Roles of Joule heating and spin-orbit torques in the direct current induced magnetization reversal

Current-induced magnetization reversal via spin-orbit torques (SOTs) has been intensively studied in heavy-metal/ferromagnetic-metal/oxide heterostructures due to its promising application in low-energy consumption logic and memory devices. Here, we systematically study the function of Joule heating and SOTs in the current-induced magnetization reversal using Pt/Co/SmOx and Pt/Co/AlOx structures with different perpendicular magnetic anisotropies (PMAs). The SOT-induced effective fields, anisotropy field, switching field and switching current density (Jc) are characterized using electric transport measurements based on the anomalous Hall effect and polar magneto-optical Kerr effect (MOKE). The results show that the current-generated Joule heating plays an assisted role in the reversal process by reducing switching field and enhancing SOT efficiency. The out-of-plane component of the damping-like-SOT effective field is responsible for the magnetization reversal. The obtained Jc for Pt/Co/SmOx and Pt/Co/AlOx structures with similar spin Hall angles and different PMAs remains roughly constant, revealing that the coherent switching model cannot fully explain the current-induced magnetization reversal. In contrast, by observing the domain wall nucleation and expansion using MOKE and comparing the damping-like-SOT effective field and switching field, we conclude that the current-induced magnetization reversal is dominated by the depinning model and Jc also immensely relies on the depinning field.

2 S1. The demonstration of the direct current generated Joule heating.
In order to demonstrate the existence of the direct current generated Joule heating, the dependence of the longitudinal voltage (Vxx) on the current (I) for Pt/Co/AlOx sample is measured using the four-point method shown in Fig. S1 (a). Fig. S1 (b) shows the corresponding dependence of the longitudinal resistance (Rxx) on the current. The nonlinear dependence indicates the existence of Joule heating. For a quantitative study of the Joule heating, we also measure the temperature (T) dependence of Rxx in a range from 100 K to 400 K at a small current of 0.1 mA. By the linear fitting, the quantitative relationship of Rxx and T can be obtained. Comparing these two sets of data (Rxx~T and Rxx~I), we can estimate the temperature changes at different direct currents, which is shown in Fig. S1 (d).

S2. Polar Kerr hysteresis loops and Kerr differential images of the domain wall nucleation and expansion measured at different temperatures.
In order to reveal the effect of the Joule heating (QJ~I 2 ) generated from the direct current on the field-induced magnetization reversal as well as DW nucleation and expansion behavior, we investigate the variation of the polar Kerr hysteresis loops and Kerr differential images at different T without applying any currents. can see that the loops gradually become narrow as T increases for Pt/Co/SmOx and Pt/Co/AlOx, indicating the decrease of Hsw with T increasing. In addition, the Kerr differential images of the domain wall nucleation and expansion were also observed when collecting the Kerr hysteresis loops. Fig. S2 (c) and (d) show representative Kerr differential images of the DW nucleation and expansion measured at different T for Pt/Co/SmOx and Pt/Co/AlOx, respectively. The light (deep) color in the images corresponds to the "up" ("down") domain or magnetized state. As the same as the case at the direct currents described in Fig. 3 of the main text, we can observe that both the nucleation field and switching field in the measured regions gradually decrease as T increases for the two stacks. The high temperature can also change the nucleation site and expansion speed, revealing that the temperature can affect the Hsw by DW nucleation and expansion. It is also noted that the resolution of images at the higher temperature reduces due to that the temperature changes the optimized focusing height of samples.

