Magnetic memory driven by spin splitting torque in nonrelativistic collinear antiferromagnet

Domain: physics
Published: 2025-12-30
Editorial outcome: major_revision

Abstract
Magnetic random-access memory (MRAM) provides a promising candidate for the next-generation memory technology with high-energy efficiency and fast operation speed. Spin splitting band structure in nonrelativistic collinear antiferromagnet with de-coupled crystal and spin symmetry provides a unique way for the flexible and efficient control of the polarization and flow directions of the spin current. Here, by integrating the potential altermagnetic (101)-RuO2 writing channel with the magnetic tunnel junction (MTJ) device, we demonstrate the all-electrical field-free altermagnetic spin splitting torque (SST)-driven switching of the perpendicular-MTJ in the 3-terminal altermagnetic SST-MRAM device, with the tilted spin polarization and the transversal flow of the spin current. The z-spin torque is further characterized by the altermagnetic SST-induced shift of the magnetic hysteresis loop, and the field-free altermagnetic SST-driven magnetic domain switching of the recording layer is directly observed by the magneto-optic Kerr effect (MOKE) microscope. Our research establishes groundwork for advancing the development of the altermagnetic SST-MRAM, paving the way for the future all-electrical, energy-efficient and high-endurance MRAM applications with separated writing/reading channels.

Introduction
Non-volatile magnetic memory technology provides a promising candidate for the next-generation memory devices beyond Moore’s law, with high-endurance, low-power, fast-speed and logic-in-computing performances. In the current magnetic random-access memory (MRAM) architecture, the magnetic tunnel junction (MTJ) serves as the memory cell, with the relative orientation of parallel and antiparallel representing the “0” and “1”, where the reading of the information based on the low/high resistance states originates from the tunneling magnetoresistance (TMR). The writing of the MRAM has undergone a revolution from the magnetic field (Toggle-MRAM) to electrical current-induced magnetization switching by spin transfer torque (STT-MRAM) towards lower power consumption and higher storage density, where the spin-polarized current is employed to exert the spin torque on the recording layer and switches the magnetization beyond the critical switching current density.

One of the major challenges for STT-MRAM is that a high writing current density needs to pass through an ultrathin-tunnel barrier (~1 nm), and thus the endurance of the MTJ is limited. Three-terminal spin-orbit torque-driven MRAM (SOT-MRAM) has a better endurance due to the separation of the writing and reading channels, where the spin torque is injected from an additional layer with strong spin-orbit coupling (SOC). Another advantage for SOT-MRAM is that abundant SOC materials can be integrated with MTJ besides conventional heavy metals such as topological insulators, 2-dimensional materials, Rashba interfaces, antiferromagnets, and so on. However, the spin polarization of SOT is typically fixed (mostly in-plane) by the symmetry breaking, and thus the high-density SOT-MRAM based on pMTJ with perpendicular magnetic anisotropy (PMA) needs an additional magnetic field or symmetry design to assist the SOT switching.

Recently, the nonrelativistic spin-splitting band structures in nonrelativistic collinear antiferromagnetism with zero net magnetization have been proposed and experimentally observed by the angle-resolved photoemission spectroscopy, with the distinctive alternation of spin polarizations in both the real-space crystal structure and the momentum-space band structure, giving rise to the term altermagnetism. Moreover, the spin-torque measurement demonstrated the Néel vector-dependent and crystal direction-dependent spin splitting torque (SST) in the altermagnet/ferromagnet heterostructures, inspiring a unique altermagnetic spin splitting torque-driven-MRAM (SST-MRAM), with flexible control of the two degrees of freedom of spin current: the spin polarization direction aligns along the Néel vector direction (N), and the spin current flow direction depends on the deviation in orientation between the electrical current and crystal axis. Therefore, the memory device-level altermagnetic SST-MRAM is urgently realized, with adjustable spin polarization and transversal spin current flow, aiming to realize the all-electrical field-free operation of MRAM with separate read/write channels, high endurance and flexible manipulation.

In this work, the altermagnetic (101)-RuO2 is employed to provide the transversal spin current with a tilted spin polarization along the Néel vector and exerts the SST on the adjacent perpendicular magnetization, under the electrical current applied along the [010] crystal direction. The out-of-plane component of SST is quantified by the current-induced hysteresis loop shift method, with an amplitude of 1.02×10–6 Oe A–1 cm2. Under this unique spin current, the field-free SST switching is achieved in the Hall device with a structure of RuO2/Mo/CoFeB/MgO/Ta. Nevertheless, the z-spin vanishes with the electrical current along the [101] direction required by the symmetry, and no spin current is caused by SST for this case. Based on these, by integrating the 250 nm-size MTJ as the memory cell with the (101)-RuO2 writing channel, the SST-MRAM device is fabricated with a 54% TMR ratio, and the field-free all-electrical SST-driven switching of the MTJ is realized with the current density of 2.1×106 A cm–2, where the field-free SST-driven magnetic domain switching of the recording layer of MTJ is further confirmed by the magneto-optic Kerr effect (MOKE) microscope. This work demonstrates the field-free altermagnetic SST-driven MRAM devices, aiming for the future SST-MRAM with flexible spin polarization and spin current directions.

