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Determination of spin-orbit torque efficiencies in heterostructures with in-plane magnetic anisotropy

It has been shown that the spin Hall effect from heavy transition metals can generate sufficient spin-orbit torque and further produce current-induced magnetization switching in the adjacent ferromagnetic layer. However, if the ferromagnetic layer has in-plane magnetic anisotropy, probing such switching phenomenon typically relies on tunneling magnetoresistance measurement of nano-sized magnetic tunnel junctions, differential planar Hall voltage measurement, or Kerr imaging approaches. We show that in magnetic heterostructures with spin Hall metals, there exist current-induced in-plane spin Hall effective fields and unidirectional magnetoresistance that will modify their anisotropic magnetoresistance behavior. We also demonstrate that by analyzing the response of anisotropic magnetoresistance under such influences, one can directly and electrically probe magnetization switching driven by the spin-orbit torque, even in micron-sized devices. This pump-probe method allows for efficient and direct determination of key parameters from spin-orbit torque switching events without lengthy device fabrication processes.


I. INTRODUCTION
Spin-orbit torque magnetic random access memory (SOT-MRAM) is a potential candidate architecture to replace now-in-mass-production spin-transfer torque MRAM (STT-MRAM) due to its virtually unlimited endurance, which benefits from the unique SOT writing mechanism that prevents the degradation of tunnel barrier in MRAM cell. The heavy transition metal/ferromagnet (HM/FM) bilayer heterostructures with in-plane magnetic anisotropy (IMA) are commonly adopted for SOTrelated research, such as W/CoFeB [1], Ta/CoFeB [2] and Pt/Py [3,4]. The spin current generated from the spin Hall effect (SHE) [5,6] of the HM layer can further exert SOT on the adjacent FM layer. The magnetization in the FM layer then can be switched via an anti-damping mechanism [7]. Unlike the cases where the FM layers have perpendicular magnetic anisotropy (PMA), whose magnetization states can be easily probed by anomalous Hall voltages [8][9][10][11], the SOT-induced magnetization switching in HM/FM heterostructures with IMA are typically probed by tunneling magnetoresistance (TMR) measurement on nano-sized three-terminal devices [1,2,12,13], differential planar Hall effect (DPHE) in Hall-bar devices [14], and magneto-optic Kerr effect (MOKE) imaging [15] to further estimate the SOT efficiencies. The challenging device fabrication processes before TMR measurement, the complicated measurement protocol of DPHE (alternating magnetic field is required), and the nonelectrical probing of magnetization through MOKE imaging are the major obstacles to develop these characterization methods into an efficient approach to meet industrial needs.
In this work, we present a reliable and simple all-electrical strategy to characterize the SOTs, both damping-like and field-like, in micron-sized magnetic heterostructures with IMA. Firstly, a current-induced shift of the anisotropic magnetoresistance (AMR) loop and an unidirectional magnetoresistance (UMR) are observed in W(3)/Co40Fe40B20(tCo-Fe-B) heterostructures with IMA (numbers in parentheses are in nanometers). The shift in the AMR indicates the existence of a currentinduced in-plane effective field, which is originated from the SHE of W. Secondly, the electrical detection of current-induced SOT-driven magnetization switching in a W/Co40Fe40B20 device is demonstrated by means of AMR measurement under the influence of this spin Hall effective field.
