Strongly heat-assisted spin–orbit torque switching of a ferrimagnetic insulator

Recently, spin–orbit torque (SOT) is being intensively investigated for various SOT device-based applications, such as next-generation SOT magnetoresistive random access memory, in-memory-computing, and neuromorphic computing.^1–5 Due to the low Gilbert damping, the absence of Ohmic loss, and long spin transmission length, magnetic insulators have received great attention because of their high energy efficiency and promising spin electronic applications.^6–13 The perpendicular magnetic anisotropy (PMA) in magnetic insulators can be engineered by controlling the interfacial strain between magnetic insulators and the substrates.^14–16 Note that the Gilbert damping can still be as low as 3 × 10⁻⁴ for some magnetic insulator with PMA.¹⁷ This PMA enables for an accurate determination of the proximity effect-induced anomalous Hall effect (AHE),^18,19 which makes SOT-driven magnetization switching easier to detect. In recent years, researchers have achieved SOT switching of ferrimagnetic insulators at room temperature, such as thulium iron garnet (Tm₃Fe₅O₁₂, TmIG) and terbium iron garnet (Tb₃Fe₅O₁₂, TbIG).^8,9,12,20,21 In addition, some ferrimagnetic insulators exhibit fast domain wall dynamics,^10,11 particularly near the compensation temperature.²² However, a systematic study of the temperature dependence of SOT switching across the compensation temperature has not been performed, and the role of thermal effect remains elusive.

In this article, we fabricate TbIG/W Hall bar devices, which show a good PMA. The SOT switching was studied at various temperatures, and we find that the SOT switching always happens in the Fe-dominated scenario since the switching polarity of SOT switching does not change. After systematically evaluating the device temperature under different channel currents, the current-induced heating effects on the field-induced switching and SOT switching were investigated. Magnetization decreases with the increase in the temperature, giving rise to the decrease in SOT. At last, we explain the destructed SOT switching loops with the external field applied under small polar angles.

We first discuss methods for film preparation and device fabrication. The TbIG target was prepared by following Ref. 16. Then, the TbIG film was grown around 473 K by using KrF excimer laser pulses with the repetition of 1 Hz and 12-wt. % ozone under 1.5-mTorr oxygen pressure. The wavelength and power were 248 nm and 150 mJ, respectively. Moreover, the sample was annealed ex situ in an O₂ environment under 1073 K for 5 min using rapid thermal annealing for magnetizing the TbIG film. Then, the W(5 nm), MgO(2 nm), and TaOx(3 nm) layers were deposited ex situ on the top of TbIG at room temperature by magnetron sputtering. As a result, we get the Gd₃Ga₅O₁₂(111)/TbIG(6 nm)/W(5 nm)/MgO(2 nm)/TaO_x(3 nm) film, and it is patterned into Hall bar devices. Figure 1(a) shows the schematic of the device and the definition of polar angle θ and azimuthal angle φ. The optical image of the TbIG/W Hall bar device is shown in Fig. 1(b), and the channel width of the Hall bar device is 20 μm.

We investigate the magnetic properties of our TbIG/W devices using AHE measurements. The PMA is confirmed by the out-of-plane hysteresis loops of TbIG under various temperatures [Fig. 1(c)]. It is worth noting that the field-induced switching polarities are inversed as the AHE signs are inversed, suggesting that the magnetization compensation temperature (T_M) is between 350 and 355 K. This higher-than-normal T_M indicates that our TbIG thin films are rare-earth-rich.¹⁴ The AHE sign change is due to the change in the dominant element in the magnetization of TbIG: when T < T_M, the magnetization of TbIG is dominated by Tb, while the AHE sign is determined by transition metal Fe;^19,23 when T_M < T < T_C (Curie temperature), the magnetization of TbIG is dominated by Fe. As shown in Fig. 1(d), the coercive field increases with the increase in the temperature for T < 350 K and then decreases with the increase in the temperature for T > 350 K, reaching its maximum at 350 K. The reason is that the net magnetization reaches a minimum around T_M. Therefore, a larger coercive field is required for achieving enough Zeeman energy and switching the magnetization to the opposite direction. Note that compared with TmIG or Gadolinium iron garnet (Gd₃Fe₅O₁₂, GdIG),^14,22 our TbIG has a higher compensation temperature (355 K), which may be beneficial in the application. We note that the positive and negative coercive fields for some out-of-plane hysteresis loops are not similar [Fig. 1(c)]. We do not understand the mechanism yet. Nevertheless, this observation will not affect our switching and SOT studies since we will show later that the magnitudes of positive and negative switching current are almost the same when the assisted field is in the plane [Figs. 2(b)–2(d)] and the second-harmonic data are antisymmetric with the zero field [Fig. 4(a)].