Results
Structural properties of the RuO2 layer
Ruthenium dioxide (RuO2), a rutile structure with the space group P42/mnm, is a prominent room-temperature metallic collinear antiferromagnet, as shown in Fig. 1a. The collinear exchange coupling between magnetic (Ru) atoms located in the anisotropic crystalline environments of nonmagnetic (O) atoms, along with an anisotropic spin splitting of the nonrelativistic electronic structure. The resulting spin-current generation exhibits odd behavior under time-reversal symmetry T, with the spin polarization aligned to the N, driven by a spin-splitting band structure. When the electric field (E) is along the ϕ=45° axis, i.e., the polar axis of the anisotropic spin-splitting band structure, only the longitudinal spin-polarized current is generated in Fig. 1b. However, when the E is away from the ϕ=45° axis (−45° < ϕ < 45°), due to the anisotropic spin-splitting band structure/conductivity, the spin-up (j↑) and spin-down (j↓) currents are not collinear with the E direction and tilt to the opposite directions, as a result, the transverse spin current (j↓-j↑) generates. For ϕ=0°, the transverse spin current reaches its maximum since j↑ and j↓ flowing along opposite directions have maximum magnitudes as shown in Fig. 1c. When the E is applied along the [010] direction [yellow arrow, left in Fig. 1a], it indeed generates a Js along the [100] direction. Notably, for the (101)-RuO2 film we used in this work, the actual film plane rotates an angle compared to the lattice in Fig. 1a (represented by the orange plane), regarding the (101) crystal surface, the Js along [100] can be decomposed into components: one perpendicular (J⊥s, purple arrows) and one parallel (Jk s, azure arrow) to the (101) plane. The perpendicular component (J⊥s) aligns with the [101] direction, with its magnitude being approximately Jsinθ. Consequently, the spin-split Fermi surface shown in Fig. 1b, c still corresponds to the excited spin current in the out-of-plane direction for (101)-RuO2. As a result, in the (101)-oriented RuO2-pMTJ film, when a charge current is applied along the [010] axis, it generates a transverse T-odd spin current flowing in the out-of-plane [101] direction, as depicted in Fig. 1d. Recent experiments have validated the presence of spin-splitting band structures in altermagnets MnTe and MnTe2, corroborating the theoretical predictions. Additionally, related studies provide evidence for the anisotropic spin splitting effect (ASSE)-induced SST in the collinear antiferromagnet RuO2.

Firstly, high-quality (101)-oriented RuO2 thin films are grown on the Al2O3 (1102) substrates by the magneton sputtering under the 350°C substrate temperature. The x-ray diffraction (XRD) pattern of a 12-nm-thick RuO2 single layer shows a strong (101) RuO2 peak with clear Laue oscillations, as shown in Fig. 1e, and the corresponding rocking curve of the (101) RuO2 peak displays a small full-width at-half-maximum (FWHM) of approximately 0.037°, indicating the high-crystalline quality and (101)-orientation of the RuO2 films (Supplementary Note 1). As depicted in Fig. 1f, the high-resolution scanning transmission electron microscopy (HR-STEM) of Al2O3 (1102)//RuO2 (101) is conducted and shows the epitaxial growth and atomic structure of the RuO2 along the [010] direction with a lattice constant of 4.51 Å, revealing the high crystal quality of the RuO2 (101) film through the high-resolution high-angle annular dark field (HADDF) image. Then, we utilized the element-specific x-ray magnetic linear dichroism (XMLD) effect, which arises from the difference in the absorption of linear polarized x-ray with polarization parallel to and perpendicular to the Néel order of the antiferromagnet (AFM), to determine the spin orientation of RuO2 films. The XMLD measurements were performed in total electron yield mode at Beamline BL08U at Shanghai Synchrotron Radiation Facility. To determine the Néel vector of RuO2, X-ray absorption spectra (XAS) measurements were performed for different crystal orientations of RuO2 films. The 12 nm-thick RuO2 film was deposited onto single crystalline substrates of MgO(001), Al2O3 (1102) and TiO2 (001) (Supplementary Note 1). The XAS were measured at normal incidence of the x-rays and the polarization orientation (ϕ=0° and 90°) at zero field, as shown in Fig. 1g, where ϕ is defined as the angle between the E vector of the incoming X-ray beam and the x-axis of the substrate. Then, the XAS spectra extracted with (110)- and (101)-RuO2 at the Ru 4+ M3 and M2 edges are shown in Fig. 1h. It can be observed that the presented XMLD data are consistent with the presence of altermagnetic order in the RuO2 film. Moreover, the XMLD effect is evident in both RuO2 (110) and RuO2 (101) films, with effect ratios of 1.68% and 2.2%, respectively. The effect ratio is calculated using the following formula: Ratios (%) = (Iϕ=0 - Iϕ=90) / (Iϕ=0 + Iϕ=90) × 100%. Then, we extracted the XMLD intensity (plotted on the same y-axis scale without any additional processing as in Fig. 1h,) between ϕ=0° and 90°, as summarized in Fig. 1i. The (110)- and (101)-RuO2 films exhibit significant XMLD signals, while XAS signals are detectable for all orientations including (110), (101), and (001)-RuO2 films (Supplementary Note 1). However, the XMLD intensity is absent in the (001)-RuO2 films. These observations suggest that the antiferromagnetic order in RuO2 films is parallel to the <001> crystal axis in RuO2. Further, magnetic field annealing was employed to align the N with the direction of the annealing field (HFA). The field-induced reorientation of the N was successful and directly reflected in the XMLD response; more details see Supplementary Note 1. The XMLD results thus provide the direct evidence of the antiferromagnetic order in RuO2 thin films, which is in agreement with the recent studies.

