Time-resolved scanning Kerr microscopy has been used to perform optically detected, phase-resolved spin–orbit torque ferromagnetic resonance (SOT-FMR) measurements on a microscale CoFeB ellipse at the center of a Pt Hall cross subject to RF and DC current. Time-resolved polar Kerr images revealed localized dynamics with large amplitude at the center and weaker amplitude at the edges. Therefore, field swept SOT-FMR spectra were acquired from the so-called center mode to probe the SOTs active at the center of the ellipse, thus minimizing non-uniform edge contributions. When the magnetic field was applied at 30° from the hard axis of the ellipse and a DC current was applied, a marked asymmetry was observed in the amplitude and linewidth of the FMR peaks as the applied field was reversed. Both absorptive and dispersive parts of the spectra were in good agreement with a macrospin calculation. The damping parameter (α) and the Slonczewski torque parameter were determined to be 0.025 and (6.75 ± 0.75) × 10−7 Oe A−1 cm2, respectively. The hard axis SOT-FMR linewidth was found to be almost independent of the DC current value, suggesting that the SOT has a minimal influence in the hard axis configuration and that thermal effects were insignificant. This study paves the way for spatially resolved measurements of SOT probed using localized modes of microscale devices that go beyond the spatially averaged capability of electrical measurement techniques.

Following the prediction1 and demonstration2 of spin transfer torque (STT) more than two decades ago, related phenomena such as spin pumping,3–5 spin accumulation,6–8 and the spin Hall effect (SHE)9–13 in metals have attracted great attention due to potential applications in magnetic random access memory (MRAM). In the SHE, the efficient generation of pure spin currents at the interface between a ferromagnet (FM) and a heavy metal (HM) such as platinum, tantalum, or tungsten results from the strong spin–orbit coupling in the HM. The so-called spin–orbit torque (SOT) devices take advantage of the SHE to reduce the device size, improve energy efficiency, and increase device longevity because the write current no longer needs to pass through the delicate tunnel barrier of an STT-MRAM cell, but instead remains predominantly in the HM underlayer.

Recent studies of SOTs in HM/FM bilayer devices have focused on FM elements with perpendicular magnetic anisotropy (PMA).9–12 However, for STT-MRAM applications, it has been reported that in-plane magnetized SOT devices have potential for lower energy consumption, faster switching times, and enhanced switching probability.14 In-plane SOT devices15,16 also permit the use of a greater variety of FM materials since they are not limited to the few choices that yield PMA. On the other hand, in-plane magnetized elements can support non-uniform equilibrium states, such as the so-called leaf, S, and C states,17 where the magnetization cants along edges of the element that are not parallel to the applied magnetic field. The corresponding non-uniform internal field allows spatially localized modes to be supported such as the so-called center and edge modes.18 Since the Slonczewski torque term in the Landau–Lifshitz–Gilbert equation of motion depends on the local magnetization,19 a non-uniform equilibrium state can lead to a non-uniform torque across the element. In electrical measurements, only the spatially averaged orientation of the magnetization is probed by magnetoresistance or Hall effect measurements, while the voltage rectification within the device does not permit the phase of the dynamic response to be determined. However, recently developed optical16,19–22 and x-ray23 techniques are now able to directly probe the local dynamic magnetization within SOT devices.

Here, time-resolved scanning Kerr microscopy24 (TRSKM) has been used to perform optically detected, phase-resolved SOT induced ferromagnetic resonance (SOT-FMR) measurements in which the center localized magnetization dynamics of a microscale SOT device were directly probed with a spatial resolution of ∼400 nm. Field swept SOT-FMR spectra were acquired from a 2 × 0.8 μm2 in-plane magnetized CoFeB(2 nm) ellipse, deposited on a Pt(6 nm) underlayer, as a function of the applied in-plane field angle. Optically detected SOT-FMR has previously been used to characterize the torque on the magnetization due to an RF current in spin Hall nano-oscillator devices.19 In the present work, an elliptical element was subject to the Oersted (Oe) field and SOT, generated by the sum of both an RF current (IRF) and a DC current (IDC). Field swept SOT-FMR spectra were recorded at the center of the ellipse so that the center mode could be utilized as a probe of the SOTs at the center of the ellipse, thus avoiding non-uniform edge effects. The dependence of the optically detected spectra on the orientation of the in-plane applied field was well reproduced by a macrospin model, allowing the values of both the damping parameter and the SOT parameter to be determined.