We then study the temperature dependence of SOT-driven switching in TbIG/W devices. We fix the x-direction external field (B_x) and record Hall resistance (R_xy) with 1 mA reading pulses, while we sweep the amplitude (I_c) of writing pulses [Fig. 2(a)]. The writing pulse duration is 1 ms in this article unless specifically mentioned, and the reading pulse duration is larger than 10 ms for accurate R_xy measurements. For all measurements, we set a sufficient time gap (>1 s) between the writing pulse and the reading pulse for the dissipation of heat generated from writing pulses in each cycle. We show the current-induced switching under T = 150 and T = 360 K with the assistance of B_x = ±20 mT in Figs. 2(b) and 2(c), respectively. At 360 K, the magnitude of the AHE signal difference in the SOT switching (0.013 Ω) is smaller than the difference in the field-induced switching (0.021 Ω), indicating that the magnetization of the TbIG/W bilayer is not fully switched by SOT. This suggests that the part of magnetization in the Hall probe region cannot be fully switched presumably due to the reduced current density in the Hall probe region. After the field direction reverses, the switching polarity is also inversed, which is consistent with the physics of SOT switching. When the temperature changes from 150 to 360 K, the magnetization changes from the Tb-dominated scenario to the Fe-dominated scenario, and thus, an opposite polarity of SOT switching is expected.^23,24 However, the same switching polarity is observed for temperatures below and above T_M in our TbIG/W devices.

To understand the same switching polarity, we investigate the thermal effect on the SOT switching as suggested by previous studies.^23,24 We measure the temperature-dependent longitudinal resistance (R_xx) to get a temperature coefficient of −0.0255 Ω/K and then estimate the temperature rise induced by current, namely, ΔT. The results are shown in the inset of Fig. 2(d) in which ΔT increases parabolically with the increase in the direct current (I_DC) in the range of 0 mA < I_DC ≤5 mA. We fit the experimental data and extrapolate ΔT to a current of 15 mA. We note that our ΔT is larger than the W/CoTb case²⁴ presumably because the magnetic insulators have a lower thermal conductivity. We also note that ΔT in our TbIG/W case is much greater than the TmIG/Pt case at the same channel current,⁹ which is consistent with a much larger resistivity of W than Pt. Experimentally, we observe that the critical switching current (I_sw) decreases with the increase in T [Fig. 2(d)]. Using the inset of Fig. 2(d), we estimate T + ΔT(I_sw) for SOT switching at different temperatures and find that all the switching happens at switching temperatures above 440 K, whereas the measurement temperature of R_xy is varying from 150 to 360 K. Therefore, all switching happens above T_M, namely, Fe-dominated scenario. While the switching is achieved at a temperature above T_M, we always measure R_xy at the operating temperature (T) since we apply a reading pulse with a small magnitude after waiting for sufficient time to let writing pulse-induced heat dissipate. This is different from the previous studies, where R_xy was measured during the large writing pulses.^24,25 Our SOT switching measurement scheme suggests a physical picture that the sublattice magnetization directions keep the same direction [Figs. 2(b) and 2(c)] after the temperature changes from T_w (=T + ΔT(I_w)) to the operation temperature (T) since we only apply in-plane fields during the SOT measurements. As a result, the net magnetization changes its direction, and the simultaneous change in the net magnetization and AHE sign leads to the same SOT switching polarity.