The emergence of the z-component spin polarization from altermagnetic RuO2
Then, the structure of RuO2 (12)/Mo (2)/CoFeB (0.85)/MgO (1.2)/Ta (2) is fabricated into a device with a diameter of 8 μm (Fig. 2a), to investigate the SST and the SST-induced field-free switching of the perpendicular magnet that can work as the recording layer of the pMTJ. And the sample firstly exhibits strong PMA based on the anomalous Hall effect (AHE) measurement. The Hk is quantified from the saturation field of the Rxy-Hx curve to be 2.5 kOe, as shown in Fig. 2b. Then, the hysteresis loop of the Rxy versus the out-of-plane magnetic field (Hz) is measured in the presence of a pulse current (Ipulse) along ϕc=0°. It is observed that the Rxy-Hz loops almost overlap under ±18 mA (Supplementary Note 2). However, an obvious loop shift occurs when the pulse current of ±21 mA is applied, as shown in the inset of Fig. 2c, and the centers of the Rxy-Hz loops shift to positive/negative fields for positive/negative pulse currents, respectively. Such a shift indicates the presence of a current-induced out-of-plane effective field He z eff by SST. Figure 2c shows the Ipulse dependence of ΔHe z eff. Beyond the threshold current with overcoming the magnetic damping of the system, the He z eff increasing, as indicated by error bars and exhibits almost linear behavior above the threshold current. We estimate the out-of-plane SST efficiency (ΔHe z eff /J, where J is the applied in-plane current density) by performing a linear fit to the effective field versus current amplitude data, specifically in the region beyond the threshold current. When applying a positive pulse current, the slope (ΔHe z eff /J) is 1.0×10–6 Oe A–1 cm2, and for a negative pulse current, the slope (ΔHe z eff /J) is −1.04×10–6 Oe A–1 cm2. By averaging the absolute values of both slopes, a value of 1.02×10–6 Oe A–1 cm2 is obtained for the out-of-plane SST efficiency. Furthermore, to investigate the presence of a threshold current, we conducted simulations without considering thermal effects. The results reveal that the loop shift ΔH exhibits an abrupt increase with rising current density (see Supporting Information). This sharp increase, observed once the current exceeds a certain threshold, aligns with previous studies. And this indicates the emergence of an out-of-plane damping-like torque (τ⊥) originating from the z-component of the spin polarization generated by the altermagnetic RuO2.

The z-component of the spin polarization from RuO2 makes it possible to achieve field-free switching of the perpendicular magnetization. Figure 2d shows the measured Rxy-Ipulse loops under various in-plane magnetic fields Hx along [101] direction, where a writing current Ipulse is applied along ϕc=0° to provide the SST firstly followed by a 0.5 mA reading current to detect the magnetization by AHE at 10 s later. Upon reversing the Hx, the polarity of the current-induced switching loop also reverses, which is consistent with the y-component of the spin polarization-driven magnetization switching, originating from the SST and the conventional SOT contributions. Most importantly, a full switching loop is achieved even in the absence of Hx, revealing the z-component of the SST besides the conventional y-torque. The critical switching current density Jc of SST is determined to be 2.15×106 A cm–2, enabling the energy-efficient writing method by exploiting the z-component of the altermagnetic SST that breaks the inversion symmetry (Supplementary Note 3, 4). In contrast, no magnetization switching occurs when the Ipulse is applied along ϕc=90° [101] without Hx (Supplementary Note 5), where the SST is absent in this case, as shown in Fig. 2e. Furthermore, the Rxy-Ipulse loops were measured for several devices on the same sample under different Hx along the [101] direction, confirming the consistent behavior and robustness of the devices (Supplementary Note 6). The z and y components of spin torque indicate the altermagnetic spin splitting induced transversal spin current with the spin polarization along the Néel vector (titled in y-z plane) from (101)-RuO2.

Then, the current-driven magnetic domain switching process is directly detected by the polar-MOKE microscopy, and the bright and dark contrasts in the Kerr images correspond to the opposite +Mz and –Mz magnetic domains. The Kerr images corresponding to the magnetic states marked in Fig. 2e are present in Fig. 2f, and the magnetic domain is switched between +Mz and –Mz under +Ipulse and –Ipulse without an external magnetic field, respectively, further confirming the altermagnetic SST-induced field-free switching of Mz upon applying the pulsed current along ϕc=0°. The standard harmonic measurements are carried out to determine the SST efficiency of 0.824×10–6 Oe A–1 cm2, and the charge-spin conversion efficiency is 0.052 (Supplementary Note 7). In addition, the behavior of RuO2 thin films at low dimensions can be influenced by lattice strains, interfacial effects, and defect concentrations (Ru or O vacancies), which may result in the antiferromagnetic orders that differ from those of bulk single crystals. Then, magnetic field annealing was performed to align the tilted N along the annealing field (HFA) to exclude the influence of the RuO2 and Mo interface (Supplementary Note 8). To further isolate the effect of Mo on magnetization switching, we prepared the reference sample Sub./Mo(2)/CoFeB(0.85)/MgO(1.2)/Ta(2) (thickness in nanometers) and observed that without the RuO2 layer, deterministic switching fails to occur at Hx=0 Oe in the Mo/CoFeB sample (Supplementary Note 9). We then estimated the Joule heating during current-induced magnetization switching. The results show that, even at the maximum Ipulse applied in the RuO2/Mo/CoFeB multilayer, the RuO2 thin films preserve a stable antiferromagnetic configuration (Supplementary Note 10). For continued investigation, the details and the stack of RuO2 (12)/Pt(1.2)/Co(0.7)/Pt(1.2)/SiO2 (3) (number in nanometers) are designed to verify the z-torque spin current generated by RuO2 (101) film (Supplementary Note 11). MOKE imaging was performed on RuO2 (12)/Pt(1.2)/Co(0.7)/Pt(1.2)/SiO2 (3) in the absence of a magnetic field to uncover magnetization switching under pulsed current (Supplementary Note 12). The dependence of ΔHz on Ipulse and harmonic measurements was carried out to reveal the z-component of the spin polarization and the effective charge-spin conversion induced by the altermagnetic (101)-RuO2 (Supplementary Note 13).

