Investigation of spin-orbit torque using current-induced magnetization curve

Manipulation of magnetization using current-induced torque is crucial for magnetic recording devices. Recently, the spin-orbit torque (SOT) that emerges in a ferromagnetic thin film on a heavy metal is focused as a new scheme for magnetization switching in perpendicularly magnetized systems. Since the SOT provides a perpendicular effective field to the system, the formation of a magnetic multiple domain state because of Joule heating is supressed in the magnetization reversal process. This means that high reliable switching is possible using the SOT. Here, by utilizing the SOT induced domain stability, we show that an electrical current directly injected to a perpendicularly magnetized Pt/Co/Pd system can magnetize itself, that is, current-induced magnetization process from multi to single domain state. A quantitative determination of the SOT is performed using the current-induced magnetization curve. The present results are of great importance as another approach to evaluate the SOT effect, as well as a demonstration of domain state switching caused by the SOT.

The SOT is known to act on magnetizations as an effective field. This contributes to the magnetization switching and DW motion. More importantly, the SOT effective field also plays a role in stabilizing the domain state against current-induced Joule heating 25,26 , which is often a severe problem in devices based on current-induced torque [27][28][29] . Owing to this characteristic of the SOT, random multiple domain formation is suppressed even under high current density as much as 10 11 -10 12 A/m 2 during the magnetization reversal. In this letter, we show that in a perpendicularly magnetized Pt/Co/Pd structure with a multi domain (MD) state in thermal equilibrium (having no net magnetization), the magnetization of the system increases with injected current, and finally, a single domain (SD) state is created (see Fig. 1a). This "current-induced" magnetization process is observed only when an external in-plane magnetic field parallel to the current exists, indicating that the SOT is responsible for the effect. A quantitative determination of the SOT effective field from the current-induced magnetization curve is performed. Figure 1b shows an optical microscope image of our device. The Hall bar component consists of asymmetrical Pt/Co/Pd layers deposited on a SiO 2 /intrinsic Si substrate (see also Methods). The width of the channel is 5 μm.
Owing to the interface magnetic anisotropy at the Pt/Co and Co/Pd interfaces, the system exhibits perpendicular magnetic anisotropy PMA. The high PMA realizes an MD state with perpendicular magnetization near the Curie temperature (~370 K in our device). Four Cr/Cu electrodes are formed to apply the current and to detect the Hall resistance R Hall . The definitions of each external magnetic field (μ 0 H x , μ 0 H y , and μ 0 H z ) and the current flow along the x-axis are indicated in Fig. 1b. The temperature of the stage T s , which is in thermal contact with the fabricated device, is controlled using a heater (see Methods). Figure 2a shows the results of the R Hall measurement when a dc current density J dc of +2.8 × 10 9 A/m 2 is injected at room temperature (T s = 304 K). μ 0 H z is swept to obtain the curves. J dc is determined by simply dividing the current by the cross-sectional area of the metallic layers. R Hall is proportional to the perpendicular component of the magnetization because of the anomalous Hall effect. A clear hysteresis loop with a coercivity μ 0 H c of 2.4 mT is observed. The remanent value of R Hall (R Hall r ) is almost equal to the saturation value, indicating that the SD state is stable at fields near zero.
Next, R Hall measurements with J dc sweeping are performed under constant in-plane magnetic fields. The procedure is as follows. First, the magnetization direction of the entire device is set upward by applying a μ 0 H z of +30 mT. After returning to ~0 T, a constant in-plane magnetic field (μ 0 H x or μ 0 H y ) of +38 mT is applied. Then, R Hall is monitored with a sweeping J dc . The positive (negative) sweep corresponds to a J dc change from 0 to +1.7 (−1.7) × 10 11 A/m 2 . Figure 2b and c show R Hall as a function of J dc measured under the application of μ 0 H y and μ 0 H x , respectively. As shown in the positive sweep (PS) in Fig. 2b, R Hall abruptly decreases when a J dc of +0.8 × 10 11 A/m 2 is applied, and drops toward zero in the region of J dc > +0.8 × 10 11 A/m 2 , indicating that the MD state is formed at J dc ≥ 0.8 × 10 11 A/m 2 due to the Joule heating. A rapid decrease in R Hall also appears symmetrically in the negative sweep (NS) case (see NS curve in Fig. 2b), suggesting that the Joule heating effect is independent of the J dc direction.
