}}}}=18{8}^{\circ }\right)\); similar results were found for other small applied field values. A low-frequency auto-oscillatory mode labeled m1 is excited for currents exceeding Idc = 1.8 mA. In contrast to the standard high-field SHO regime, the emission frequency initially red-shifts with increasing Idc and reaches a minimum of 0.78 GHz at Idc ≈ 2.44 mA. For Idc > 2.44 mA, the emission frequency blue-shifts. Figure 3d shows the integrated power of the SHO in this low-field regime as a function of Idc. A non-monotonic dependence of microwave emission power is observed with the maximum value of 217 pW reached at Idc = 2.39 mA, near the frequency minimum. We also observe the 2nd and 3rd harmonics of the mode m1, labeled as m2 and m3 in Fig. 3b. The presence of the harmonics is indicative of large-amplitude nonlinear oscillations of magnetization. A higher-order mode not harmonically related to m1 is observed at frequencies near m2 and m3.

The non-monotonic SHO frequency dependence on Idc in the low-field regime of Fig. 3b is due to the tuning of HPMA by Joule heating, which alters the energy landscape in the xz-plane as shown in Fig. 4. With increasing temperature, the PMA is reduced. For Idc < 2.4 mA, the perpendicular anisotropy field dominates the z-axis demagnetization field \({H}_{{{{{{{{\rm{PMA}}}}}}}}}\, > \, {H}_{{{{{{{{{\rm{D}}}}}}}}}_{{{{{{{{\rm{z}}}}}}}}}}\) and the energy landscape can be described as a dominant easy xz-plane anisotropy with a secondary easy z-axis anisotropy within the xz-plane, as shown in Fig. 4a. For Idc > 2.5 mA, the reduced HPMA can no longer compensate \({H}_{{{{{{{{{\rm{D}}}}}}}}}_{{{{{{{{\rm{z}}}}}}}}}}\), and the energy landscape becomes easy-xz-plane with a secondary easy x-axis, as shown in Fig. 4c. The perfect easy xz-plane characterized by \({H}_{{{{{{{{\rm{PMA}}}}}}}}}={H}_{{{{{{{{{\rm{D}}}}}}}}}_{{{{{{{{\rm{z}}}}}}}}}}\) is achieved at the value of Idc = 2.5 mA, as shown in Fig. 4b. Figure 3 shows that the microwave power P = 217 pW in this EP-SHO regime is significantly enhanced compared to the maximum power P = 74 pW in the S-SHO configuration. These output power levels exceed those previously demonstrated in nanowire S-SHOs without significant PMA (25 pW21) and in nano-constriction SHOs (28 pW58).

Fig. 4: Easy plane energy landscape.
figure 4

Figures show the xz-plane side view of bilayer ferromagnet (FM) and non-magnetic heavy metal (HM) nanowire devices. Dashed ellipsoids show constant energy contours of magnetization in the easy xz-plane, and double-headed arrows indicate the easy axis. a When the perpendicular anisotropy field HPMA is larger than the demagnetization field \({H}_{{{{{{{{{\rm{D}}}}}}}}}_{{{{{{{{\rm{z}}}}}}}}}},z\)-axis is an easy axis within the dominant xz easy plane. b When \({H}_{{{{{{{{\rm{PMA}}}}}}}}}={H}_{{{{{{{{{\rm{D}}}}}}}}}_{{{{{{{{\rm{z}}}}}}}}}}\), perfect easy plane anisotropy is realized in the xz plane. c For \({H}_{{{{{{{{\rm{PMA}}}}}}}}}\, < \, {H}_{{{{{{{{{\rm{D}}}}}}}}}_{{{{{{{{\rm{z}}}}}}}}}},x\)-axis is an easy axis within the dominant xz easy plane.

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The amplitude of resistance oscillations \(\delta {R}_{{{{{{{{\rm{ac}}}}}}}}}(\delta {R}_{{{{{{{{\rm{ac}}}}}}}}}^{rms}=\delta {R}_{{{{{{{{\rm{ac}}}}}}}}}/\sqrt{2})\) shown in Fig. 3e and f for the S-SHO and EP-SHO, respectively, are calculated as19:

$$\delta {R}_{{{{{{{{\rm{ac}}}}}}}}}=\frac{R\left({I}_{{{{{{{{\rm{dc}}}}}}}}}\right)+{R}_{50}}{| {I}_{{{{{{{{\rm{dc}}}}}}}}}| }{\left(\frac{2P}{{R}_{50}}\right)}^{\frac{1}{2}},$$
(1)

where R50 = 50 Ω is the load impedance and \(R\left({I}_{{{{{{{{\rm{dc}}}}}}}}}\right)\) is the resistance of the nanowire at current Idc (Methods).