RuO2-based SST-MRAM design and characterization
By using the Mo/CoFeB/MgO as the recording layer and the synthetic antiferromagnetically-coupled structure as the reference layer, the full RuO2-pMTJ stack of RuO2 (12)/Mo(2)/Co20Fe60B20 (0.85)/MgO(1.8)/Co20Fe60B20 (1.1)/Ta(0.5)/Co(0.3)/Pt(1.3)/Co(0.4)/Pt(0.6)/Co(0.4)/Ru(0.85)/[Co(0.4)/Pt(0.6)]4/Ru(5) (thickness in nanometer) is prepared. The RuO2-pMTJ stack includes a Mo layer to decouple the exchange interaction between the RuO2 and CoFeB. Mo is selected due to its minimal intermixing with Fe and Co and high thermal tolerance, and its smaller SOC compared to heavy metals, so the contribution of spin current from RuO2 dominates. A 250°C annealing process is carried out on the RuO2-pMTJ devices in a vacuum to enhance the PMA. The RuO2-pMTJ stack is then patterned into 3-terminal SST-MRAM devices by using a combination of electron-beam and photolithography, along with Ar ion milling. As shown in Fig. 3a, the MRAM cell with the cross-sectional scanning transmission electron microscopy (STEM) image shows the well-defined interface between RuO2 and MTJ in Fig. 3c, as well as the sharp interface between the CoFeB ferromagnetic electrodes and the MgO barrier. The pMTJ is located at the intersection between the bottom RuO2 electrode and the top Ti/Au electrodes, marked by a white-dotted circle with a diameter of 250 nm as illustrated in Fig. 3b. The writing current is applied along the channel between T1 and T2, and the TMR of MTJ is read by applying a small dc current between the T1–T3 channel. The microscopic (top view) and cross-sectional TEM (side view) images of the patterned SST-MRAM device clearly show the RuO2 writing channel (T1-T2), MTJ device, and the reading channels (T1-T3). Additionally, HAADF image and energy-dispersive X-ray mappings of RuO2-pMTJ further demonstrate the clear and sharp interfaces, indicating high interfacial spin transparency, as shown in Fig. 3d, e. Then, the polarized neutron reflectivity (PNR) for the whole stack is measured to analyze the layer-resolved atomic and magnetization distribution along the thickness direction. As shown in Fig. 3f, g the theoretical curves are consistent with the experimental results, capturing all the major features. The best fit to the data includes a magnetization of 526 kA m–1 for CoFeB layer and 1332 kA m–1 for Co layer in the 19 kOe measurement. The PNR analysis provides detailed insights into the structure and quality of the RuO2-pMTJ sample.

All-electrical field-free switching of SST-MRAM
Figure 4a shows the schematic of the SST-driven switching measurement for the RuO2-pMTJ device. A 1-ms writing current J is applied in the RuO2 writing channel between T1 and T2, followed by a reading current (2 μA) applied along the T1 and T3 to detect the switching of MTJ by TMR. The normalized magnetic hysteresis (M/Ms-Hz) loop of the RuO2-pMTJ stack with the magnetic field applied along the out-of-plane direction (Hz) in Fig. 4b show the individual magnetic switching process for the whole stack, where the light blue/dark blue, yellow, and purple arrows represent the magnetic moment direction of the two AFM-coupled Co/Pt multilayers, the top CoFeB reference layer, and the bottom CoFeB recording layer, respectively. The magnetic field-driven tunneling resistance R/TMR-Hz curves for the RuO2-pMTJ device in Fig. 4c clearly show the high- and low-resistance states for antiparallel and parallel magnetic configurations, with a TMR ratio of 54%, indicating the high quality of MTJ.

Then, the all-electrical SST-driven switching is performed in the RuO2-pMTJ device: 500 μs writing Ipulse is applied in the RuO2 writing channel between T1 and T2 to induce the SST for switching the CoFeB recording layer, followed by a small reading current of 2 μA passing through the MTJ between T1 and T3 to detect the tunneling resistance R of the MTJ device after 10 s. Figure 4d illustrates the MTJ resistance as a function of the writing current in the RuO2 layer (R-Ipulse) at room temperature. The most significant feature is the remarkable tunneling resistance switching of pMTJ induced by altermagnetic SST at zero external field, with the critical switching current density Jc is 2.1×106 A cm–2, enabling the all-electrical field-free writing method by exploiting the z-component of the altermagnetic SST that breaks the inversion symmetry for +Mz and –Mz. The opposite switching polarity for R-I loops under Hx = ±40 Oe shows the standard switching behavior induced by the y-component spin polarization originating from ASSE and conventional SOC. Here, the MTJ device exhibits a lower switching current density Jc compared to the single magnetic layer film. This difference may result from current shunting in the multilayer MTJ stack, variations in the magnetic properties of the CoFeB layer caused by differences in device structure and fabrication processes, and distinct device geometries that influence current distribution, edge effects, and thermal behavior. Indeed, the partial switching observed in our experiments is a known phenomenon in such systems, often attributed to thermal effects leading to partial demagnetization. Several studies have reported similar observations. In our case, the local heating effects might have contributed to the partial demagnetization of magnetic domains. We believe that this technical/engineering point can be further optimized in future work, particularly by refining parameters such as anisotropy, device dimensions, pulse width, and others.

To obtain the thermal stability factor Δ of the nanoscale RuO2-pMTJ devices, we measured the switching probability P(τ) as a function of the magnetic field amplitude and evaluated Δ using the following relationship based on the Stoner–Wohlfarth model, as shown below
P(τ) = 1 - exp [ - (τ/τ0) exp(-Δ(1 - H/Hk)2)] (1)
Where τ is the pulsed duration time (1 s) of external magnetic field H, τ0 is the inverse of attempt frequency (typically around 1 ns). Hk is the effective magnetic anisotropy field, and H is the shift field of the resistance-field curves; H is the external magnetic field amplitude. The minor normalized ΔTMR/TMR-Hz loops of the nanoscale RuO2-pMTJ were measured 60 times in Fig. 4e, to determine the switching probability P. In these measurements, reversible switching occurs solely in the CoFeB recording layer, and the shift of the loop center is mainly due to the stray field generated by the partially compensated magnetization of the pinning layer. Figure 4f shows the experimentally obtained results represented by squares, while the solid line represents a fit calculated from Eq. (1), illustrating the relationship between P and H. A thermal stability factor of Δ=64 was obtained for the nanoscale RuO2-pMTJ, satisfying the requirement (Δ=60) for a 10-year retention time in MRAM.