The layout of the device and the experimental setup are shown in Fig. 1(a). Additional details of the device fabrication and characterization have been reported previously.14 Magnetron sputtering was used to deposit a Pt(6)/Co40Fe40B20(2)/MgO(1)/TaOx(4) (thicknesses in nm) film onto an Si substrate with a SiO2(250 nm) thermally oxidized overlayer. The stack was then annealed, after which electron beam lithography and ion milling were used to form a Hall cross device consisting of a 2 × 0.8 μm2, CoFeB/MgO/TaOx ellipse centered on a Pt(6 nm) cross. Outside the perimeter of the ellipse, Pt was intentionally overmilled by approximately 1 nm.

FIG. 1.

(a) Optically detected, phase-resolved SOT-FMR in a TRSKM. Ultrafast laser pulses with a duration <100 fs, a repetition rate of 80 MHz, and a wavelength of 800 nm are converted to a wavelength of 400 nm by SHG. The pulses are synchronized with the GHz-frequency RF output of a microwave synthesizer. The phase of the RF waveform was monitored using a sampling oscilloscope (inset, measured waveform showing amplitude modulation). RF and DC currents were passed to the device simultaneously via a bias tee, high frequency microscale coaxial probes, and the wider (2 μm) current lead of the Pt Hall cross. The width of the current lead was approximately equal to the length of the long, EA of the ellipse, which was perpendicular to the current direction. The resulting Oe-field [h(t)] and injected spin polarization [σ (t)] at the Pt/CoFeB interface were, hence, parallel to the EA, from which the in-plane applied field H angle θH is also defined. (b) and (c) TR polar Kerr images acquired at successive antinodes of precession (separated in RF phase by 180°) of a center-localized mode show large opposite (black and white) contrast at the center of the ellipse as the magnetization cants in- and out-of-plane and weaker contrast at the edges. (d) Reflectivity image of the ellipse. The outline of the ellipse is indicated by a dashed line within each image.

FIG. 1.

(a) Optically detected, phase-resolved SOT-FMR in a TRSKM. Ultrafast laser pulses with a duration <100 fs, a repetition rate of 80 MHz, and a wavelength of 800 nm are converted to a wavelength of 400 nm by SHG. The pulses are synchronized with the GHz-frequency RF output of a microwave synthesizer. The phase of the RF waveform was monitored using a sampling oscilloscope (inset, measured waveform showing amplitude modulation). RF and DC currents were passed to the device simultaneously via a bias tee, high frequency microscale coaxial probes, and the wider (2 μm) current lead of the Pt Hall cross. The width of the current lead was approximately equal to the length of the long, EA of the ellipse, which was perpendicular to the current direction. The resulting Oe-field [h(t)] and injected spin polarization [σ (t)] at the Pt/CoFeB interface were, hence, parallel to the EA, from which the in-plane applied field H angle θH is also defined. (b) and (c) TR polar Kerr images acquired at successive antinodes of precession (separated in RF phase by 180°) of a center-localized mode show large opposite (black and white) contrast at the center of the ellipse as the magnetization cants in- and out-of-plane and weaker contrast at the edges. (d) Reflectivity image of the ellipse. The outline of the ellipse is indicated by a dashed line within each image.

Close modal

A diffraction-limited spatial resolution of ∼400 nm was achieved by reducing the wavelength of the probing laser pulses from 800 nm to 400 nm by means of second harmonic generation (SHG).25,26 A filter was used to remove residual 800 nm light, and the beam was expanded (×5) to reduce its divergence. The beam was then linearly polarized and attenuated to an average power of ∼200 μW before being focused by a ×50 (N.A. 0.55) long working distance (∼11 mm) microscope objective lens. A 4 ns optical delay line was used to acquire time-resolved signals and accurately set the phase of the probe laser pulse with respect to the RF current passing through the device.