By contrast, the situation is completely different when μ 0 H x , which is parallel to J dc , is applied. For the PS curve in Fig. 2c, a full R Hall switching from positive to negative, which corresponds to the abrupt reversal of the magnetization direction from up to down, is observed at J dc = +0.5 × 10 11 A/m 2 . In the NS curve, no switching occurs up to J dc = −1.7 × 10 11 A/m 2 . When the sign of μ 0 H x is reversed, switching is observed only for a negative J dc (not shown). The switching direction in the present configuration is consistent with the SOT induced switching previously reported in the Pt/Co structure 2,26 . Although the sign of the spin Hall angle of the top Pd is the same as that of the Pt, the SOT in the present device is dominated by the spin current injection from the bottom Pt because the magnitude of the spin Hall angle of Pd is one order smaller than that of Pt 30,31 . We also checked that in a similar device structure, the top Pd effect on the SOT is negligibly small 32 . In order to evaluate the magnitude of SOT effective fields, i.e. the Slonczewski-like torque μ 0 H SL and field-like torque μ 0 H FL , the harmonic Hall measurement, which is widely used for the quantitative determination of the SOT 33 , was conducted for a similar device structure. The procedure is shown in the Supplementary Information. μ 0 H SL and μ 0 H FL are determined to be 6.55 ± 0.20 mT/10 11 A/m 2 and 1.57 ± 0.13 mT/10 11 A/m 2 , respectively. These values are close to those previously reported for Pt/ferromagnet bilayer structure 22 . Another important point here is that under μ 0 H x application, |R Hall | always represents a value close to saturation even at |J dc | ≥ 0.8 × 10 11 A/m 2 , indicating that the MD formation is completely suppressed against Joule heating. In the present case, the magnetization experiences a finite perpendicular effective field μ 0 H eff derived from μ 0 H SL because the magnetization tilts slightly toward the x-direction. When the current direction is the same as the μ 0 H x direction, the sign of μ 0 H eff becomes negative in the Pt/Co system. As a result, the SD state becomes stable because of the gain by the Zeeman energy reduction. Thus, the SOT plays an important role in stabilizing the SD state.
In the above experiments, T d was increased by injecting a current. In the following, the MD state at thermal equilibrium is prepared by simply increasing T d using a heater. Figure 3a shows the results of the Hall measurements performed at T s = 343 K. J dc for this measurement is 2.8 × 10 9 A/m 2 , and the Joule heating effect is negligibly small. In this case, an anhysteric R Hall curve with the almost zero remanent is observed. This indicates that the MD state is realized and the system is demagnetized. Figure 3b shows R Hall as a function of J dc obtained under μ 0 H z of ~0 T. R Hall is almost independent of J dc in the range of ±0.5 × 10 11 A/m 2 . Similarly, no change in R Hall is observed for a μ 0 H y of +38 mT, as shown in Fig. 3c. The slight R Hall deviation from zero is probably due to the small z-component of the field. The slight J dc dependence on R Hall shown in Fig. 3b and c might be a result of the Oersted field. Based on these results, it can be concluded that in both cases, the MD state is kept under current injection. The result obtained under μ 0 H x = +38 mT is completely different, as shown in Fig. 3d.   In order to check whether the device is fully in the SD state, a cooling experiment under current is carried out. The procedure is as follows. After making R Hall saturation using current under μ 0 H x = +38 mT, T d is gradually decreased from 343 K to room temperature with remaining the current and x-field application. J dc of −0.25 × 10 11 A/m 2 is continuously applied during the cooling. During the T d decrease, R Hall is monitored. The result is shown in Fig. 3e. One can see that R Hall gradually increases with decreasing T d and at room temperature it shows ~0.4 Ω, which is the value for the SD state. This indicates that the SD state is created by the current at 343 K and is maintained during cooling. On the other hand, when the above experiment is performed with an injection of J dc = −2.8 × 10 9 A/m 2 , R Hall shows a small value of ~0.1 Ω even at room temperature, suggesting that the MD state formed at 343 K is retained even at room temperature. Therefore, the R Hall saturation in Fig. 3(d) corresponds to the complete SD state, i.e. a situation where no domain with an opposite magnetization exists in the device is realized against thermal agitation. The result presented here demonstrates that the magnetization curve of Pt/Co/ Pd system can be obtained by only sweeping electrical current owing to the stability caused by the SOT. In addition, the magnetization direction can be reversibly controlled by simply changing the current polarity.
