Planar Hall effect based characterization of spin orbital torques in Ta/CoFeB/MgO structures

As semiconductor devices scaled down, they are facing numerous issues including static power consumption due to the leakage current of transistors.^1–4 Spintronic devices are one of the promising alternative candidates that utilizes spin of electron for data storage and processing.^5–7 Spintronic devices use magnetic materials as the main computational and storage element.^8,9 Efficient electrical switching of nanomagnets at low energy is the key for the successful realization of magnetic based electronic devices (magnetoelectric devices).^10,11 Spin-orbit coupling (SOC) is an electron scattering mechanism that separates electrons according to their spin orientation.^12–14 Spin Hall effect is a phenomenon that utilizes SOC to generate spin accumulation.^15,16 This effect has been experimentally demonstrated in heavy metals^17–19 and more recently in topological insulators^20–22 and can be used to effectively switch a nanomagnet.¹⁹ Proper characterization of current induced SOC generated torques also known as spin orbital torques (SOT) is a key to provide a platform for comparison of different materials. For perpendicular magnetic layers, the anomalous Hall effect (AHE) could be used to characterized SOT for an input dc-current.¹⁷ However, this concept cannot be used for an in-plane magnetic layer. There are some high frequency characterization techniques such as spin torque ferromagnetic resonance²³ and spin pumping²⁴ that can be applied to the in-plane magnetic films to estimate the SOT in bilayer nonmagnetic/magnetic structures. The high frequency rf-current tends to leak: for example, it may leak to the substrate due to the parasitic capacitances. Because of this tendency, it is hard to get an accurate estimate of the actual rf-current flowing into the devices; hence, evaluation of SOT is challenging. Recently, there have been some quasi-dc techniques developed for characterization of SOT effective fields for in-plane magnetized samples, such as the planar Hall effect (PHE) technique,^25–28 second harmonic Hall²⁹ and spin Hall magnetoresistance.^30–32 Recently, there has been some reports that utilize the PHE in in-plane magnetic films to characterize SOT.^26–28 In this study, we have adapted PHE to characterize SOT in the trilayer Ta/CoFeB/MgO structure.

In this work, we have investigated SOT in a trilayer Ta/Co₂₀Fe₆₀B₂₀/MgO structure with an in-plane magnetic anisotropy under different input currents and temperatures. A sizable anti-damping torque is observed in the structure that amplifies upon increasing the input current while no significant field-like is obtained. By cooling down the sample, SOT is enhanced and gained a spin Hall angle of about 20.5% at 100 K. Further cooling down of the sample does not improve the conventional anti-damping torque significantly; however, cooling of the structure introduces a new effect that cannot be explained based on the current SOT physics.

A schematic of the PHE device and the measurement setup is given in Fig. 1(a). Initially, Ta(5 nm)/CoFeB(4 nm)/MgO (2 nm)/Ta(5 nm) is sputter deposited on a Si/SiO₂ (300 nm) substrate. The bottom Ta layer provides SOT on the CoFeB layer while the top Ta layer is a capping layer and is isolated from the CoFeB by the MgO layer. The stack structure is deposited using an ultra-high vacuum (UHV) six-target Shamrock sputtering system with a base pressure better than 5 × 10⁻⁸Torr at room temperature. Photolithography and subsequent argon ion milling are been used to define the Hall bars. The width of the Hall bar is 10 μm and the length is 40 μm. The electrodes are defined using lithography and a lift-off technique. For the electrodes, Ti(5 nm)/Au(100 nm) is deposited using an e-beam evaporator. Vibrating sample magnetometer characterization of the thin film sample shows that the CoFeB thin film has a saturation magnetization of M_s = 1240 emu/cc. In order to measure the resistivity of the Ta and CoFeB, separate control samples of Ta (5 nm) and CoFeB (4 nm) are deposited. Using the standard 4-probe characterization, we have characterized the resistivity of individual thin film. The resistivity of Ta and CoFeB are obtained to be 203 and 219 μΩ cm at the room temperature, respectively.

For the PHE measurement, an in-plane magnetic field of 0.5 T is applied. A dc-current is injected along the y-direction while the magnetic field is rotated between −7° and 365°. At each field angle, the Hall resistance is tested by measuring the transverse voltage using a nanovoltmeter. The PHE is assumed to have a sin(2θ) field angle dependence. Due to the possible misalignment of the magnetic field with the magnetic layer plane, there could be a sin(θ) component in the PHE signal as well; therefore, the PHE signal is in the form of C₀ + C₁ sin(θ) + C₂sin(2θ), where C₀ accounts for the offset of the Hall voltage. As it will be shown in Sec. III, presence of SOT introduces additional effective fields into the magnetic layer and modifies the PHE signal.