The RF current was generated by a microwave synthesizer with an RF power of 22 dBm and a frequency of 3.2 GHz = n × 80 MHz, where n = 40 and 80 MHz is the synchronous repetition rate of the laser. The RF current amplitude was 8 mA after accounting for the reflection coefficient of 0.87 at the device due to the transition from 50 Ω coaxial cable and probes to the ∼700 Ω device load. The current flowed in the wider 2 μm current lead perpendicular to the long, easy axis (EA) of the ellipse so that the injected spin polarization and Oe field were parallel to the EA. The RF and DC Oe fields acting on the ellipse were calculated to be approximately 25 Oe and 30 Oe (for IDC = 10 mA), respectively. Non-linear effects were not observed in either the measured or calculated spectra, and measurements were found to be insensitive to resonance thermal effects.27 The RF current amplitude was modulated at ∼3.14 kHz and the resulting modulation of the out-of-plane component of the dynamic magnetization was detected via the polar Kerr effect, using a balanced polarizing photodiode bridge detector and a lock-in amplifier. Amplitude modulation was used in analogy to electrical SOT-FMR measurements.19 The DC current was generated by a precision current source and combined with the RF current using a bias tee.

Macrospin calculations of the field swept SOT-FMR spectra were based on the model described in Ref. 19, but extended to include both the SOT and Oe field generated by both RF and DC currents. Following Ref. 28, the Landau–Lifshitz Gilbert (LLG) equation of motion for the magnetization in the presence of Slonczewski (in-plane) and field-like (out-of-plane) spin transfer torque terms may be written as

dŝdt=γŝ×Heff+αŝ×dŝdt+γSTJŝ×ŝ×σ̂+γFTJ×σ̂,
(1)

where ŝ and σ̂ are unit vectors parallel to the magnetization and injected spin polarization, respectively, J is the total current density, ST and FT are the amplitudes of the Slonczewski and field-like torque terms, and γ=gμB/, in which g is the spectroscopic splitting factor, μB is the Bohr magneton (and has negative sign), and is Planck's constant divided by 2π. Heff is the effective magnetic field and includes contributions from the applied in-plane magnetic field, the uniaxial shape anisotropy field, the demagnetizing field, and the Oe fields generated by the DC and RF currents passing through the device. Quasi-alignment of the magnetization with the applied field was not assumed in order to provide an accurate description of measurements made at applied field values comparable to the uniaxial anisotropy field. Instead, the orientation of the equilibrium magnetization was determined from the solution of the time-independent part of Eq. (1) after linearization. It was, therefore, not possible to obtain explicit expressions for the linewidth of the field swept resonance. Further details of the macrospin model are presented in the supplementary material.

Preliminary time-resolved measurements and images were acquired to determine the conditions (frequency and field) for SOT-FMR and are presented in the supplementary material. TR polar Kerr images acquired at resonance [see Figs. 1(b) and 1(c) and the supplementary material] show that the dynamic magnetization corresponds to a center-localized mode. The laser spot was then positioned at the center of the ellipse to acquire optically detected, phase-resolved SOT-FMR spectra corresponding to the center mode, so as to investigate SOTs active at the center of the ellipse, thus minimizing non-uniform edge contributions.

Figure 2 shows experimental spectra (symbols) acquired for different orientations of the in-plane applied magnetic field. The time delay between the RF current and the probing laser pulse was set so that the laser pulse probed the absorptive (rather than the dispersive) component of the dynamic magnetic susceptibility. The dispersive component is presented in the supplementary material. Calculated spectra are overlaid (solid red lines) and show good agreement with the experimental data, confirming that the response of the center mode can be described as a single macrospin. When the field was applied along the EA (θH = 0°, 180°), FMR peaks were not observed because no torque is exerted on the magnetization when the Oe-field and spin polarization lie parallel to the equilibrium magnetization. In contrast, when the field is applied along the hard axis (HA, θH = 90°, 270°), FMR peaks are clearly observed as the Oe field and injected spin polarization exerts maximum torque. However, no discernible asymmetry with respect to field polarity was observed in either the amplitude or the linewidth of the HA FMR peaks as IDC was increased from 0 to 10 mA, suggesting that SOTs are weak or inactive when the ellipse is magnetized along the HA (see the supplementary material). Moreover, insensitivity of the HA linewidth to the value of IDC suggests that the measurements are insensitive to resonance thermal effects for IDC up to 10 mA, the maximum value applied in this work.