Micromagnetic simulations

Micromagnetic simulations of current-driven magnetization dynamics for both the S-SHO and the EP-SHO configurations are carried out using Mumax3 micromagnetic code59 at T = 0 K. Geometry, cell-size, and material parameters used in these simulations are listed in “Methods” and experimental measurement of material parameters are discussed in Supplementary Note 2. Technical details of the simulations are given in Supplementary Note 3.

Spin Hall torque is applied to the 145 nm long active region in the middle of the nanowire. In addition, we account for the current-induced Oersted field and Joule heating. The Oersted field applied to the FM magnetization in the −y direction arises from the electric current in the Pt layer. In Supplementary Note 3, we show that the magnitude of this field is 66.9 Oe per mA Idc (6.69 mT per mA Idc). We also take into account the current-induced reduction of HPMA via Joule heating in the SHO active region. Outside the active region, we assume PMA to be equal to its film value at T = 4.2 K, HPMA = 11.7 kOe (μ0HPMA = 1.17 T). This value of PMA results in the z-axis being the easy axis within the easy-xz-plane outside of the active region. In the active region, HPMA (μ0HPMA) is assumed to be a linearly decreasing function of Idc with the experimentally determined slope of −494 Oe mA−1 (−4.94 T A−1) as described in Supplementary Note 3. The combination of the Oersted field and reduced HPMA in the active region creates a magnetic potential well for spin waves, resulting in the localization of the auto-oscillatory dynamics to the active region, as observed in our simulations.

We first simulate the S-SHO configuration by applying in-plane external field H = 2.2 kOe (μ0H = 220 mT) at ϕH = 68° and θH = 89. 9°. The tilt of the external field by 0. 1° away from the film plane is used to eliminate simulation artifacts possible in highly symmetric systems. The system is initialized to uniform magnetization along ϕH and then relaxed to its minimum energy state prior to turning on the spin Hall torque. We conduct a series of simulations for applied currents in the range from Idc = 0.5 mA to 3.0 mA. The resulting x and y components of the dynamic magnetization, \({m}_{x}\left(t\right)\) and \({m}_{y}\left(t\right)\), are used to calculate variation of the sample resistance with time due to AMR and SMR,

$${R}_{{{{{{{{\rm{ac}}}}}}}}}\left(t\right)=\Delta {R}_{{{{{{{{\rm{AMR}}}}}}}}}{\langle {m}_{x}\left(t\right)\rangle }^{2}-\Delta {R}_{{{{{{{{\rm{SMR}}}}}}}}}{\langle {m}_{y}\left(t\right)\rangle }^{2},$$
(2)

where ΔRAMR = 0.4 Ω is the experimentally measured magnitude of AMR, ΔRSMR = 0.4 Ω is the experimentally measured magnitude of SMR, and 〈. . . 〉 represents averaging over the active region of SHO.

Figure 5a shows the spectra of the current-driven auto-oscillatory dynamics calculated via fast Fourier transforms (FFT) of \({R}_{{{{{{{{\rm{ac}}}}}}}}}\left(t\right)\). This figure shows that auto-oscillatory dynamics appear at Idc exceeding 1.25 mA. The magnitude of the resistance oscillations strongly increases when Idc exceeds 2.25 mA. For Idc > 2.25 mA, the observed auto-oscillatory mode exhibits a nonlinear blue frequency shift. Figure 5c shows the amplitude of resistance oscillations δRac versus Idc.

Fig. 5: Micromagnetic simulation of spin-orbit torque nano-oscillator.
figure 5

Figures show analysis of micromagnetic simulation data of resistance auto oscillations at each value of applied direct current Idc a for high field standard spin Hall oscillator (S-SHO) configuration (via FFT) b for low field easy-plane spin Hall oscillator (EP-SHO) configuration (via time domain analysis). Calculated amplitudes of resistance oscillations for c high-field S-SHO and d low-field EP-SHO. ϕH and θH indicate the angle of applied field H following the coordinate system shown in Fig. 2a.

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Simulations in the EP-SHO dynamics were made for H = 140 Oe (μ0H = 14 mT), ϕH = 188°, and θH = 89. 9°. These simulations revealed the bi-stable behavior of the system in the presence of Idc: at a fixed current above the critical, the system can be either in a dynamic state of large-amplitude magnetization oscillations or in a static state. An example of this behavior is shown in Supplementary Fig. S5. We thus expect that the system may exhibit random telegraph switching between the dynamic and the static states. While such switching is detrimental to the operation of this device as a coherent microwave source and must be suppressed via design improvements, it may be beneficial for the operation of the device as a neuron because small external stimuli result in large-amplitude output voltage spikes10,32,34. This type of random telegraph noise between large-amplitude dynamics and static states has been previously observed in spin transfer torque oscillators based on nanopillar spin valves60.

The bi-stability of the dynamic and static states in the EP-SHO regime warrants the use of the time domain analysis described in Supplementary Note 3 instead of the FFT analysis in order to determine the amplitude of magnetization and resistance oscillations in the dynamic state. Figure 5b shows the bias current dependence of the auto-oscillation frequency determined from this analysis. The data reveals a frequency minimum arising from the heating-induced rotation of the easy axis between the z and x axes. These simulation data are in excellent agreement with the experiment, as illustrated by the nearly perfect overlap of the micromagnetic and experimental data in Fig. 3b.

Figure 5d shows the amplitude of resistance oscillations δRac versus Idc given by our micromagnetic simulations in this EP-SHO regime (see Supplementary Note 3 for details). The data show that the amplitude of resistance oscillations is maximized near the frequency minimum where the perfect easy-xz-plane anisotropy is realized. This non-monotonic dependence of the amplitude of auto-oscillations on Idc is expected for the EP-SHO dynamics and is consistent with the experimental data in Fig. 3f.

Supplementary Movie 1 shows the spatially resolved time evolution of current-driven magnetization dynamics given by our micromagnetic simulations for Idc = 2.44 mA, which corresponds to the maximum of δRac(Idc). Figure 6a–c shows three snapshots from this Movie within one period of the auto-oscillations. Figure 6a shows the dynamic micromagnetic state in the active region at t = 20.18 ns after the application of spin Hall torque. At this time, the magnetization in the active region points predominantly in the +z-direction. The magnetization in the active region subsequently processes towards the +x-direction, as shown in Fig. 6b at t = 20.69 ns. These dynamics are consistent with those expected for an ideal EP-SHO shown in Fig. 1b. The next expected stage of the ideal EP-SHO dynamics is the precession of magnetization towards the −z-direction. Instead of these ideal dynamics, the magnetization of the nanowire EP-SHO rotates towards the −y-direction, as shown in Fig. 6c at t = 20.93 ns. From here, the magnetization precesses toward the −x-direction before returning to the +z-direction, just like in the case of the ideal EP-SHO in Fig. 1b. This precession cycle repeats with small cycle-to-cycle variations of the micromagnetic states, as may be expected for a nonlinear dynamical system with many degrees of freedom61.

Fig. 6: Micromagnetic snapshots of easy-plane spin Hall oscillator (EP-SHO) auto-oscillations at applied direct current Idc = 2.44 mA.
figure 6

a Magnetization starts from predominantly +z-direction at t = 20.18 ns, b then processes toward the +x-direction at t = 20.69 ns, c subsequently rotates toward the −y-direction at t = 20.93 ns. Black dashed lines indicate the boundaries of the active region. d Average magnetization of the active region traced over two periods of auto-oscillations. ϕ indicates the in-plane angle of the local magnetic moment, following the coordinate system shown in Fig. 2a.

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Supplementary Movie 2 shows the auto-oscillatory dynamics of the magnetization vector averaged over the EP-SHO active region. Figure 6d displays a frame from this Movie showing the path traced by the averaged magnetization vector for two consecutive cycles of precession. Figure 6d illustrates that large-angle dynamics expected for an EP-SHO are indeed excited by spin Hall torque. However, compared to the ideal EP-SHO, these dynamics are limited to the +z half-space. This departure from the ideal EP-SHO dynamics is due to exchange coupling to the static magnetization outside of the active region that is magnetized along the +z-direction. Supplementary Movie 3 and Supplementary Fig. 6 show the corresponding S-SHO auto-oscillatory dynamics of the magnetization vector averaged over the S-SHO active region.