Next, we further confirm our arguments about heat-assisted SOT switching and net magnetizations by studying out-of-plane hysteresis under the combination of writing and reading pulses. This is different from Fig. 1(c), where only a small reading pulse is used to measure out-of-plane hysteresis. First, we would like to reassure readers that induced ΔT by the 1 mA reading pulse is negligible, while ΔT by the writing pulses can be very significant. We follow the same measurement schematic as in Fig. 2(a) with a writing pulse duration as large as 10 ms and keep track of the longitudinal resistance R_xx while pulses are applied. As shown in Fig. 3(a), measured R_xx during the writing pulse decreases parabolically with the writing pulse amplitude (I_w), while subsequently measured R_xx during the reading pulse amplitude of 1 mA has a negligible variation as I_w varies. The estimated temperature due to the writing pulse (T_w) can be significantly different from the temperature during the reading pulse, which is close to the operation temperature T [Fig. 3(a)]. In the SOT switching experiments, in-plane external fields do not change sublattice magnetization directions across the compensation temperature. Here, we investigate the behavior of sublattice magnetizations across the compensation temperature under the out-of-plane field by using 5 mA writing pulses with durations of 5 ms and 1 mA reading pulses [Fig. 3(b)]. From the I_c dependence of the temperature, the 5-mA pulses and 1-mA pulses correspond to the Fe-dominated scenario (T_w > T_M) and the Tb-dominated scenario (T_w < T_M). Thus, we anticipate that two coercive fields with different amplitudes will appear when we use 5-mA writing pulses and 1-mA reading pulses to detect field-induced switching because of the temperature dependence of the coercive field [Fig. 1(d)]. The results shown in Figs. 3(c) and 3(d) are consistent with our hypothesis. We observe a larger coercive field of around 60 mT for writing pulse hysteresis loops in Fig. 3(c) (T_w > T_M) and a smaller coercive field of around 30 mT for reading pulse hysteresis loops in Fig. 3(d) (T is the room temperature). However, there are AHE sign changes between 30 mT < |B_z| < 60 mT for the T_w > T_M case [Fig. 3(c)]. We explain these phenomena as follows. When $Bz>$ 60 mT, the field is sufficient to align the net magnetization to the field direction and AHE resistance signs are opposite in Figs. 3(c) and 3(d) since they are corresponding to Fe- and Tb-dominated scenarios, respectively. For 30 mT < |B_z| < 60 mT, the out-of-plane field could switch the net magnetization of the Tb-dominated scenario when reading pulses are applied [Fig. 3(d)]. When we apply writing pulses, the device will warm up without changing the magnetization direction of Tb and Fe sublattices since the field is smaller than the coercive field at the T_w. Nevertheless, under 5-mA writing pulses, the net magnetization is reversed, resulting in a sign change in the AHE resistance. For |B_z| < 30 mT, the external field cannot switch the net magnetization of both Tb- and Fe-dominated scenarios. Therefore, there is no sign change in the AHE resistance when the magnetic field strength is reduced below 30 mT. Our results suggest that the net magnetization changes the direction across the compensation temperature if the fixed external field is smaller than the coercive field at the target temperature. In our SOT switching case, the in-plane field is much smaller than the in-plane coercive field, and thus, the net magnetization directions are different in Figs. 2(b) and 2(c) after the same combination of external field direction and current direction.

After studying the thermal effect on SOT switching, we investigate its role on SOT efficiency ξ_DL. We measure the current-induced damping-like effective field B_DL using the second-harmonic method. Under the single domain approximation, with the assisting in-plane field (H_ext), the second-harmonic Hall resistance (⁠$RH2ω$⁠) is given by^26,27

where R_AHE and R_PHE are the anomalous Hall resistance and transverse planar Hall resistance, respectively. H_FL, H_DL, and H_K represent the current-induced field-like effective field, the current-induced damping-like effective field, and the PMA effective field, respectively. R_SSE is the resistance induced by the spin Seebeck effect. For extracting the value of H_DL, we only apply the field along φ = 45° to eliminate contribution from H_FL. For measuring $RH2ω$⁠, we apply a low-frequency alternating current (AC) with the root mean square of the current (I_rms) ranging from 0.5 to 1.5 mA. The corresponding range of the AC peak value (I_ac) is from 0.7 to 2.1 mA. The measurement results are shown in Fig. 4(a). After fitting, the measurement results of B_DL and $BDLIac$ are shown in Fig. 4(b). Although B_DL slightly increase with the increase in I_rms, $BDLIac$ decreases with the increase in I_rms. $ξDL=2eMstTbIGBDLℏJac$⁠,²⁷ where ℏ is the reduced Planck constant, J_ac is the channel current density, e is the electron charge, M_s is the net saturation magnetization, and t_TbIG is the thickness of TbIG. Therefore, ξ_DL is proportional to $MsBDLIac$⁠. To clarify the influence of temperature on ξ_DL, the temperature dependence of M_s is necessary. Considering the three sublattices of TbIG,²⁸ we simulate the temperature dependencies of total magnetization of TbIG (⁠$MTbIGtotal$⁠), net magnetization of TbIG (⁠$MTbIGnet$⁠), total magnetization of Tb (⁠$MTbtotal$⁠), and net magnetization of Fe (⁠$MFenet$⁠), as shown in Fig. 4(c). $MTbIGtotal$⁠, $MTbtotal$⁠, and $MFenet$ decrease with the increase in the temperature up to T_C. As the temperature increases, $MTbIGnet$ decreases to 0 at T_M and then increases slightly. Finally, $MTbIGnet$ drops and reaches 0 at T_C, as shown in the inset of Fig. 4(c). From $MsBDLIac$ shown in Fig. 4(b), we can conclude that ξ_DL decreases significantly as I_rms increases, which is different from the well-accepted understanding of current-independent ξ_DL. The decrease in ξ_DL is in line with the increasing temperature due to the current-induced Joule heating effect. It is consistent with previous results from experiments and theory: ξ_DL decreases when the interfacial (total) magnetization (not the net magnetization) decreases in heavy metal/magnetic insulator systems since the number of spin channels is positively dependent on the magnetic moment density.^12,29

At last, current-induced SOT switching is characterized at various polar angles with the assistance of a fixed external field B = 18.75 mT [Fig. 4(d)]. θ_B is the polar angle of the external field. The SOT switching appears with θ_B ranging from 78° to 102° because for θ_B ≤ 78° or θ_B ≥ 102°, the z-component of B (B_z) is sufficient to pin the magnetization in the field direction. As a result, there is no switching for θ_B ≤ 78° or θ_B ≥ 102°. For the angles around threshold switching angles such as 84° [Fig. 4(e)] and 96° [Fig. 4(f)], the SOT switching loops show anomalous switching back phenomena. In the case of θ_B = 84°, when −10 mA ≤ I_c < −9.2 mA, the writing temperature T_w is around T_C. Therefore, the magnetization is negligible, and the SOT effective field becomes very weak. After applying I_c, the device cools down under B_z, giving rise to the net magnetization direction along the direction of B_z, and the sign of AHE resistance is inversed. When −9.2 mA ≤ I_c < 9.2 mA, the heat generated from I_c is not adequate to make the SOT effective field less than B_z, resulting in no field-induced switching. As for 9.2 mA ≤ I_c < 10 mA, although the SOT effective field is very weak, the constant B_z pins the magnetization along the same direction when −10 mA ≤ I_c < −9.2 mA. As a result, no field-induced switching happens across I_c = 9.2 mA, and this anomalous switching back curve only appears in the range of −10 mA ≤ I_c < −9.2 mA. On the other hand, for θ_B = 96°, the only difference is the direction of B_z, so this anomalous switching back curve appears in the range of 9.2 mA ≤ I_c < 10 mA rather than −10 mA ≤ I_c < −9.2 mA.

In summary, we have systematically characterized the role of the current-induced Joule heating effect on a TbIG/W SOT device. The thermal effect affects the SOT- and field-induced switching and B_DL. Because of the current-induced heating, SOT switching happens at a writing temperature above T_M despite that the operating temperature is well below T_M. The current dependence of ξ_DL is not constant since ξ_DL decreases as the total magnetization density decreases due to the increase in the temperature. In addition, the competition between B_z and the SOT effective field leads to anomalous switching back phenomena for SOT switching loops under external fields with small polar angles. Our results suggest a significant role of Joule heating in magnetic insulator/heavy metal heterostructures and help build future spintronic applications based on magnetic insulators.

Q.S. acknowledges early help from Device Research Laboratory at UCLA regarding device preparation and some of the measurements. The authors at HKUST acknowledge funding support from the Research Grant Council—Early Career Scheme (Grant No. 26200520) and the Research Fund of Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology (Grant No. 2020B1212030010). M.A. and J.S. were supported by Spins and Heat in Nanoscale Electronic Systems (SHINES), an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award No. DE-SC0012670.