FIG. 2.

Optically detected, phase-resolved SOT-FMR spectra (gray open symbols) corresponding to the imaginary component of the dynamic susceptibility and acquired over the full range of azimuthal angles θH defined with respect to the EA (0°). fRF and IDC had values of 3.2 GHz and 10 mA, respectively. Calculated spectra for a single macrospin are overlaid (red curves). The calculations assumed fRF= 3.2 GHz, IDC = 10 mA, IRF = 8 mA, ST = 6.75 × 10–7 Oe A1 cm2, a uniaxial anisotropy field of 90 Oe, demagnetizing field = 7500 Oe, g-factor = 2.05, α = 0.025, Pt lead width = 3.5 μm, and Pt thickness = 6 nm. The measured spectra are shown for both field sweep directions, while for clarity, the calculated spectra are shown only for a single sweep direction (avoiding field sweep segments for which the energy minimization routine can yield metastable equilibrium states after sweeping through remanence). The measured (calculated) spectra have been offset by 2 mdeg (0.08 Mz/Ms) for clarity. Example broad and narrow FMR peaks are labeled B and N, respectively.

FIG. 2.

Optically detected, phase-resolved SOT-FMR spectra (gray open symbols) corresponding to the imaginary component of the dynamic susceptibility and acquired over the full range of azimuthal angles θH defined with respect to the EA (0°). fRF and IDC had values of 3.2 GHz and 10 mA, respectively. Calculated spectra for a single macrospin are overlaid (red curves). The calculations assumed fRF= 3.2 GHz, IDC = 10 mA, IRF = 8 mA, ST = 6.75 × 10–7 Oe A1 cm2, a uniaxial anisotropy field of 90 Oe, demagnetizing field = 7500 Oe, g-factor = 2.05, α = 0.025, Pt lead width = 3.5 μm, and Pt thickness = 6 nm. The measured spectra are shown for both field sweep directions, while for clarity, the calculated spectra are shown only for a single sweep direction (avoiding field sweep segments for which the energy minimization routine can yield metastable equilibrium states after sweeping through remanence). The measured (calculated) spectra have been offset by 2 mdeg (0.08 Mz/Ms) for clarity. Example broad and narrow FMR peaks are labeled B and N, respectively.

Close modal

The value of the damping parameter α was first determined from the HA linewidth for the case of IDC = 0 mA, where the linewidths within the SOT-FMR spectra are found to be insensitive to the ST parameter. The linewidth is defined as the full width at half maximum of a Lorentzian curve fitted to the peaks in the calculated and experimental SOT-FMR spectra. Figure 3(a) shows the linewidth of the calculated HA spectrum for different values of the damping parameter. The average linewidth determined from experimental HA spectra measured for two different field histories (horizontal blue line) agree best with the calculations for α = 0.030 ± 0.003, compared to α = 0.035 reported for smaller (80 × 205 nm2) devices of the same composition.14 

FIG. 3.

(a) Calculated HA linewidth (black squares) vs damping parameter α for IDC = 0. The horizontal blue line shows the average value measured for different field histories, while the light gray band represents their standard deviation. (b) Calculated linewidth vs ST parameter for the broad (B) (black squares) and narrow (N) (red circles) peaks at +H and –H, respectively, for θH = 120° and IDC = 10 mA (see Fig. 2). The filled (open) symbols assume α = 0.030 (= 0.025). Comparison is made with the linewidth determined from 8 equivalent measurements of both the B and N peaks. The blue horizontal lines indicate the average experimental linewidth values, while the light gray band represents their standard deviation.

FIG. 3.

(a) Calculated HA linewidth (black squares) vs damping parameter α for IDC = 0. The horizontal blue line shows the average value measured for different field histories, while the light gray band represents their standard deviation. (b) Calculated linewidth vs ST parameter for the broad (B) (black squares) and narrow (N) (red circles) peaks at +H and –H, respectively, for θH = 120° and IDC = 10 mA (see Fig. 2). The filled (open) symbols assume α = 0.030 (= 0.025). Comparison is made with the linewidth determined from 8 equivalent measurements of both the B and N peaks. The blue horizontal lines indicate the average experimental linewidth values, while the light gray band represents their standard deviation.

Close modal

When the applied field orientation lies between the EA and HA, and for IDC = 10 mA, both experimental and calculated spectra in Fig. 2 show a marked asymmetry in the amplitude and linewidth of the FMR peaks at positive and negative field values. At these intermediate field angles, the equilibrium magnetization has a component that lies either parallel or antiparallel to the Oe-field and spin polarization, depending on the field polarity. This leads to either an enhancement or reduction of the effective damping and the corresponding SOT-FMR linewidth as most clearly observed in Fig. 2 at angles ±30° from the HA. For example, broad (B) and narrow (N) peaks are observed for –H and +H values at θH = 60°, while B and N peaks occur for +H and –H values at 120°.

Spectra calculated for ST = 0, but including the Oe field due to the DC current (not shown), also show asymmetry in the amplitude and linewidth with respect to field polarity similar to that observed in the experiment. Therefore, the asymmetry observed in the experiment is due to the combined effect of the Oe field and SOT. Changing the HM from Pt to, e.g., W could confirm this conclusion since spin Hall angles of opposite sign are observed for these materials.13 

The dependence of the resonance field and linewidth on the orientation of the applied field is plotted for both positive and negative field polarities in Fig. 4. The variation of the resonance field can be described as the superposition of a twofold sin2(2θH) term due to the uniaxial shape anisotropy and a onefold cos2(θH) term due to the DC Oe field. The latter term results in a difference in the resonance field with respect to field polarity for certain angles and causes the values of the resonance field to differ between θH = 60° and 120°, whereas these values would be equivalent in the absence of the Oe field [gray arrows highlight the difference in Fig. 4(a)].

FIG. 4.

(a) Measured resonance field vs applied field angle for IDC = 10 mA. The field was swept from positive to negative values (large filled gray squares, down arrow) and then from negative to positive (small black filled squares, up arrow). The length of the error bar indicates the measured linewidth. The resonance fields determined from the calculated spectra assuming α = 0.025 and ST = 6.75 × 10–7 Oe A1 cm2 are also shown (open red circles). The guide to the eye (red curves) contains sin2(2θH) and cos2(θH) terms, while the difference in the resonance field at an angle of 30° on either side of the HA (θH = 90) is shown by small gray arrows. (b) Measured linewidth vs applied field angle (gray and black symbols), for different segments of the field sweep; positive to remanence (S1), remanence to negative (S2), negative to remanence (S3), and remanence to positive (S4). The linewidths of the calculated curves are shown for segments S1 and S2 only for clarity.

FIG. 4.

(a) Measured resonance field vs applied field angle for IDC = 10 mA. The field was swept from positive to negative values (large filled gray squares, down arrow) and then from negative to positive (small black filled squares, up arrow). The length of the error bar indicates the measured linewidth. The resonance fields determined from the calculated spectra assuming α = 0.025 and ST = 6.75 × 10–7 Oe A1 cm2 are also shown (open red circles). The guide to the eye (red curves) contains sin2(2θH) and cos2(θH) terms, while the difference in the resonance field at an angle of 30° on either side of the HA (θH = 90) is shown by small gray arrows. (b) Measured linewidth vs applied field angle (gray and black symbols), for different segments of the field sweep; positive to remanence (S1), remanence to negative (S2), negative to remanence (S3), and remanence to positive (S4). The linewidths of the calculated curves are shown for segments S1 and S2 only for clarity.

Close modal

To obtain the best agreement between the resonance fields of the calculated and experimental SOT-FMR spectra, it was necessary to increase the assumed width of the current lead from 2 μm to 3.5 μm. This increases the area through which the current flows and reduces the current density and Oe field at the ellipse. Separate finite element simulations suggest that the DC current may spread out into the perpendicular Hall leads that are positioned at either end of the ellipse and perpendicular to the current direction. Spreading of the RF current was previously inferred within spin Hall nano-oscillators19 due in part to the reactance of the device structure. It is, therefore, quite difficult to establish the current distribution within the device.

Calculated spectra (not shown) indicate that the resonance field has a negligible dependence on the ST parameter, and so to observe the influence of SOT, it is necessary to look in detail at either the amplitude or the linewidth of the observed FMR peaks. Figure 4(b) shows that there is a distinct crossover in the linewidth value as the field angle crosses the HA and as the component of magnetization that is collinear with the Oe field and spin polarization changes its sign.

In light of the symmetry of the anisotropy and Oe fields, the spectra for θH = 60°, 120°, 240°, and 300° are equivalent, each containing one B and one N peak with similar resonance fields and linewidths. It is, therefore, sufficient to compare these measured B and N linewidths with those calculated for a single field angle of θH = 120°. Using the value of α = 0.030 determined from the HA measurement, spectra were first calculated for different values of ST and the B and N linewidths extracted. Figure 3(b) shows a clear linear increase (decrease) in the linewidth of the B (N) peaks as the ST parameter is increased from 0 to 10 × 10−7 Oe A−1 cm2. Comparison is made with the 8 equivalent measurements (field swept up and down for θH = 60°, 120°, 240°, and 300°) of both the B and N peaks. The blue horizontal lines indicate the average of the 8 experimental linewidth values.

Assuming α = 0.03, the calculated linewidth of the B peak for θH = 120° shows best agreement with the average measured linewidth (blue line) for ST = 0.6 × 10−7 Oe A−1 cm2. In contrast, a value of ST >10 × 10−7 Oe A−1 cm2 is needed to bring the calculated linewidth of the N peak in agreement with the measured values. However, if a smaller value of α = 0.025 is assumed, good agreement between experiment and the calculation is obtained for both B and N peaks when ST = (6.75 ± 0.75)×10−7 Oe A−1 cm2. Comparable values of the ST parameter have been obtained from quasi-static measurements of the out-of-plane deflection in response to a modulated DC current.29 Presumably, the larger value of α = 0.030 determined from the HA spectra when IDC = 0 mA is an overestimate, suggesting that the HA linewidth is more strongly affected by extrinsic relaxation mechanisms such as two-magnon scattering and/or a more non-uniform equilibrium state. Measurements of the field-swept linewidth at different frequencies would allow the different contributions to the damping to be better understood.30 

Angular-dependent SOT-FMR measurements performed for IDC = 1 mA do not show the marked asymmetry in amplitude and linewidth seen for measurements with IDC = 10 mA (see the supplementary material). When the field was applied parallel to the HA with IDC = 1 mA, comparison with macrospin calculations yielded α∼0.033, while the expected smaller, linear variation of the linewidth as a function of ST parameter was found to lie within the experimental uncertainty. The fact that the value of α decreased somewhat as IDC was increased from 1 mA to 10 mA suggests improved spatial uniformity of the equilibrium state and rules out a significant role for thermal effects up to IDC = 10 mA. For IDC = 1 mA, the calculated dependence of the linewidth on the field orientation was found to be smaller than the experimental uncertainty, and so only the measurements made at IDC = 10 mA were used to determine the value of the ST parameter.

In summary, TRSKM has been used to perform optically detected, phase-resolved SOT-FMR measurements. A center-localized mode was used to probe the SOTs active at the center of a microscale ellipse, thus avoiding non-uniform edge effects. Macrospin calculations reveal that a combination of both Oe-field and SOT is required to reproduce the marked asymmetry of the FMR spectra with respect to the polarity of the applied field. By comparing the measurements with the calculations, the values of the damping parameter and ST parameter can be determined, while the insensitivity of the measured HA linewidth to DC current suggests that thermal effects do not influence the spectra for IDC values up to 10 mA. The use of TRSKM as a direct probe of localized modes of microscale devices in SOT-FMR measurements goes beyond the spatially averaged capability of popular electrical measurement techniques and paves the way toward spatially resolved measurements of SOT.

See the supplementary material for details of the preliminary time-resolved Kerr measurements and imaging, the phase resolution of optically detected SOT-FMR and the dependence on DC current, in situ vector-resolved Kerr magnetometry, the macrospin model, and a comparison of TRSKM with other techniques.

The authors gratefully acknowledge the support of the Engineering and Physical Sciences Research Council under Grant Ref. No. EP/P008550/1.

The data that support the findings of this study are openly available in Open Research Exeter (ORE) at http://hdl.handle.net/10871/125071.

1.
J. C.
Slonczewski
,
J. Magn. Magn. Mater.
159
(
1–2
),
L1
L7
(
1996
).
2.
J. A.
Katine
,
F. J.
Albert
,
R. A.
Buhrman
,
E. B.
Myers
, and
D. C.
Ralph
,
Phys. Rev. Lett.
84
(
14
),
3149
3152
(
2000
).
3.
Y.
Tserkovnyak
,
A.
Brataas
, and
G. E. W.
Bauer
,
Phys. Rev. Lett.
88
(
11
),
117601
(
2002
).
4.
M. K.
Marcham
,
L. R.
Shelford
,
S. A.
Cavill
,
P. S.
Keatley
,
W.
Yu
,
P.
Shafer
,
A.
Neudert
,
J. R.
Childress
,
J. A.
Katine
,
E.
Arenholz
 et al,
Phys. Rev. B
87
(
18
),
180403
(
2013
).
5.
J.
Li
,
L. R.
Shelford
,
P.
Shafer
,
A.
Tan
,
J. X.
Deng
,
P. S.
Keatley
,
C.
Hwang
,
E.
Arenholz
,
G.
van der Laan
,
R. J.
Hicken
 et al,
Phys. Rev. Lett.
117
(
7
),
076602
(
2016
).
6.
Y.
Otani
and
T.
Kimura
,
Philos. Trans. R. Soc. A
369
(
1948
),
3136
3149
(
2011
).
7.
T.
Kimura
,
Y.
Otani
, and
J.
Hamrle
,
Phys. Rev. Lett.
96
(
3
),
037201
037204
(
2006
).
8.
T.
Yang
,
T.
Kimura
, and
Y.
Otani
,
Nat. Phys.
4
(
11
),
851
(
2008
).
9.
I.
Mihai Miron
,
G.
Gaudin
,
S.
Auffret
,
B.
Rodmacq
,
A.
Schuhl
,
S.
Pizzini
,
J.
Vogel
, and
P.
Gambardella
,
Nat. Mater.
9
(
3
),
230
234
(
2010
).
10.
I. M.
Miron
,
K.
Garello
,
G.
Gaudin
,
P.-J.
Zermatten
,
M. V.
Costache
,
S.
Auffret
,
S.
Bandiera
,
B.
Rodmacq
,
A.
Schuhl
, and
P.
Gambardella
,
Nature
476
(
7359
),
189
193
(
2011
).
11.
L.
Liu
,
O. J.
Lee
,
T. J.
Gudmundsen
,
D. C.
Ralph
, and
R. A.
Buhrman
,
Phys. Rev. Lett.
109
(
9
),
096602
(
2012
).
12.
L.
Liu
,
C.-F.
Pai
,
Y.
Li
,
H. W.
Tseng
,
D. C.
Ralph
, and
R. A.
Buhrman
,
Science
336
(
6081
),
555
(
2012
).
13.
C.
Stamm
,
C.
Murer
,
M.
Berritta
,
J.
Feng
,
M.
Gabureac
,
P. M.
Oppeneer
, and
P.
Gambardella
,
Phys. Rev. Lett.
119
(
8
),
087203
(
2017
).
14.
G.
Mihajlović
,
O.
Mosendz
,
L.
Wan
,
N.
Smith
,
Y.
Choi
,
Y.
Wang
, and
J. A.
Katine
,
Appl. Phys. Lett.
109
(
19
),
192404
(
2016
).
15.
X.
Fan
,
J.
Wu
,
Y.
Chen
,
M. J.
Jerry
,
H.
Zhang
, and
J. Q.
Xiao
,
Nat. Commun.
4
(
1
),
1799
(
2013
).
16.
X.
Fan
,
H.
Celik
,
J.
Wu
,
C.
Ni
,
K.-J.
Lee
,
V. O.
Lorenz
, and
J. Q.
Xiao
,
Nat. Commun.
5
(
1
),
3042
(
2014
).
17.
O.
Fruchart
and
A.
Thiaville
,
C. R. Phys.
6
(
9
),
921
933
(
2005
).
18.
P. S.
Keatley
,
V. V.
Kruglyak
,
A.
Neudert
,
E. A.
Galaktionov
,
R. J.
Hicken
,
J. R.
Childress
, and
J. A.
Katine
,
Phys. Rev. B
78
(
21
),
214412
(
2008
).
19.
T. M.
Spicer
,
P. S.
Keatley
,
T. H. J.
Loughran
,
M.
Dvornik
,
A. A.
Awad
,
P.
Dürrenfeld
,
A.
Houshang
,
M.
Ranjbar
,
J.
Åkerman
,
V. V.
Kruglyak
 et al,
Phys. Rev. B
98
(
21
),
214438
(
2018
).
20.
J.
Yoon
,
S.-W.
Lee
,
J. H.
Kwon
,
J. M.
Lee
,
J.
Son
,
X.
Qiu
,
K.-J.
Lee
, and
H.
Yang
,
Sci. Adv.
3
(
4
),
e1603099
(
2017
).
21.
K.
Ishibashi
,
S.
Iihama
,
Y.
Takeuchi
,
K.
Furuya
,
S.
Kanai
,
S.
Fukami
, and
S.
Mizukami
,
Appl. Phys. Lett.
117
(
12
),
122403
(
2020
).
22.
K.
Jhuria
,
J.
Hohlfeld
,
A.
Pattabi
 et al,
Nat. Electron
3
,
680
686
(
2020
).
23.
M.
Baumgartner
,
K.
Garello
,
J.
Mendil
,
C. O.
Avci
,
E.
Grimaldi
,
C.
Murer
,
J.
Feng
,
M.
Gabureac
,
C.
Stamm
,
Y.
Acremann
 et al,
Nat. Nanotechnol.
12
(
10
),
980
986
(
2017
).
24.
P. S.
Keatley
,
T. H. J.
Loughran
,
E.
Hendry
,
W. L.
Barnes
,
R. J.
Hicken
,
J. R.
Childress
, and
J. A.
Katine
,
Rev. Sci. Instrum.
88
(
12
),
123708
(
2017
).
25.
C. H.
Back
,
J.
Heidmann
, and
J.
McCord
,
IEEE Trans. Magn.
35
(
2
),
637
642
(
1999
).
26.
P. S.
Keatley
,
P.
Gangmei
,
M.
Dvornik
,
R. J.
Hicken
,
J. R.
Childress
, and
J. A.
Katine
,
Appl. Phys. Lett.
98
(
8
),
082506
(
2011
).
27.
S.
Karimeddiny
,
J. A.
Mittelstaedt
,
R. A.
Buhrman
, and
D. C.
Ralph
,
Phys. Rev. Appl.
14
(
2
),
024024
(
2020
).
28.
A. A.
Tulapurkar
,
Y.
Suzuki
,
A.
Fukushima
,
H.
Kubota
,
H.
Maehara
,
K.
Tsunekawa
,
D. D.
Djayaprawira
,
N.
Watanabe
, and
S.
Yuasa
,
Nature
438
(
7066
),
339
342
(
2005
).
29.
P.
Androvitsaneas
, “
Quasi-static measurements for extraction of spin orbit torques
,” (unpublished).
30.
L.
Liu
,
T.
Moriyama
,
D. C.
Ralph
, and
R. A.
Buhrman
,
Phys. Rev. Lett.
106
(
3
),
036601
(
2011
).

Supplementary Material