For a thorough understanding of the all-electrical field-free switching in the 3-terminal RuO2-pMTJ device, we perform the micromagnetic simulations based on Landau-Lifshitz-Gibert equation, including SST term (the details see Supplementary Note 14). Considering the effective field Heff and spin polarization direction σ=(0, sinδ, cosδ), with δ being the angle between the σ and the z-axis. As shown in Fig. 5a, the field-free magnetization switching occurs with Je = 6.8×106 A cm–2 for δ≈35°, corresponding to an ideal crystal structure and the electrical current applied along the [010] direction in (101)-RuO2, with both z- and y-polarized spin components (Supplementary Note 14). Additionally, Fig. 5b illustrates the relationship between the magnetization switching loops of mz-He and Je, showing a notable positive or negative shift when applying a current density of ±6×106 A cm–2, which is consistent with the experimental results in Fig. 2c. Figure 5c also shows the critical current density Jc under different angles δ. It can be observed that Jc scales down with increasing the z-component of the spin polarization, and δ≈35° with tiled N in our experiment has a relatively lower Jc and a better energy-efficiency.

In this work, by utilizing the unique altermagnetic spin-splitting band structure from (101)-RuO2, the transversal spin current with a tilted spin polarization along the Néel vector is employed to provide an altermagnetic SST, and thus to generate the z-component spin torque on the adjacent magnetic moment with PMA. Based on these, the field-free SST-driven switching is achieved in both the Hall devices and the pMTJ devices, where the z-component effective field of altermagnetic SST is characterized by the current-induced shift of the Rxy-Hz hysteresis loop. Our work demonstrates the altermagnetic SST-driven magnetic memory, with great potential for next-generation MRAM technology with flexible control of the spin polarization and spin current flow directions.

Methods
Sample growth and device fabrication
The film stacks consist of:
i) Al2O3 (1102)//RuO2 (12)/Mo(2)/Co20Fe60B20 (0.85)/MgO(1.8)/Ta(2)
ii) Al2O3 (1102)//RuO2 (12)/Pt(1.2)/Co(0.7)/Pt(1.2)/SiO2 (3)
iii) Al2O3 (1102)//RuO2 (12)/Mo(2)/Co20Fe60B20 (0.85)/MgO(1.8)/Co20Fe60B20 (1.1)/Ta(0.5)/Co(0.3)/Pt(1.3)/Co(0.4)/Pt(0.6)/Co(0.4)/Ru(0.85)/[Co(0.4)/Pt(0.6)]4/Ru(5) (thickness in nanometers)

All these stacks are grown on the Al2O3 (1102) substrates by magneton sputtering in a system with a base pressure of 3×10−8 Torr. During the deposition, the Ar atmosphere was maintained with a pressure of 2.5 mTorr. The RuO2 layer was deposited by radio frequency sputtering. Then, (i) the stack of Mo(2)/Co20Fe60B20 (0.85)/MgO(1.8)/Ta(2) and (iii) the p-MTJ stack of Mo(2)/Co20Fe60B20 (0.85)/MgO(1.8)/Co20Fe60B20 (1.1)/Ta(0.5)/Co(0.3)/Pt(1.3)/Co(0.4)/Pt(0.6)/Co(0.4)/Ru(0.85)/[Co(0.4)/Pt(0.6)]4/Ru(5) were deposited on RuO2 by using a Singulus ROTARIS magnetron sputtering system at room temperature with a base pressure of 1×10–6 Pa. For (ii) stack, the Pt and Co layers were deposited by dc sputtering, and the sputtering power was 25 W and 50 W, respectively, and a 3-nm-thick SiO2 capping layer was deposited as protection. Then, the Hall bar device was fabricated by standard photolithography combined with an argon ion etching technique.

The 3-terminal SST-MRAM devices were fabricated by using two electron-beam lithography (EBL), one photolithography and two Ar ion milling steps. First, an electron beam lithography (JEOL JBX-6300 FS) with a ma-N 2403 negative-tone resist was performed to pattern the RuO2 underlayer. After etching all the layers and removing the photoresist, MTJ pillars with circular shapes and diameters of 250 nm were fabricated using second electron beam lithography with a ma-N 2403 negative-tone resist. The film was etched down to the RuO2 layer, followed by sputtering a 32 nm-thick SiO2 film to electrically isolate the top and bottom contacts of the tunnel junctions. Finally, a photolithography step was carried out using AZ5214 positive-tone photoresist to pattern the electrodes, which were then formed by sputtering 10 nm of Ti and 80 nm of Au. The fully patterned RuO2-MTJ devices were finally annealed in a vacuum at 250°C for 0.5 h with an 8 kOe perpendicular magnetic field.

Structural characterizations
High-resolution XRD scans were conducted using a Panalytical MRD X’Pert3 diffractometer with Cu Kα radiation. X-ray reflectivity (XRR) measurements were also performed to verify the layer thickness, interface and surface roughness, as well as the densities of the thin films.

Transport measurements
The anomalous Hall resistance and current-induced magnetization switching were measured using a room-temperature multipurpose transport measurement system. A Keithley 2182A nanovoltmeter and a Keithley 6221 current source were utilized for DC and pulse measurements, respectively. For the harmonic Hall voltage measurement, a low-frequency alternating current (133.33 Hz) from Keithley 6221 was passed into the device, and the first and second harmonic Hall voltages were measured using two SR830 lock-in amplifiers.

The SST switching in the 3-terminal RuO2-pMTJ device was characterized using a probe station system equipped with an electromagnet. A Keithley 2612 current source was used to apply the pulse current, while the voltage across the MTJ was measured using a Keithley 2182A voltmeter. The magnetic properties of the RuO2-pMTJ stack were measured using a vibrating sample magnetometer system. All measurements were conducted at room temperature.

PNR measurement
The PNR was carried out at the Multipurpose Reflectometer beamline of the Chinese Spallation Neutron Source. The RuO2-pMTJ film with size is 10×10 mm2. Neutron reflectivity curves were measured as a function of the momentum transfer Q=4π sinθ/λ, where λ is the neutron wavelength and θ is the incident angle between the neutron beam and the film plane. To cover a broad range of momentum transfer, reflected neutrons were collected at various incident angles. Measurements recorded both R++ and R-- for neutrons with spins parallel and antiparallel to the applied field, corresponding to spin-up and spin-down neutrons, respectively. The PNR data were fitted to a model that included layer thickness and chemical roughness, using parameters obtained from XRR fitting with the GenX software.

Micromagnetic simulation
The micromagnetic simulations were conducted using the GPU-accelerated software Mumax3 at a temperature of 300 K. The magnetization dynamics were determined by solving the Landau–Lifshitz–Gilbert equation, which included additional terms for SST, as described in reference 67:
∂m/∂t = -γ(m×Heff) + α(m×∂m/∂t) + γHST(m×σ×m) + γξSTHST(m×σ) (2)
where m is the reduced magnetization, Heff=Hk mz bz is the effective field, Hk is the effective anisotropy field, γ is the gyromagnetic ratio, α is the Gilbert damping factor, σ=(0, sinδ, cosδ) is the spin polarization direction from the SST, δ is the angle between the σ and the z-axis, ξST is the ratio of field-like torque to damping-like torque of the SST, respectively. In our model, α=0.01568, ξST=0.1, Ms=1994 kA/m measured by the SQUID, and Hk=0.18 T.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this round, the authors have revised the manuscript by responding to the comments by me as well as the other reviewer. While they have addressed some of the comments satisfactorily, I think that some responses are not scientifically sound. Because the remaining issues are critical enough in this work, I still cannot recommend the publication of this manuscript. Let me elaborate below.\n[Response 1-4]\nThe authors attribute the existence of threshold in Fig. 2c to the thermal effect, but this does not sound to me reasonable. In this measurement, they evaluate the shift of switching field under pulse current that possibly induces the spin-splitter torque. For this type of measurement, the external magnetic field lowers the energy barrier via the Zeeman energy, meaning that even though the original energy barrier is too high, the energy barrier just before the switching takes place should be low enough because of the Zeeman energy and thus a finite effect of spin-splitter torque should appear. Therefore, the existence of such a threshold cannot be explained from the energy of the system. I think that the authors should be able to confirm a non-zero shift of the switching field for a small current even without considering the thermal effect using simulation. Thus, I think the authors should completely revisit their understanding of all the results.\n[Response 1-5]\nR_xx vs I_pulse data also looks quite strange. It also has a threshold, below (above) which the resistance is constant (almost linearly increases) with current. The authors should first present a figure showing the temperature rise as a function of I_pulse. While the authors state that the Joule heating is described by I^2, I think the result clearly deviates from the authors’ statement.\nI would also strongly suggest that the authors make a survey or measurement on the Neel temperature of RuO2 thin film, because it is close to or below the temperature they estimated at which the switching takes place (381 K).\n[Response 1-6]\nThe method to derive the out-of-plane spin-splitter torque efficiency should not be reasonable. As I mentioned in my previous review report, the spin-splitter torque should be proportional to the current and should not have any x-intercept. Therefore, linear fit to the date in the region beyond the threshold should be invalid. Considering the fact that the bistable property almost disappears above the threshold, I think it is more reasonable to derive the out-of-plane spin splitter torque efficiency from a linear fit below the threshold.\nI would also mention that the data point above the threshold in Fig. 2c, in particular the ones for negative current, do not look to me “almost linear”.\n[Response 1-7]\nThe fact that the current induces only a partial switching and their speculated reason should be described in the main text.\n[Response 1-8]\nI am not sure the authors properly understood the intention of my previous comment. If the same effect governs the results shown in Fig. 2 (anomalous Hall measurement) and those shown in Fig. 4 (tunnel junction measurement), the switching loop direction (CW or CCW) at H = 0 should be the same with either Hx < 0 or Hx > 0 for both measurements. However, still in the revised manuscript, the switching loop direction at H = 0 (CW) is the same with the one at H > 0 for Fig. 2, whereas for Fig. 4 that at H =0 (CCW) is the same with the one at H < 0.\n[Response 1-9]\nTheir revision in line 64 on page 3, “ultrahigh-writing current”, is non-scientific and lacks a respect for researchers/engineers working on STT-MRAM considering the fact that STT-MRAM has been successfully commercialized whereas the present work shows magnetization switching only with a significant effect of the Joule heating.\n[Response 1-10]\nThe authors’ explanation that “during the current driven switching measurement, the applied writing current provides a large external energy to induce the non-equilibrium dynamic magnetic switching process, and this writing energy is enough to overcome the energy barrier between two magnetization states. (…) Thus, these two aspects are different and not directly related.” does not sound to me physically sound, or at least fully supported. I think that for the case of spin-orbit torque or spin splitter torque, the current driven switching can be completed by overcoming an energy barrier whose height can be approximated by the one that needs to be overcome during the field-driven switching. If the authors stick to this scenario, they need more thorough and scientific explanations.\nLast but not least, it is quite tough for reviewers to catch how the authors have reflected the reviewers’ comments to the manuscript, because it is not explicitly described in the response letter how the manuscript is revised. Accordingly, the reviewers need to go back and forth between the response letter and the manuscript. I would request that the authors describe in their response letter how they reflected the reviewers’ comments into the manuscript, if they have a chance to resubmit this manuscript.", "reviewer_2": "The authors presents XAS/XMLD data at the Ru-M2,3 resonant edges to support the claim that their RuO2 films are magnetically ordered and to determine the direction of the Neel axis of the RuO2. However the presence of XMLD is not conclusive proof of magnetic order, because it can be also originated by distortion of the local crystalline environment, generated by strain, usually referred to as natural linear dichroism. The magnetic/strain contribution to the linear dichroism can only be disentangled by proving that the XMLD intensity follows a Curie-Weiss law upon temperature change. However performing additional temperature dependent XMLD measurements above the quoted Tc of 300K (Zhu et al., PRL 122, 017202 (2019)) might not be practical or technically feasible, therefore I consider the inclusion of additional XMLD temperature dependent data to be a desirable addition to the paper but not a required element for the publication.\nInstead I would suggest to cite a recent publication (Fedchenko et al., Sci. Adv. 10, eadj4883 (2024)) where, for the first time, experimental evidence of altermagnetism on RuO2/Ti(110) are presented. The XMLD data included in the paper can support the claim and can be shown to be in agreement with the presence of altermagnetism, although it must be clarified that they cannot prove it.\nTo my best knowledge, with the exception of a conference abstract cited below, there are no XMLD data in literature on RuO2 and the results presented by the authors are novel. As such I think they should be included in the paper, but only if the my requests can be addressed.\nIn the following I will make a few point that should be addressed for the paper to be considered for publication.\n1) The authors present XAS/XMLD data at the Ru-M2,3 resonant edges, referring to them as L2,3 edges. I would recommend that to be corrected.\n2) The [101] surface axes written in black of figure R7a,b ( and figure 1a on the main text) are wrong. The z is correct, but the x//[010] and y//[-101] are in the wrong directions in the figure. The long black dashed line along the z[101] axis in fig R7a is confusing because it overlaps with the yellow E-vector and is painted above the Ru purple atom, making the 3d view confusing. Some effort should be made to improve the readibilty of fig. R7 because the Js vectors labels are barely visible when printed. See attached sketch of to correct fig R1b\n3) The XMLD spectrum in figure 1h is barely visible and not clearly distinguishable from the base line and the noise. It should be magnified vertically, and possibly plotted on versus the right vertical axis, and shifted vertically to avoid overal with the XAS. The XMLD of all the 3 measured surface orientations should be displayed on the same scale to allow visual quantitative comparison of the XMLD intensity.\n4) The fig 1i, presented in the caption as “The relative intensity of Ru4+ L3 for (110)-, (101)- and (001)-RuO2” is obscure: it is not clear what how the “relative intensity” is defined. The definition of relative intensity is not presented (line 180). The same should be said for line 180-182: “Then, we extracted the relative intensity between phi = 0° and 90°, as summarized in Fig. 1i.”. The formula used to calculate the percentage XMLD intensity should be presented.\n5) It is stated that “neither XMLD nor any x-ray absorption” is observed in the RuO2(001) film (line 183), which is impossible because, if the Ru is present in the film, the XAS signal cannot go to zero. The disappearance of the Ru XAS on the (001) surface declared by the authors casts doubt over the quality of the sample and on the understanding of the physical meaning of the experimental results. It is possible that the text describing the results might not be accurate and that I misunderstood the findings, however the authors should present the XAS/XMLD results of the three RuO2 surface orientations to clarify this point and show that the XAS signal on the RuO2(001) does not disappear (while the XMLD does). If this request cannot be satisfied, I am afraid that the validity of the whole XAS/XMLD dataset cannot be trusted to support the present of magnetic order in the Ru film.\n6) To the best of my knowledge, there are not published data on RuO2 XMLD at the M2,3 edges, therefore, the data presented in the paper are novel and interesting. The only mention to similar data I could find are from a conference abstract titled “Detecting Altermagnetism in RuO2 by Angular-Dependent X-ray Magnetic Linear Dichroism” , by Jun Okabayashi1, Zhenchao Wen, Hiroaki Sukegawa and Seiji Mitani. (https://pub.confit.atlas.jp/en/event/jsap2023a/presentation/21a-C501-5) Their results appear to be unpublished and I had no access to their results, but they might be useful as a term of comparison with the data presented in the paper under review, to support their claim of altermagnetic character of their films.\n7) Line 177 : “It can be observed that the XMLD effect at the L3 edge in this structure is purely magnetic origin at the normal incidence of x-rays.“ should be removed because it is not possible to attribute an XMLD signal purely to magnetic order in absence of a temperature scan, as stated before. Instead the author could claim that the XAS/XMLD data presentes are compatible with the presence of altermagnetic order.\n8) Line 180-182: “Then, we extracted the relative intensity between phi = 0° and 90°, as summarized in Fig. 1i.”: it is not clear how the “relative intensity” is calculated and what the traces in figure 1i represents. The re"}, "author_response": "Response: Thank you for your constructive feedback. We have carefully considered your comments and made the necessary revisions to the manuscript. We have provided additional clarification, supporting data, and revisions to strengthen the manuscript.\n[Comment 1-1]:\n[Response 1-4]\nThe authors attribute the existence of threshold in Fig. 2c to the thermal effect, but this does not sound to me reasonable. In this measurement, they evaluate the shift of switching field under pulse current that possibly induces the spin-splitter torque. For this type of measurement, the external magnetic field lowers the energy barrier via the Zeeman energy, meaning that even though the original energy barrier is too high, the energy barrier just before the switching takes place should be low enough because of the Zeeman energy and thus a finite effect of spin-splitter torque should appear. Therefore, the existence of such a threshold cannot be explained from the energy of the system. I think that the authors should be able to confirm a non-zero shift of the switching field for a small current even without considering the thermal effect using simulation. Thus, I think the authors should completely revisit their understanding of all the results.\nResponse 1-1: We sincerely thank the reviewer for the thoughtful and detailed comments.\n(1) Firstly, regarding the threshold behavior observed in Fig. 2c, we agree with the reviewer’s observation. You are correct, in the measurement in (101)-RuO with z component (), the switching field is evaluated under a pulse current, the external z magnetic field does indeed lower the energy barrier through the Zeeman effect. Here, the observed shift of the R -H loop exhibits threshold behavior in SOT measurements xy z of the system with , which is commonly observed in similar studies. S. C. Baek, et z al., reported that this behavior arises because a current with a specific polarity generates an out-of-plane spin current with a spin z component, inducing an anti-damping torque on the perpendicular magnetization. Once the current exceeds a certain threshold, the loop shift increases sharply, surpassing the intrinsic damping [S. C. Baek, et al., Nat. Mater. 17, 509 (2018)]. This phenomenon has also been observed in our work and is consistent with findings from previous studies, such as L. Liu, et al., Nat. Nanotechnol. 16, 227 (2021), S. Hu, et al., Nat. Commun. 13, 4447 (2022), C. M. Cao, et al., 14, 5873 (2023) and Q. Yang, et al., Nat. Commun. 15, 1814 (2024), as shown in Fig. R1 with the generation of the z-polarized spin current in the systems. This is a general method that is widely adopted in the SOT area and is not the major point of our current work, therefore, we think this point doesn’t affect the novelty of our work.\nFig. R1. a. The current dependence of shift (H) in a. the CuPt/CoPt bilayer, b. Mn Sn thin 3 film, c. CoFeB/Ti/CoFeB/MgO trilayers, and d. TaIrTe /Fe GaTe heterostructure. Pictures 4 3 2 from L. Liu, et al., Nat. Nanotechnol. 16, 227 (2021), S. Hu, et al., Nat. Commun. 13, 4447 (2022), C. M. Cao, et al., 14, 5873 (2023) and Q. Yang, et al., Nat. Commun. 15, 1814 (2024).\n(2) We agree that a deeper investigation into the existence of the threshold current using simulation, without considering thermal effects, is necessary, as you suggested. To make the threshold effect significant, the damping constant is set to 0.1, while all other parameters are retained at their original values in our simulations. As shown in Fig. R2, the loop shift ΔH exists an abrupt increase with the current density increase, which can be attributed to the anti-damping torque for the perpendicular magnetization under the spin current with z component. This is consistent with previous reports.\nWe have cited the relevant references in the revised manuscript (Pages 10-11) and the simulation has been added to the revised Supporting Information. (Page 22 in Supporting Information). As shown below:\n“Furthermore, to investigate the presence of a threshold current, we conducted simulations without considering thermal effects. The results reveal that the loop shift ΔH exhibits an abrupt increase with rising current density (see Supporting Information). This sharp increase, observed once the current exceeds a certain threshold, aligns with previous studies [S. C. Baek, et al., Nat. Mater. 17, 509 (2018), L. Liu, et al., Nat. Nanotechnol. 16, 227 (2021), S. Hu, et al., Nat. Commun. 13, 4447 (2022), C. M. Cao, et al., 14, 5873 (2023) and Q. Yang, et al., Nat. Commun. 15, 1814 (2024)]”.\nFig. R2. Micromagnetic simulation results of the current density J as a function of the loop shift ΔH without considering thermal effects.\n(3) Furthermore, through MOKE-microscope observations of the RuO₂/Mo/CoFeB/MgO/Ta system (Fig. R3a), we observed that under a small applied direct current (1 mA), the system retains a single-domain state with no magnetic domain wall formation and undergoes coherent magnetization reversal. However, when the direct current increases to 15 mA (Fig. R5a), multiple domains nucleate, and the magnetization switching characteristics exhibit a significant enhancement following domain wall formation. Typically, the domain wall motion in multiple domains would lower the switching energy than the coherent magnetization reversal in single domains and thus the SOT plays a much prominent effect, which may explain the threshold behavior that we observed.\nFig. R3. a. Hysteresis loops in the z directions for the RuO /Mo/CoFeB/MgO/Ta structure, 2 measured using MOKE microscopy under a 1 mA direct current. b. MOKE images of the film display the out-of-plane magnetization corresponding to the magnetic field conditions labeled ① to ③ in (a).\nFig. R4. a. Hysteresis loops in the z directions for the RuO /Mo/CoFeB/MgO/Ta structure, 2 measured using MOKE microscopy under a 15 mA direct current. b. MOKE images of the film display the out-of-plane magnetization corresponding to the magnetic field conditions labeled ① to ④ in (a).\nFig. R5. a. Hysteresis loops in the z directions for the RuO /Mo/CoFeB/MgO/Ta structure, 2 measured using MOKE microscopy under a 16 mA direct current. b. MOKE images of the film display the out-of-plane magnetization corresponding to the magnetic field conditions labeled ① to ④ in (a).\n[Comment 1-2]:\n[Response 1-5]\nR vs I data also looks quite strange. It also has a threshold, below (above) which the resistance is constant (almost linearly increases) with current. The authors should first present a figure showing the temperature rise as a function of I . While the pulse authors state that the Joule heating is described by I2, I think the result clearly deviates from the authors’ statement.\nI would also strongly suggest that the authors make a survey or measurement on the Neel temperature of RuO thin film, because it is close to or below the temperature they estimated at which the switching takes place (381 K).\nResponse 1-2:\nFig. R6. a. The R as a function of the amplitude of I for the RuO /Mo/CoFeB multilayer. xx pusle 2 b. The R as a function of T (top axis, purple) and I (bottom axis, black) for the xx pusle RuO /Mo/CoFeB multilayer. 2\nThank you for your constructive feedback. Yes, we agree with your suggestions.\nWe have re-measured the R vs I data for the RuO /Mo/CoFeB multilayer, as xx pulse 2 presented in Fig. R6a. When the I increases from 0 mA to 20.5 mA (the maximum pusle current applied during current-induced magnetization switching in the RuO /Mo/CoFeB multilayer), an increase in R from 1170.5  to 1180  was observed. 2 xx\nThen, we adopted the reviewer’s suggestion to present the R as a function of T (top xx axis, purple) and I (bottom axis, black) for the RuO /Mo/CoFeB multilayer in Fig. pusle 2 R6b, to clarify the relationship between current-induced thermal effects and resistance behavior. Based on the R -T curve (top, purple) in Fig. R6b, 1180  corresponds to xx 375 K. Therefore, the temperature rise (T) during the writing process is about 75 K. (Pages 13-14 in revised Supporting Information)\nWe appreciate your insight regarding the Néel temperature of RuO₂ thin films. In response, we conducted a survey to determine the Néel temperature (T ) of the RuO N 2 thin film. A neutron diffraction study by T. Berlijn et al. [T. Berlijn et al., Phys. Rev. Lett. 7, 077201 (2017)] revealed that single-crystal RuO exhibits antiferromagnetic 2 (AFM) order at room temperature, accompanied by magnetic moments of approximately 0.05 μB. