Spin torque nano-oscillator driven by combined spin injection from tunneling and spin Hall current

Spin-transfer torque nano-oscillators (STNO) are important candidates for several applications based on ultra-tunable microwave generation and detection. The microwave dynamics in these STNOs are induced by spin currents that are typically generated either by spin polarization in an adjacent ferromagnetic layer or through the spin Hall effect. In this paper, a 3-terminal STNO based on a magnetic tunnel junction is excited by both of these spin injection mechanisms. The combination of these two mechanisms excites the free layer into dynamic regimes beyond what can be achieved by each excitation mechanism individually, resulting in enhanced output powers, a key figures of merit for device performance. The system response can be coherently quantified as a function of the total injected spin current density. The experimental data shows an excellent consistency with this simple model and a critical spin current density of 4.52 ± 0.18 × 109ħ/2 e−1 Am−2. Spin torque nano-oscillators are important candidates for several device applications. The authors demonstrate that the combination of two excitation methods, spin-polarised tunnelling current and pure spin Hall current, allows them to achieve greater injected spin current densities and power output than by each individual mechanism.

S pin torque nano-oscillators (STNOs) based on the spintransfer torque (STT) associated with net spin currents are important candidates for several applications including frequency signal generation 1 , signal modulation 2 , spin wave generation 3 , neuromorphic computing 4 and ultra-tunable microwave generators [5][6][7][8] . Such devices are conventionally manufactured from spin valve or magnetic tunnel junction (MTJ) stacks nanofabricated in different geometries, including nanocontacts [9][10][11] and nanopillars [12][13][14] . In the early years of the field, all these devices were excited into an auto-oscillatory state using a spin-polarized current injected in the free layer after being spinpolarized by the reference layer. This mechanism of excitation is particularly challenging for devices based on MTJ stacks since the large currents required to excite auto-oscillations are often large enough to irreversibly damage the devices. The onset of the dynamic effects in MTJ devices can only be observed if the tunneling spin current exerts a torque in the free layer that compensates the Gilbert damping. For in-plane ferromagnetic free layers, this condition can be expressed as 15 : Here, μ 0 is the permeability of free space, ħ is the reduced Planck constant, M s is the free layer saturation magnetization, α is the Gilbert damping constant, t is the thickness of the free layer, H app is the applied field along easy axis, J tunneling c;crit is the critical tunneling current density and η is the spin injection efficiency associated with the injection of the spin-polarized tunneling current from the reference layer into the free layer. The effective magnetization of the free layer is given by M eff ¼ ðM s À 2 K p =ðμ 0 M s ÞÞ with the perpendicular magnetic anisotropy (K p ) 16,17 .
The injected spin-polarized tunneling current in the free layer is limited by the voltage that can be sustained by the tunnel barrier before irreversible dielectric breakdown. Achieving the onset of dynamic auto-oscillations before the dielectric breakdown of the tunnel barrier requires a large spin injection efficiency η, which is related to the tunneling current polarization p by η ¼ p=ð2 þ 2p 2 cos φÞ with φ = 0°in the low resistance configuration and φ = 180°in the high resistance configuration 18,19 . Realizing nano-oscillators from stacks incorporating ultra-thin tunnel barriers is required in order to increase the maximum current sustained by the devices, but as the MgO becomes thinner the tunnel magnetoresistance (TMR) and p tend to decrease. Balancing these two effects is required to realize devices that can sustain large DC currents for long periods of time 13 . This particularly rigid requirement of STNOs is not shared with nonvolatile magnetic memory (magnetoresistive random-access memory (MRAM)) devices which can be switched with short current pulses of large amplitude.
An important breakthrough was achieved using the spin Hall effect (SHE) 20,21 which generates transverse spin currents in nonmagnetic materials such as Pt 22,23 , Ta 24-27 and W 28,29 and also compensates the effective damping. The SHE was subsequently used in two-terminal devices to induce persistent autooscillations in the ferromagnetic layer [30][31][32][33][34][35][36] or even switch the ferromagnetic layer completely 24,37,38 . Later, the pioneering work of Liu et al. 6 induced auto-oscillations using the SHE in a threeterminal device based on an MTJ. While there are already a significant number of reports concerning three-terminal MRAM devices, the number of papers employing spin Hall currents as an excitation mechanism for auto-oscillations in MTJ nanopillars is very scarce 6,39 and the output powers achieved in such devices are considerably lower than those achieved in devices where the autooscillations are induced by spin-polarized tunneling currents. The likely reason for this discrepancy is the low charge to spin conversion ratio. Although the adjacent spin Hall materials do not suffer dielectric breakdown, the current densities that they can sustain are limited by the electromigration 40 .
An MTJ nanopillar was fabricated on a Ta micro-stripe adjacent to the free layer and measured in a three-terminal geometry with independent control of the tunneling current and the spin Hall charge current. In such device, it is possible to combine both types of excitations, concurrently injecting a spin-polarized tunneling current together with a transverse spin current generated by the SHE and driving the free layer into an auto-oscillation dynamic regime before any destructive mechanism is manifested (tunnel barrier breakdown or Ta line electromigration). For this reason, combining both spin injection mechanisms can result in spin current densities that are beyond those achievable with each isolated mechanism, allowing the exploration of otherwise unreachable dynamic states.
To describe this experiment, a more general version of Eq. 1 is necessary. The onset of auto-oscillation in the free layer is reached when the left-hand side of the Eq. 1 is replaced by the total critical injected spin current density, which is the sum of both contributions: Here, J In this work, it is shown that both excitation sources can be combined to drive the free layer into auto-oscillations that exceed the output power obtained with each individual input current within the limits that prevent irreversible damage to the device (from barrier breakdown or Ta electromigration). Furthermore, it is shown that Eq. 2 quantitatively describes a system with concurrent spin injection, providing a coherent description of spin injection in the free layer regardless of the excitation mechanism (tunneling charge current or spin hall charge current).

Results
Sample geometry and experimental details. In order to quantify the injected spin current density using Eq. 2, the parameters θ and η must be known. The spin Hall angle θ was quantified from separate stacks consisting of a 10 Ta/3 Co 0.4 Fe 0.4 B 0.2 /5 MgO (thicknesses in nanometre). From these samples, θ was quantified by modulation of the effective damping of an adjacent ferromagnet 32,41,42 , measured using the time-resolved magnetooptic Kerr effect. A spin Hall angle θ of (2.4 ± 0.1) % was computed as described in detail in the Supplementary Note 1.
The spin injection efficiency η was estimated from the TMR value in the final devices 43 . These were made from MTJ nanopillars with a diameter of 200 nm, patterned on a Ta spin Hall micro-stripe (see Methods section) as shown in Fig. 1a /5 Ru (thickness in nanometre) was used. The MgO thickness was tuned to a resistance-area product (R × A) of 15 Ω µm 2 , previously found as an optimum value to maximize the output power of STNOs with auto-oscillations excited from spin-polarized currents 13 . The devices, measured in a four-contact point geometry curves with magnetic field sweeps along the reference layer magnetization, exhibit quasi-DC transfer curves which are consistent with an in-plane magnetization of the 1.4 nm thick Co 0.4 Fe 0.4 B 0.2 free layer. The free layer saturation magnetization M s is determined from the saturation field of a magnetic film of the same thickness 44 . The measured R × A distribution in the final devices is shown in Fig. 1b with the large majority of the devices exhibiting a TMR between 100% and 120%. From the materials point of view, the large TMR of these devices is the key difference with respect to prior works 6,39 enabling the concurrent spin injection to be explored. With a TMR value of 115%, a tunneling current spin polarization p of 60% is estimated.
Tunneling current STT and spin Hall current STT. The highfrequency response of the devices was characterized in a threeterminal configuration for each excitation mechanism independently, as shown in  were swept keeping the charge current in the adjacent Hall line at zero as shown in Fig. 2b. The power spectral density shows a peak at 2.8 GHz with an output power that increases with increasingly The auto-oscillations are observed for currents of negative polarity with an amplitude above a critical value of about −0.15 mA, corresponding to a tunneling current density of J tunneling c = −4.65 × 10 9 Am −2 . Compared with the parameters found in the literature, this critical current density for the onset of auto-oscillations is low 46 . This is a consequence of the thin free layer, which leads to a low critical current density according to Eq. 1, together with the relatively large MgO barrier thickness leading 47 to a large TMR and spin polarization, which also contributes to decrease the critical current density as reported recently 13 . However, the threshold for auto-oscillations is difficult to determine precisely from the data in Fig. 2. A more precise discussion of the critical threshold takes place in the section on the determination of the critical spin current.
In a second experiment, shown in Fig. 2c-e, the magnetic autooscillations were excited by a spin Hall current. To that end, a weak tunneling current (I Besides the critical current, P matched and f were also extracted in this experiment as a function of the charge current in the Ta line, as shown in Fig. 2d, e. The auto-oscillation peak in the power spectral density increases with increasing magnitude of negative J spin Hall c , as expected. At J spin Hall c values greater than −6 mA, multiple auto-oscillating modes are detected. The two largest peaks (P 1 and P 2 ) are fitted and included in the integrated power. The peak P 1 is only observed above I spin Hall c ¼ À6 mA and the associated frequency (red squares) can be seen in Fig. 2d. In the STT auto-oscillation regime, a typical red-shift 6 of the frequency is observed as the magnitude of I spin Hall c increases. At large J spin Hall c values, the P matched reaches 8.6 nW as shown in Fig. 2e. This power is 5 times larger than the values reported in the literature 5,6,31,48,49 for spin torque oscillators based on SHE (both in nanopillar and nano-constriction geometries). This improvement over previous three-terminal devices 6 was mostly due to a 5 times larger J spin Hall c passed through Ta Hall microstripe which increases the total spin current accordingly. This is the maximum charge current that can be passed in the Ta line before irreversible damage to the line is observed.

Concurrent spin injection.
After demonstrating the excitation of free layer auto-oscillation in the same nanopillar by either a tunneling current or a transverse spin current, the next step is to combine both spin injection methods. The output power spectrum was acquired while I spin Hall   (Fig. 2c-e), this value of the tunneling current is large enough to generate free layer auto-oscillations at zero J spin Hall c . The J spin Hall c will either act with or against the tunneling spin current and, thus, either reinforces or damps the auto-oscillations depending on the polarity. As J spin Hall c is swept from zero to a maximum negative value, the P matched increases due to the increase of the total spin current in the system, as expected from the theoretical models 50,51 . For positive J spin Hall c , P matched initially reduces, before leveling out at an almost constant power of 13.8 nW with Γ > 200 MHz, which corresponds to the thermal FMR.
An alternative interpretation of the data in Fig. 3 could be that the increased output power is related to an increase of the average MTJ temperature 52 53,55,56 can be neglected in this experiment. According to the simulations the temperature difference across the junction is around 1 K, and thus the resulting thermal current is expected to be several orders of magnitudes below the applied bias current.
Critical spin current determination. A coherent and quantitative description of the system can be obtained with the spin current density defined in Eq. 2. In order to determine the critical spin current (J s ) of the device, at first, the thermal FMR power at the positive spin Hall current values were subtracted from the P matched to determine the STT-dependent contributions (P STT ). For additional details see Supplementary Note 3. The resulting matched root mean square (rms) microwave power P STT can be described by the following equation 7,57 .
with the applied tunneling current I and the static resistance of the device R, which is approximately the MTJ resistance in the AP state. The observed microwave power results from the resistance oscillation ΔR due to the magnetization auto-oscillation of the free layer. The factor 32 results from the combination of a factor of 8 due to the peak-to-peak to rms conversion and a factor of 4 due to the power splitting in a matched circuit. The normalized auto-oscillation amplitude can finally be expressed as a ratio between ΔR and ΔR max = R AP − R P as expressed by: Expressing the auto-oscillation in the normalized amplitude ΔR/ ΔR max , rather than P STT , allows the direct comparison of all the spin current configurations since this normalization accounts for the remaining tunneling current dependencies. Note that ΔR max and η were determined as a function of J tunneling c to remove the influence of the decreasing TMR ratio. Any value of ΔR/ΔR max describes a certain excitation amplitude and the contours lines in . The slopes of these contour lines correspond to the ratio of θ/η with the previously obtained value of θ = 2.4% and the η values between 44% and 28% (see Supplementary Note 4). Thus, the relation given by Eq. 2 seems to be valid and can be used to convert the charge current densities into J s values. The ratio ΔR/ΔR max can be now expressed as a function of J s , as shown in Fig. 4b.
The consistency of results of the same J s with varying tunneling and spin Hall contributions clearly shows that both J tunneling c and J spin Hall c contribute to the STT and can be described by Eq. 2. It should be emphasized that only a correct ratio of θ/η leads to the presented relation and any deviations would lead to a significant spread from the observed homogenous behavior in Fig. 4b. In the proximity of the critical spin current density ðJ s; crit Þ the ratio ΔR/ΔR max is predicted to be equal to p 0 = (J s − J s,crit )/(J s + J s,crit ·Q), with the non-linear damping constant Q 58,59 . This prediction describes the result very well and the fit results in J s; crit = − 4.52 ± 0.18 × 10 9 ħ/2 e −1 Am −2 and a non-linear damping Q = 3.8 ± 0.3 which is comparable to the literature 59 Fig. 4a. The normalized auto-oscillation amplitude ΔR/ΔR max describes the excitation directly and excludes unrelated effects such as the bias dependence of the polarization or the bias dependence of the output power. Although the output power remains a central parameter for applications, this normalized auto-oscillation amplitude is crucial for a quantitative analysis.
The Γ as a function of J s decreases with increasing autooscillation amplitude, as shown in Fig. 4c, which is typical for auto-oscillatory behavior and in agreement with the previous reports 61 . However, f shows a blue-shift with increasingly negative J s and an additional spread of the data. This spread is linearly related to the currents in the system, I tunneling c and I spin Hall c , as shown in Fig. 4d. This perturbation could be related to effects such as radial Oersted field in the nanopillar 62 , voltage-controlled anisotropy changes 6 , field-like torques 63 , lateral Oersted field around the Ta line 31 and temperature effects 15,30 . Thus, the true frequency shift cannot be distinguished with certainty from these additional effects. As a result, the observed frequency spread cannot be compared to the predicted red-shift 15 . It is interesting to note that the amplitude of the excitation does not show a similar spread and only depends on the J s .