Upon injection of a charge current through a layer with strong SOC like Ta in our experiment, electrons are scattered according to $σ→×J→$ where σ is the electron spin direction and J is the input current density. Therefore, electrons with spin in x-direction scatter toward the top surface and electrons with spin in –x-direction scatter toward the bottom surface. The electrons on the top surface apply spin torque on the CoFeB magnetic layer according to the following equation:^17,33

The first term in the right side of Eq. (1) represents the spin Hall torque also known as anti-damping torque and the second term is Rashba torque also known as field-like torque. The effective field associate to the anti-damping and field-like torques can be written as $H→AT=f1(J)M→×σ̂$ and $H→FT=f1(J)σ̂$⁠, respectively. It is interesting to note that the direction of anti-damping effective field is out of the magnetic film plane, causing an additional AHE signal contribution in the Hall measurements; while the effective field, due to the field-like torque, is in the magnetic film plane and transverse to the current. This directly modifies the PHE signal. The anti-damping torque effective field can be expressed as $H→AT=−[ℏ/(2eMst)]Js(σ×m)$²⁸ where $ℏ$ is the Dirac constant, M_s is the saturation magnetization, t is the thickness of the magnetic layer, and J_s is the spin current. In order to characterize the SOT from the PHE signal, the Hall resistance is measured at ±current and the differential resistance, which is the difference between the PHE resistance at positive and negative currents, is calculated. The components of PHE resistance that are not a function of current cancel out in the differential resistance while the current dependent terms are enhanced as the input current increases. In Fig. 1(b), the direction of effective SOT fields overlaid with the external field and magnetization direction is presented. Due to the large external field H (0.5 T in our experiment), magnetization is oriented along the external field and it is slightly deviated from H due to the generated SOT fields. The effective field is the superimposition of all the existing fields, $H→eff=H→+H→AT+H→FT$⁠, and the magnetization is located along the effective field. From Fig. 1(b), we have $Heff sin φ=H sin θ$ and $Heff cos φ=H cos θ±HFT$⁠; therefore, $φ=arctan sin θ cos θ±δ$ where $δ=HFTH$⁠. Knowing that the anti-damping effective field is perpendicular to the plane, the Hall signal generated due to H_AT can be written as²⁸ 

By solving the above equations numerically, the angle dependence of the anti-damping and field-like torques can be found which is demonstrated in Fig. 1(c) assuming δ = 0.1. As seen, the anti-damping torque has a simple sin(θ) angle dependence while the field-like torque is much more complex.

The angle dependence of PHE resistance at ±10 mA corresponding to a current density of about 8 × 10⁶A/cm² in the wire assuming uniform conductivity in all layers is given in Fig. 2(a). As mentioned in Section II, the resistivity of both Ta and CoFeB layers are almost the same in the structure hence it is assumed that a uniform current distribution exists at the wire cross section. The current density is estimated based on the total thickness of the structure (14 nm).

As expected, the PHE signal shows mostly sin(2θ) angle dependence with an additional weak sin(θ) component. The differential resistance is shown in the right axis of Fig. 2(a). As seen, the differential resistance mostly has a sin(θ) angle dependence that according to Eq. (2), suggesting a sizable anti-damping torque in the Ta/CoFeB interface. Moreover, it is clear that the field-like torque is insignificant compared to the anti-damping torque. Fig. 2(b) presents the differential resistance at 5, 10, and 15 mA input currents overlaid with the curve fitting results. At all the currents, the differential resistance has a sin(θ) angle dependence that fits with the curve fitting results well. Moreover, upon increasing of the input current, the differential resistance increases in amplitude consistent with the assumption that the differential resistance originates from SOT.

In order to investigate the effect of the sample temperature on the strength of SOT, the sample is cooled down in a physical property measurement system (PPMS) down to 10 K. Fig. 3(a) shows the differential resistance of the Hall bar at 300, 200, 100, and 10 K. By decreasing the sample temperature down to 100 K, the differential resistance increases first but further cooling down the sample introduces (amplifies) an oscillatory component of resistance which is not significant at room temperature. This oscillatory component of differential resistance is not due to noise and is reproducible. Based on the current theory of SOT, we could not explain this oscillatory component and further investigation is required to better understand the origin of this effect. The amplitude of the differential resistance is given in Fig. 3(b). Upon cooling down the sample, the differential resistance increases by about 34% up to 50 K. Further cooling down the sample enhances the oscillatory component and the amplitude of the differential resistance drops.

In order to extract the strength of anti-damping torque, it is required to estimate dR_AHE/dH_perp, independently. We have characterized the Hall signal by application of a perpendicular field. Fig. 3(c) presents the AHE resistance when a magnetic field angle changes from the in-plane toward the out of plane direction for the field intensities of 0.5, 1, and 2 T. At the angle = 90° magnetization is fully in-plane and for the angle above or below of that, the magnetization is pulled out of the plane by the field. We have calculated the slope of R_AHE at 90° which is almost independent of the magnetic field. In this case, the in-plane component of the field remains almost the same (⁠$H cos(θ−π2)≈H$⁠) while the perpendicular component changes almost linearly with the angle (⁠$H sin(θ−π2)≈H(θ−π2)$⁠) for the field angle around 90°. We have determined the dR_AHE/dH_perp from the slope of the R_AHE versus the field. The dR_AHE/dH_perp is given in Fig. 3(d) for different sample temperatures. The slope slightly changes by the temperature and increases by about 15% upon reducing the temperature down to 10 K.