The magnetization processes shown in Fig. 3(a) and (d) are caused by μ 0 H z and μ 0 H eff , which is proportional to J dc , respectively. The current-induced magnetization process is expected to develop with the DW motion in the current direction, while the magnetic domains isotropically expands when the magnetization process is caused by the external field. Here, we focus on the gains of the Zeeman energy for each case and determine μ 0 H eff , and consequently μ 0 H SL , by comparing them. First, E Z obtained by μ 0 H z (E Z _ H ) is calculated for the up magnetization case. Figure 4   where M s is the saturation magnetization of the system. The integral term of (1) is defined by the coloured area of Fig. 4(a), and E Z _ H /M s is determined to be 0.180 mT. Subsequently, using the current-induced magnetization curve shown in Fig. 3(d), E Z resulting from μ 0 H eff (E Z _ J ) is calculated. R Hall n as a function of J dc in the negative J dc sweep, where the positive μ 0 H eff is applied to the system, is shown in Fig. 4(b). The small J dc offset is corrected in this figure. Since μ 0 H eff is expected to be proportional to J dc , E Z _ J can be determined from the following: Next, we calculated μ 0 H SL (per 10 11 A/m 2 ) using μ 0 H eff determined above. Figure 4(c) shows a schematic where the direction of μ 0 H SL under the x-field is denoted. μ 0 H eff is the perpendicular component of μ 0 H SL and θ is the tilting angle of the magnetization from the z-axis. Thus, μ 0 H SL is expressed as μ 0 H eff /sinθ. From the x-field dependence of the anomalous Hall resistance, θ at μ 0 H x = +38 mT is approximately 19° in our Pt/Co/Pd structure. Therefore, μ 0 H SL of 7.67 ± 0.04 mT/10 11 A/m 2 is obtained. This value shows good agreement with that obtained by the harmonic measurement in our Pt/Co/Pd system. μ 0 H eff was also calculated using a Langevin fit and the result is consistent with the direct Zeeman energy calculation (see Supplementary Information). The calculation results presented here indicate that the SOT effective field can be quantitatively determined from the current-induced magnetization curve.
Finally, we demonstrate current-induced alternate switching between the MD and SD states. Figure 5(a) shows the sequence of J dc injection into the device. A pulsed J dc with three values of +0.4 × 10 11 , +2.7 × 10 9 , and −0.4 × 10 11 A/m 2 is injected in series to create the SD state with up and down magnetization. The duration of each J dc pulse is 1.0 s, and a μ 0 H x of +38 mT is applied during the measurement. The R Hall value is measured during the pulse injection, and the result is shown in Fig. 5(b). Maximum and minimum R Hall values corresponding to the up and down SD states appear alternately with the injections of +0.4 and −0.4 × 10 11 A/m 2 . At J dc = 2.7 × 10 9 A/m 2 , R Hall always exhibits an intermediate value, that is, the MD state is restored. We checked that the current-induced SD state returns to the MD state within 1 ms after pulse off. This result indicates that an arbitrary switching of domain states between MD and SD can be achieved by injecting a current. Although in the present case, 1-ns-long pulses were used for the convenience of the measurement, sub-ns domain state switching is expected to be possible because the SOT induced magnetization switching occurs in this time scale 34 .
When the SOT effectively acts on the magnetization, the electrical current flowing in the system enhances the stability of the single domain state. In this study, owing to this domain stability, we show that the magnetization curve of the nonmagnetic/ferromagnetic metal structure can be obtained by sweeping electrical current, while it is conventionally obtained by sweeping external magnetic field. This effect would be marked in smaller size applicable to current IT devices because the SOT field is proportional to the current density flowing in the heavy metal layer. Anisotropy-wedged film 16 , an interlayer exchange coupled system 17 , and an antiferromagnet/ferromagnet layered structure 18 , where in-plane field free magnetization switching by the SOT was achieved, may also enable domain state switching without an in-plane field. In addition, this work offers a novel method to determine the SOT effective field from the current-induced magnetization curve.

Methods
Film deposition and device fabrication. Multilayered Ta (2.7 nm)/Pt (3.0)/Co(0.36)/Pd (0.8) film was deposited on a thermally oxidized Si substrate using rf sputtering, and a 0.5-nm-thick Ta layer was formed on the film as a cap. The base pressure of the sputter chamber was below 1.0 × 10 −6 Pa, and Xe process gas was used for the deposition. The X-ray diffraction profile indicates that the Pt layer has an fcc (111) texture. The film was patterned into a Hall bar structure by photolithography and Ar ion milling. Cr (1.0)/Cu (100) electrodes were deposited by thermal evaporation and defined by a lift-off process using photolithography. Measurement setup. Measurements were performed using a prober system in which a vector magnetic field can be applied. The device temperature was controlled by a plate-shaped heater placed under the device and monitored using a Pt thermometer (Pt-100). A current source (Yokogawa 7651) and nano-voltmeter (Keithley 2182A) were used for anomalous Hall measurements.