From switching measurements, the zero-thermal critical switching current I c0 , thermal stability ∆, and effective damping-like SOT (DL-SOT) efficiency ξ DL eff of these W-based heterostructures can be further determined. |ξ DL eff | ≈0.32 is estimated for devices with 2.0 nm ≤ t Co-Fe-B ≤ 3.5 nm, which is fairly consistent with the magnitude for thin W layer obtained by other approaches [1,[16][17][18]. Fieldlike SOT (FL-SOT) efficiency can be simultaneously estimated and is found to be influenced by placing a MgO layer on top of Co40Fe40B20, with a magnitude much smaller than its damping-like counterpart (|ξ FL eff | ≤ 0.05). Lastly, we demonstrate that for heterostructures with a well-defined inplane easy axis, as prepared from an 8-inch CMOS-compatible fabrication facility, the probing of SOT switching can also be realized by the UMR readouts. Our results suggest that this pump (DL-SOT)probe (AMR or UMR) method can be used to determine key parameters of SOT switching phenomenon from IMA heterostructures without complicated fabrication and measurement processes. spin Hall material layer is chosen to ensure a sizable SHE can be produced. The Ta(2) will naturally oxidize in air (denoted as TaOx with ρ TaO x ≈ 850 μΩ • cm, which is way more resistive than other layers) and serves as a capping layer to prevent further oxidation of the underlayers [19] (See supplementary material S1 for TEM inspection of the deposited films). We characterize the in-plane anisotropy and the saturation magnetization of these as-deposited W/Co40Fe40B20 films by vibrating sample magnetometer (VSM). The coercive fields for these films remain constants (Hc ≈ 20 Oe) by sweeping in-plane magnetic fields along various different directions, which suggests an easy-planelike anisotropy for our samples. Saturation magnetization of the Co40Fe40B20 layer for this series is found to be M s ≈ 700 emu cm 3 ⁄ , which is smaller than that from a standard Co40Fe40B20. The reduction of MS might be originate from the unexpected larger B-concentration [20] and amorphous phase [19,21] for CoFeB layer after sputter deposition. For devices used in AMR and current-induced SOT switching measurements, we pattern the as-deposited films into micron-sized Hall-bar devices with channel width of 5 μm through standard photolithography and subsequent Ar-ion milling processes.

III. SPIN HALL EFFECTIVE FIELD AND USMR
As schematically shown in Fig. 1(a), to measure magnetoresistance with four-point probe method, we sweep the in-plane magnetic field along y direction (Hy) while applying a dc current along x direction (Idc). Representative normalized AMR loops for a W(3)/Co40Fe40B20(1.8) sample with I dc = ± 3mA are shown in Fig. 1 therefore suggest that the current-induced H eff y and ∆R step are both having a SHE-related origin. We call this effective field the spin Hall field (SHF), which has also been observed in other HM/FM heterostructures when the FM layer is thin (≤ 4 nm) [22]. The UMR effect ∆R step , on the other hand, is most likely to be originated from the unidirectional spin Hall magnetoresistance (USMR) [23][24][25][26][27], which is caused by the variation between spin accumulation vector in HM/FM interface and magnetization of the FM layer. The magnitude of USMR is typically defined as (R H + I + -R H -I + ), (R H -I --R H +  I -) or ∆R step 2 ⁄ . The magnitude of our USMR obtained by dc measurements in Pt and W are also in agreement with a previous report as obtained by an ac (2 nd harmonic) approach [23].
The Co40Fe40B20 thickness dependence of USMR/I dc and H eff y /I dc obtained from the W(3)/Co40Fe40B20(tCo-Fe-B) devices are summarized in Fig. 1 opposite to that of the Oersted field. Also note that it is possible to have thermal contribution in the detected USMR signal [23,24,26]. However, this thermal effect will not affect the SOT switching measurement and characterization protocol that will be discussed in the following sections.

IV. SPIN-ORBIT TORQUE SWITCHING
Next, we demonstrate that current-induced SOT switching of a FM layer with IMA can be probed by AMR measurements with the aid of the SHF. The protocol of the measurement is straightforward: We apply a write current pulse I write along x to switch the magnetization M between ±y directions with DL-SOT and inject a sense current I sense to detect the SHF-modified AMR signal. With the measurement sequences shown in Fig. 2(a) and (c), we measure the longitudinal resistance Rxx by sweeping the write current pulses from negative to positive values and back to negative (details of pulsed current can be found in supplementary material S2). It is found that Rxx of a representative W(3)/Co40Fe40B20(1.8) device can be switched between a high resistance state and a low resistance state at critical switching currents of I c ≈ ± 1.2 mA with I sense = + 1 mA (Fig. 2(b)) or I sense = -1 mA (Fig. 2(d)) . The measured critical switching current is reproducible even after 100 switching cycles (supplementary material S3) and is not strongly affected by the amplitude of sense currents (supplementary material S4). Note that the polarities of the current-induced switching loops are opposite for using sensing currents of opposite signs.
The origin of these two different resistance states in Rxx is schematically shown in Fig. 2(e). In the absence of sense current (I sense = 0 mA), the ideal AMR response is not shifted due to the absence of SHF. Under this circumstance, Rxx is not distinguishable between the states with M pointing along ±y directions. When I sense is non-zero, the states with M pointing along +y and -y directions will have different Rxx values due to the influence from the SHF. The corresponding resistance for M pointing along ±y, either being high or low, will also depend on the sign of I sense . Therefore, this SHF-modified AMR can be used to probe the direction of M. When I write is applied, the SHE generated in the W layer will also result in an in-plane (anti) damping-like torque [28,29] acting on the Co40Fe40B20 layer. When the write current is large enough, this DL-SOT will overcome the intrinsic damping and switch M along y axis, which can be further detected by the variation of the SHFmodified AMR.