Discussion
A three-terminal STNO based on an MTJ stack patterned into nanopillars with an adjacent Ta line acting as a transverse spin current source was realized. This MTJ stack exhibits a large TMR ratio (~115%) and a tunnel barrier of intermediate thickness allowing an excitation of free layer auto-oscillations by spin injection from a tunneling current, a transverse spin Hall current or a combination of both injection methods. Earlier works that explored comparable stacks and geometries did not demonstrate the ability to promote auto-oscillations of the free layer by both effects in the same device 6 .
The benefits of combining these two sources of excitations are simple. The total spin current injected in the free layer can be larger than what is possible from each isolated mechanism before irreversible damage arises (the tunneling current is limited by the tunnel barrier breakdown and the spin Hall current is limited by electromigration in the Ta line). Thus, the free layer can be excited in to dynamic states that are not accessible unless the two excitation sources are combined. This is clearly demonstrated in this paper when an output power of 48 nW is obtained with the two combined currents, well above the output power achieved with each individual excitation source. Furthermore, the data exhibit an excellent quantitative agreement with theoretical models expressed as a function of the total spin current injected into the free layer. The spin current can be calculated from the applied tunneling current and the applied spin Hall current and is used to predict the critical spin current of the system. The quantitative model confirms the values of key parameters in the system, such as the spin polarization of the tunneling current η and the spin Hall angle θ. substrate in physical vapor deposition system with a base pressure of 1 × 10 -9 Torr. Nanopillars with a 200 nm diameter were patterned from the stack, incorporating a MgO barrier targeting a resistance-area product (R × A) of 9.7 Ω µm 2 . Here a Ta layer was used as a seed layer for the growth of the MTJ stack and was pattered into a lead with the twofold function of establishing electrical contact to the bottom electrode of the MTJ nanopillars as well as constituting the current line converting the charge current into a transverse spin current being injected into the free layer.

Methods
The STNO fabrication can be segmented into three major parts: nanopillar patterning, bottom electrode definition and planarization. The electron beam lithography (EBL) was used to define the nanopillar and bottom electrode and the direct write laser lithography was used to define the top electrode of the device. Throughout nanofabrication process, ion beam etching was used for all the etching purpose.
At first, the nanopillar patterning was done using conventional EBL followed by etching in ion beam milling. The secondary ion mass spectrometer which is incorporated with the etching system was used to monitor the etching process. A negative photoresist (AZ7520) has been used for EBL exposure. Following the nanopillar patterning, another EBL was done to define a Hall bar structure of 24 µm long with a width of 1 µm using same photoresist. The length, width and height were chosen in order to ensure that the large J spin Hall c can be reached in the Hall current micro-stripe with reasonable current values. Upon the bottom electrode definition, the nanopillar was buried into 600 nm Al 2 O 3 and planarize in ion beam milling with grazing angle to expose the top of the nanopillar. The stopping point for this process was established by monitoring the evolution of the oxide topography on top of the nanopillar using scanning electron microscopy. The rest of the lithographies were performed in order to electrically contact the bottom electrode with the top electrode. A picture of a finished device is shown in Fig. 1a.
Upon nanofabrication, the devices were annealed at 330°C, with a dwell time of 2 h and magnetic field of 1 T to pin the synthetic antiferromagnet of the reference layer. The free layer of these devices aligns with the applied magnetic field leading to a parallel configuration (P) with low electrical resistance in positive magnetic field direction and an anti-parallel configuration with high R in the negative magnetic field direction.
Concurrent spin injection setup. Two DC current sources with common ground were employed to independently control two currents: the spin Hall charge current through the MTJ nanopillar. The high-frequency component of the output signal was then amplified by 43 dB and measured in a spectrum analyzer. To obtain the output power (P matched ), the power spectral density of the auto-oscillation peak is integrated and the impedance mismatch between the MTJ and the 50 Ω load is taken into account in order to calculate the output power delivered by the MTJ to the matched load 13,64 . Specifically, the following formula is used to convert the measured voltages into P matched : P matched = P measured (R MTJ + R L ) 2 /(4R MTJ R L ). Where P measured is the integrated power measured in the spectrum analyzer, R MTJ is the resistance of the MTJ and R L is the load resistance of the system. All output power values given in this work are corrected by this mismatch and represent the integrated (rms) output power delivered to a matched load. It should be noted that reported P matched is around 20% of the matched power of a circuit without the high resistive Ta lead, which dissipates a large amount of the generated power. These specific losses can be potentially decreased by optimizing design and materials. LabVIEW was used in this study to control, record and process data from the measurement setup.
Data availability