By having dR_AHE/dH_perp, the anti-damping effective field can be extracted according to Eq. (2). The anti-damping field at different input currents is demonstrated in Fig. 4(a). The strength of the anti-damping field in our Ta/CoFeB is consistent with the strength of the anti-damping field in other bilayer structures like Ta/Fe and Pt/Fe reported by other groups.^27,34 As expected, the anti-damping field increases by increasing the input current. Moreover, the effective anti-damping field is slightly larger at lower temperature. By the curve fitting of a linear curve over the experimental results, a slope of 1.85 and 2.1 Oe/mA are obtained at 300 and 100 K, respectively. Moreover, a nominal error value of 3.7% at 300 K and 2.1% at 100 K are measured which represent the deviation from the linear behavior. Having the anti-damping effective field, the spin current in the Ta layer is calculated utilizing the formula $HAT=−[ℏ/(2eMst)]Js$⁠. In addition, the charge current in the Ta layer J_c is calculated having the resistivity of individual layers. The spin Hall angle (SHA) is the ratio of spin over charge current SHA = J_s/J_c. The SHA is estimated in the Ta/CoFeB bilayer structure as a function of the input current at 300 and 100 K as presented in Fig. 4(b). At low current, the SHA gradually increases and at high current values of about 5 mA, the SHA saturated to about 18 ± 0.6% at room temperature. At 100 K, SHA is enhanced and increases up to about 20.5 ± 0.43%. The increase of the SHA at low current is possibly due to the weak differential resistance for very small SOT fields compared to the external field that makes the curve fitting less accurate. The SHA characterized at high current is consistent with the SHA reported by other groups.^19,33,35 It should be mentioned that Joule heating is not important in our characterizations since its effect is similar at ±I and cancels out in the differential resistance. There are several reports on the spin orbital torques characterization in Ta/CoFeB/MgO structure with a perpendicular magnetic anisotropy (PMA) utilizing AHE.^36–38 In order to obtain a PMA strong enough to overcome the demagnetization field, the CoFeB layer thickness should be very thin (∼1 nm). Moreover, the structure usually needs to be annealed to obtain a good PMA and crystalline CoFeB layer. In our experimental setup, the CoFeB layer is thick (4 nm) with an in-plane magnetic anisotropy and the structure is not annealed.

Compared to the spin orbital torques characterization using AHE in Ta/CoFeB/MgO structure with PMA, the temperature dependence of anti-damping torque obtained in our experiment is consistent with the one reported before that are characterized by AHE.³⁶ The anti-damping torque shows a week temperature dependence and it is slightly increased by cooling down the sample down to 10 K.³⁶ Characterization of the temperature dependent resistivity of the Ta (5 nm) thin film shows that the Ta resistivity increases by about 8.7% upon cooling down the sample down to 10 K. Hence, part of the enhancement of the spin Hall angle can be understood in the context of the enhancement of the Ta layer resistivity. However, the 14% enhancement of the spin Hall angle in our experiment suggests that the spin orbit coupling of the Ta layer could also improve at lower temperature. Since the anti-damping field obtained in our experiment is similar to what is reported in perpendicular Ta/CoFeB/MgO structure,³⁷ one can conclude that the major contribution to the anti-damping torque is originated from the spin Hall effect of the bulk of the Ta underlayer. Therefore, as long as the thickness of Ta is above a certain threshold (∼1 nm), one can expect to obtain a consistent and sizable anti-damping torque. Moreover, our experimental results suggest that the anti-damping torque is not modified significantly by the annealing temperature.

Absence of the field-like torque in our experimental results is consistent with our previous work in Ta/TbFeCo (1–2 nm)/MgO with perpendicular magnetic anisotropy.³³ Utilizing the standard AHE based spin orbital torque characterization, no sizable field-like torque was observed in the previous work.³³ Based on our studies, we have found that while the anti-damping torque is quite consistent and one can get similar results from different sputtering systems, the field-like is very sensitive and the results vary significantly from system to system. We believe that the interface quality and atomic intermixing at the interface is critical for the field-like torque component. Investigation of field-like torque as a function of the interface quality, annealing temperature, and magnetic anisotropy (in-plane or perpendicular) may shed the light in better understanding of the field-like torque component of the spin orbital torque and it is out of scope of our current work.

In summary, spin-orbital torques are experimentally studied in the Ta/CoFeB/MgO structure utilizing planar Hall effect at different temperatures. A sizable anti-damping torque with no significant field-like torque is observed. The spin Hall angle of about 18 ± 0.6% at room temperature and about 20.5 ± 0.43% at 100 K is estimated. This characterization of SOT is a reliable universal technique that relies on dc-current free from spurious effects of rf-current and can be applied to any in-plane magnetic structure. It provides a consistent platform to compare the strength of SOT in heavy metals and topological insulators.

This work was partially supported by the National Science Foundation Nanoelectronics Beyond 2020 (Grant No. NSF NEB 1124831), NSF MRSEC Program at University of Minnesota (Grants No. DMR-0819885), and by the C-SPIN center, one of six STARnet program research centers. A portion of this work was carried out in the Minnesota Nano Center.