Discussion

Our experimental data in Fig. 3 demonstrate that the easy-plane regime of SHO operation results in a significant power boost compared to the conventional SHO regime. For the nanowire SHO geometry, we observe a power increase by a factor of three in the EP-SHO regime. Micromagnetic simulations of magnetization dynamics for the EP-SHO and the S-SHO regimes are in qualitative agreement with the experimental observations.

We find full quantitative agreement between the measured and simulated dependence of the EP-SHO generation frequency as a function of direct current bias Idc, as shown in Fig. 3b. The frequency minimum in these data is observed at the bias current corresponding to the perfect easy-xz-plane anisotropy achieved via PMA tuning by Ohmic heating.

The experimentally measured dependence of the amplitude of resistance oscillations δRac on Idc in the EP-SHO regime shown in Fig. 3f is qualitatively similar to that given by the simulations in Fig. 5d: in both cases, the auto-oscillation amplitude maximum is observed near Idc corresponding to the perfect easy-xz-plane anisotropy. However, the experimentally measured auto-oscillation amplitude is higher than that predicted by the simulations. We attribute this discrepancy to weak exchange coupling between crystallographic grains of the FM film. The reason for the auto-oscillation amplitude being limited to the +z half-space in the simulations is strong exchange coupling to static magnetization outside of the active region. Therefore, a decrease of exchange coupling to the static magnetization is expected to extend the auto-oscillatory dynamics into the −z half-space, increase δRac, and bring the auto-oscillations closer to the ideal EP-SHO shown in Fig. 1b. Recent studies clearly demonstrate significant granularity in Co∣Ni superlattices deposited by magnetron sputtering and the associated weakening of the inter-grain exchange in such films62.

The observed excursion of the auto-oscillating magnetization into the −y-direction seen in Fig. 6d enhances the amplitude of resistance oscillations due to the SMR term in Eq. (2). Such SMR contribution to the resistance oscillations is absent in an ideal EP-SHO in Fig. 1b where large-amplitude circular dynamics in the xz-plane is expected. Therefore we do not expect significant microwave power generated by an ideal EP-SHO at the frequency of its magnetization auto-oscillations. However, the ideal EP-SHO would produce large-amplitude microwave power at twice the magnetization auto-oscillation frequency due to the AMR term in Eq. (2). Such large-amplitude second-harmonic microwave emission may be beneficial for applications requiring high-frequency microwave signals. The output power of the EP-SHO can be further boosted in a 3-terminal device geometry by embedding a magnetic tunnel junction with large tunneling magnetoresistance on top of the EP-SHO active region in a manner similar to that demonstrated for S-SHOs 7,63.

A recent paper34 presented micromagnetic simulations of auto-oscillatory dynamics in a geometry similar to that studied here. The auto-oscillatory dynamics found in these simulations are similar to those in an ideal EP-SHO shown in Fig. 1b. These simulations assume the same value of PMA in the active region and outside of the active region, which is challenging to realize due to the enhanced Ohmic heating of the active region. Our simulations show that the inclusion of the enhanced heating-induced PMA reduction in the active region may decrease the amplitude of the auto-oscillations of EP-SHO compared to the ideal case.

We also find qualitative agreement between the experiment and simulations for the high-field S-SHO regime. The frequency in the S-SHO regime is found to blue shift with increasing Idc in the experiment (Fig. 3a), and a clear blue frequency shift is seen in the simulations for Idc > 2.25 mA as shown in Fig. 5a. This blue shift is a nonlinear dynamical effect expected for a spin torque oscillator with an easy plane magnetic anisotropy and saturating applied magnetic field with a large component perpendicular to the easy plane24,57.

However, the auto-oscillation frequency seen in the experiment is approximately 1 GHz higher than that predicted by the simulations. This discrepancy is explained by the assumption of the ideal magnetic edge of the nanowire used in the simulations: the simulations assume that the FM material properties at the nanowire edge are the same as in the middle of the wire. This assumption has been previously shown to be incorrect in real devices19,64 due to the non-ideal properties of the magnetic edge, such as edge roughness65 and magnetic edge dilution66. It has been previously shown that the experimentally measured frequency of spin-wave modes in transversely magnetized thin-film nanowires is higher than expected due to the magnetic edge modification67. The magnetic edge modification is also likely to be responsible for deviations of the measured S-SHO frequency from the simulations in the low-bias current regime Idc < 2.25 mA. The magnetic edge modification has the largest impact on the spin wave frequency for magnetization saturated near the y-axis67. This is the reason for the much smaller impact of this effect on auto-oscillation frequency in the EP-SHO regime.

In the high-field regime of S-SHO operation, the simulations predict a continuous increase of the auto-oscillation amplitude δRac with increasing Idc up to the largest currents used in the simulations, as shown in Fig. 5c. In contrast, the experimentally measured δRac(Idc) shown in Fig. 3e has a maximum near Idc = 2.15 mA. The experimentally observed non-monotonic dependence δRac(Idc) is consistent with previous studies of S-SHOs7,50. The decrease in the auto-oscillation amplitude in the high current regime has been previously observed in S-SHO nanowire devices and explained21 via nonlinear magnon scattering68 of the auto-oscillatory mode to thermal magnons. The population of thermal magnons increases in the high-current regime due to the unavoidable Joule heating, resulting in an enhancement of the nonlinear scattering from the auto-oscillatory mode and the associated decrease of its amplitude.

Micromagnetic simulations do not account for thermal magnons, and thus the auto-oscillation amplitude continues to increase with increasing Idc in the simulations, as shown in Fig. 5c. It has been demonstrated that nonlinear magnon scattering in S-SHOs increases with increasing ellipticity of the spin wave modes25. Given the nearly easy-xz-plane character of anisotropy in our SHO devices, one may expect low ellipticity of spin-wave modes and, thus, low nonlinear scattering rates in the standard mode of the SHO operation when the magnetic field is applied along the y-axis. However, the magnetic field in our experiment is applied at a significant angle with respect to the y-axis (ϕH = 68°), and its magnitude is similar to the easy-xz-plane anisotropy field. This results in a significant ellipticity of spin-wave modes in the system and turns on the nonlinear scattering to thermal magnons. For this reason, the auto-oscillatory mode amplitude in the high-current regime decreases with increasing Idc as seen in the experimental data in Fig. 3e.

Three major pathways to enhance the microwave power output of SOT oscillators are: (i) increase the amplitude of magnetization auto-oscillations, (ii) increase the conversion efficiency of magnetic oscillations into electric microwave signal and (iii) take advantage of phase locking in arrays of spin torque oscillators to harness phase coherence of their collective dynamics. While it is likely that the ultimate future high-power SOT oscillator devices will combine all three approaches, an important immediate task is to find optimal solutions to all three individual approaches prior to combining them into a device with the ultimate high-power performance. It is interesting to note that this problem has been largely solved for spin transfer torque oscillators where the large amplitude of magnetization oscillations is achieved in vortex-based oscillators69, high conversion efficiency is achieved via tunneling magneto-resistance (TMR) in MTJs70, and phase locking of several of vortex oscillators has been demonstrated71,72. Achieving this degree of success is a grand challenge for SOT oscillators. If realized, this goal can lead to high-power SOT oscillator devices that are more energy-efficient than spin transfer torque oscillators and operate at higher microwave frequencies than vortex-based oscillators.

Our experimental demonstration of an EP-SHO solves the problem of achieving large-amplitude auto-oscillations in a single SOT oscillator. A common approach to increasing the amplitude of magnetic auto-oscillations in spin transfer torque devices is the excitation of auto-oscillations of a magnetic vortex69. However, vortex oscillators driven by spin Hall torque have not been realized due to the direction of the current polarization being in the FM∣HM bilayer plane. The artificial EP approach shown to work in this paper presents a practical solution for large-amplitude SHO devices.

Recently, tunable PMA in an SHO based on a Pt∣Co∣Ni multilayer was used to decrease the detrimental nonlinear magnetic damping by minimizing the ellipticity of magnetization precession25. This SHO based on a 0.5 μm diameter disc was shown to operate with small nonlinear damping in the standard high-field SHO regime. However, the disc geometry does not support the artificial easy-xz-plane anisotropy demonstrated in this work.

The high conversion efficiency of magnetic auto-oscillations into electric microwave signals can be achieved in SHO devices with high magnetoresistance. To this end, the most promising approach is SHOs utilizing TMR, such as 3-terminal devices where a nanoscale MTJ is patterned on top of the HM material7,73. In such SHOs, the drive and the readout currents can be separately controlled, which allows for low power consumption combined with high output power. Another promising approach to boosting SHO output power while keeping Ohmic losses low utilizes current-in-plane giant magnetoresistance in a two-terminal device50. This approach takes advantage of the identical angular symmetries of spin Hall torque and giant magnetoresistance to simultaneously maximize the amplitude of resistance oscillations and spin Hall torque efficiency.

Finally, phase locking in one- and two-dimensional arrays of SHOs14,74 has been experimentally demonstrated to significantly boost the SHO output power. Therefore, with the addition of the present work, all three individual components needed for making high-power SHO oscillator systems have been experimentally demonstrated. We thus expect that integrated SHO devices capable of generating the ultimate high microwave power are now within reach.

The artificial EP nanowire created by balancing the demagnetization energy with the PMA could serve as a convenient platform for hosting a spin texture referred to as a spin superfluid75,76,77. Such a texture can be created via injection of spin current polarized orthogonal to the EP of an FM, which leads to the generation and propagation of an exchange-mediated winding of the magnetic order parameter—the spin superfluid state. This winding is topologically robust and is predicted to carry long-range spin current78,79. The EP nanowire system presented here is potentially suitable for the excitation of spin superfluid by spin Hall torque applied to the active region and its propagation along the nanowire beyond the active region. However, our micromagnetic simulation show that spin superfluid is not excited due to spatial inhomogeneity of PMA induced by Ohmic heating of the active region. Further improvements of the device design via e. g. the use of magnetic materials with PMA that weakly depends on temperature may enable spin superfluid in this geometry.

In conclusion, our work provides the first experimental realization of an EP SHO. This oscillator can operate without a biased magnetic field and generate high output microwave power due to the large amplitude of resistance auto-oscillations excited by spin Hall torque. The easy plane magnetic anisotropy perpendicular to the film plane is engineered by tuning the nanowire shape anisotropy and interfacial PMA. Our micromagnetic simulations of the oscillator performance are in good qualitative agreement with the measurements. Our results set the stage for the development of artificial spiking neurons driven by spin Hall torque34 and for further enhancement of the oscillator output power via integration with a tunneling magnetoresistance readout7,63.

Methods

Sample description

The multilayer films were deposited by dc magnetron sputtering on Al2O3(0001) substrates in 2 mTorr of Ar process gas. A highly resistive, amorphous Ta seed layer was used to reduce film roughness and absorb spin Hall current from Pt propagating opposite to the Co∣Ni superlattice. The highly resistive Ta cap was used to prevent oxidation of the Co∣Ni. The multilayers were patterned into 50 nm wide, 40 μm long nanowires by means of electron-beam lithography using DOW-Corning HSQ negative resist and Ar ion mill etching. The electrical leads to the nanowire were patterned via electron-beam lithography using a methyl methacrylate/poly(methyl methacrylate) positive resist bilayer followed by the sputter deposition of Ta(5 nm)/Au(40 nm)/Ta(5 nm) and liftoff. The spacing between the leads defined an SHO active region ranging in length from 50 nm to 450 nm long in the central part of the nanowire.

Microwave emission measurements

The microwave power emitted from the SHO was detected using a standard circuit based on a microwave spectrum analyzer56. A direct current Idc was applied to the sample through the low-frequency port of a bias tee. The signal from the SHO was amplified by a low-noise microwave amplifier with 45 dB gain, applied to the high-frequency port of the bias tee, and recorded by the microwave spectrum analyzer. For these measurements, the sample was placed in a He flow cryostat at a bath temperature of T = 4.2 K. The values of the microwave power reported here are those delivered to a 50 Ω load with the frequency-dependent circuit attenuation and amplification calibrated out. Resistance oscillations are calculated by treating the SHO as a mismatched microwave generator connected to a 50 Ω transmission line terminated with matched load (spectrum analyzer)80.

Micromagnetic simulations

Micromagnetic simulations were made using the Mumax3 software. We simulate a 4 μm × 50 nm × 5.85 nm ferromagnetic nanowire composed of 2048 × 16 × 1 micromagnetic cells representing the length, width, and thickness, respectively. The simulations were made using the experimentally determined material parameters of the Co∣Ni superlattice: saturation magnetization Ms = 997 emu cm−3 (997 kA m−1), Gilbert damping α = 0.027, and Landé g-factor g = 2.18. Exchange constant Aex = 1 × 10−6 erg cm−1 (10 pJ m−1) and spin Hall angle θSH = 0.07 were used. Constant PMA of HPMA = 11.7 kOe (μ0HPMA = 1.17 T) was used outside of the SHO active region. Current-dependent PMA was used in the SHO active region to capture the effects of Joule heating on anisotropy (see Supplementary Note 3 for details).