To further enhance the detected signal, we record the difference of resistance ∆R = (R xx I + -R xx I -) using opposite sense currents (I sense = ± 1 mA) during field sweep ( Fig. 3(a)) and write current sweep ( Fig. 3(b)). Representative field sweep and current sweep results are respectively shown in Fig. 3(c) and (d). The presented raw data show that both field-driven and current-driven switching will cause a reversible variation of ∆R between -4.0 Ω and -7.5 Ω with I sense = ± 1 mA , which suggests an almost full magnetization switching caused by the DL-SOT under zero-field condition. We further perform current-induced switching measurements with different pulse widths (0.05 s ≤ t pulse ≤ 1 s) of I write . Since SOT-driven magnetization switching is a thermally-activated process, the dependence of critical switching current I c on write current pulse width t pulse can be expressed as [28]: where Ic0 is the zero-thermal-fluctuation critical switching current, ∆ ≡ U k B T ⁄ is the thermal stability factor (U being the energy barrier between two magnetic states), and τ 0 ≈ 1 ns is the attempt rate for thermally-activated switching [30]. By linearly fitting the pulse width dependence switching results, as shown in Fig. 3(e), we find that I c0 ≈ ±2.3 mA (J c0 ≈ ± 9.57 ×10 10 A m 2 ⁄ ) and ∆ ≈ 53 for the W(3)/Co40Fe40B20(1.8) Hall-bar device. The spin-torque switching efficiency ε ≡ ∆ I c0 ⁄ [31], which is considered as the key figure of merit for addressing STT-MRAM performance, is further quantified for all W(3)/Co40Fe40B20(tCo-Fe-B) Hall-bar devices. As shown in Fig. 3(f), the value of ε is estimated to be ~ 2×10 -2 μA -1 for these 5-μm-wide devices.
Once the zero-thermal-fluctuation critical current density Jc0 is obtained from switching data, the DL-SOT efficiency of a heterostructure with IMA can be calculated by [7,28,32] : and the FL-SOT efficiency can be obtained by [33,34]: where M s , μ 0 M eff , and α 0 are saturation magnetization, effective demagnetization field, and  [18]. The slight increase of |ξ DL eff | from t Co-Fe-B = 3 nm to 3.5 nm is following the trend of ST-FMR-determined damping constant, which suggests that not only the critical switching current density J c0 , but also the damping constant α 0 of the measured device will affect the estimation of DL-SOT efficiency. To compare, the FL-SOT efficiency is much smaller than its DL counterpart and decreases from |ξ FL eff | ≈ 0.054 for t Co-Fe-B = 1.8 nm to |ξ FL eff | ≈ 0.014 for t Co-Fe-B = 3.5 nm.
To examine the effect of oxide capping layer to the DL and FL-SOT efficiencies, we also prepare and test on a series of W(3)/Co40Fe40B20(2.5)/MgO(tMgO)/TaOx samples, with 0 nm ≤ tMgO ≤ 2 nm.
We find that as tMgO increases from 0 nm to 1.2 nm, |ξ FL eff | also gradually increases and saturates at resistance states, which is attributed to the USMR. Note that a similar switching signal has been seen in an epitaxial paramagnet-(Ga,Mn)As/ferromagnet-(Ga,Mn)As bilayer system [36], but the switching mechanism therein is mainly attributed to the Oersted field. Also note that some smaller hysteresis jumps can be seen in Fig. 5(a) due to the imperfect alignment of the applied field with respect to the hard axis. ∆R of the device with I⊥EA is further recorded by sweeping magnetic field (Fig. 5(c)) and pulsed currents (Fig. 5(d)). Note that the intermediate states in Fig. 5 ⁄ ) can also be quantified from the switching data. For a representative micron-sized device that has a well-defined easy axis as fabricated from an 8-inch CMOS fab facility, the SOT-driven switching can also be probed by USMR measurement. The development of this measurement protocol therefore allows for mitigating the complexness of characterizing SOT-driven switching parameters in micron-sized magnetic heterostructures with IMA.