S3. Polar Kerr hysteresis loops and Kerr differential images of the domain wall nucleation and expansion measured at different pulse voltages.
In order to investigate the effect of the current-induced SOT (τ~I) on the field-induced magnetization reversal as well as DW nucleation and expansion behavior, we explore the variation of the polar Kerr hysteresis loops and Kerr differential images at different pulse voltages (Vp) using a 300 picosecond pulse generator (Tektronix: PSPL10300B) by fading out the Joule heating effect. Fig. S3  To measure the planar Hall resistance (ΔRPHE), a large in-plane magnetic field of 5 T was applied to fully make the magnetization in the x-y plane. And then, the Hall resistance (RHall) was recorded as a function of the in-plane angle φ (the angle is shown in the inset of Fig. S4 (a)). Fig. S4 (a) and (b) show the variation of RHall against φ for Pt/Co/SmOx and Pt/Co/AlOx, respectively. The ΔRPHE is defined as the half of the difference between the maximum and minimum values of RHall, which is depicted in Fig. S4 (a). Therefore, ΔRPHE is obtained which equals to 0.26 and 0.29 Ω for Pt/Co/SmOx and Pt/Co/AlOx stacks, respectively. The anomalous Hall resistance (ΔRAHE) with the same definition as ΔRPHE can also be obtained by the measurement shown in Fig. 1 (b) and (c) of 4 the main text. The corresponding ξ (= ΔRPHE /ΔRAHE) is found to be 0.15 for both the stacks.
Before the planar Hall effect (PHE) correction, the calculated damping-like effective field (HDL) and field-like (HFL) effective field using Eq. (2) in the main text as a function of the amplitude (I0) of the sinusoidal current are shown in Fig. S4 (c)-(f). Fig. S4 (c) and (d) show HDL against I0 for Pt/Co/SmOx and Pt/Co/AlOx stacks, respectively, which presents a roughly linear relationship. Thus, HDL per unit current density (βDL) can be found to be -3.67 ± 0.02 Oe/(10 6 A/cm 2 ) (2.40 ± 0.12 Oe/(10 6 A/cm 2 )) for the "up" ("down") magnetized state for Pt/Co/SmOx and -3.30 ± 0.12 Oe/(10 6 A/cm 2 ) (3.35 ± 0.13 Oe/(10 6 A/cm 2 )) for the "up" ("down") magnetized state for Pt/Co/AlOx using βDL=HDL/Je (Je is the charge current density). It is evident that the damping-like SOT induced effective field is almost equivalent, which is due to the same contribution from the heavy metal Pt. Besides, the HFL is also plotted as a function of I0 in the same manner for both devices displayed in Fig. S4  In order to exclude the effect of the anisotropy field (Hk) on the depinning mechanism due to the existence of Joule heating, we investigate the Hk as a function of T in a range from 100 K to 400 K for Pt/Co/SmOx and Pt/Co/AlOx samples. The Hk is determined by measuring RHall versus the in-plane field (Hx) loops at different temperatures using the Eq. (1) in the main text. As shown in Fig. S5 (a) and (b), the Hk decreases weakly as T increases for Pt/Co/SmOx, especially the Hk still keeps a large value (≈6000 Oe) at 400 K and the Hk remains roughly constant for Pt/Co/AlOx at different T. Meanwhile, we also measures Hk against T for other Pt/Co/SmOx and Pt/Co/AlOx bars in the batch, which is shown in Fig. S5 (c) and (d). Although the size of Hk shows some 5 differences, the tendency of Hk against T remains similar, indicating that Hk indeed presents a weak temperature dependence.
In addition, RHall-Hz loops are measured at the large current (large Joule heating) for Pt/Co/SmOx and Pt/Co/AlOx samples shown in Fig. S6 (a) and (b). They both still keep the sharp square-shaped loops and relatively large RHall, confirming the presence of well PMA at large Joule heating. By contrast, the switching field becomes very small for both samples. Therefore, the depinning model should be dominant.

(B) The temperature dependence of the saturated magnetization (Ms) and
damping-like effective field per unit current density (ΔHDL/Je).  Fig. 6 (a) and (c) in the main text also demonstrates the influence of Joule heating. Although the Joule heating generated from the sinusoidal current is smaller than that from the direct current at the same current amplitude, the Joule heating becomes also non-negligible at the large I0, which can lead to the ΔHDL deviating the linear relationship at the I0 of 3 mA. The Joule heating effect is considered to be a non-linear behavior in the I0 dependence of ΔHDL as reported in the previous work. 4, 5 Therefore, the decreasing Ms makes the ΔHDL/Je increasing. However, the ΔHDL/Je is still relatively small and does not change by the order of the magnitude, even though the ΔHDL/Je increases as T or Joule heating increases gradually. For instance, the ΔHDL/Je at 300 K is -3.58 ± 0.19 Oe/(10 6 A/cm 2 ) 6 (3.29 ± 0.19 Oe/(10 6 A/cm 2 )) for the "up" ("down") magnetized state for Pt/Co/SmOx and -3.64 ± 0.07 Oe/(10 6 A/cm 2 ) (3.91 ± 0.09 Oe/(10 6 A/cm 2 )) for the "up" ("down") magnetized state for Pt/Co/AlOx. However, the ΔHDL/Je is -4.27 ± 0.17 Oe/(10 6 A/cm 2 ) (3.91 ± 0.24 Oe/(10 6 A/cm 2 )) for the "up" ("down") magnetized state for Pt/Co/SmOx and -4.04 ± 0.15 Oe/(10 6 A/cm 2 ) (4.42 ± 0.13 Oe/(10 6 A/cm 2 )) for the "up" ("down") magnetized state for Pt/Co/AlOx when the T increases to 400 K. It means that the magnitude of ΔHDL/Je for both samples is still a small value at higher T.
Whereas, Jc is~4.35×10 6 Acm -2 for Pt/Co/SmOx and Pt/Co/AlOx, the ΔHDL is estimated to be small and ΔH z DL =ΔHDLsinδ may be smaller, indicating that ΔHDL is also still a relatively small value so that it cannot overcome the large anisotropy field according to the coherent switching model.
As a consequence, the switching mechanism should be the domain wall nucleation and expansion based on a depinning model.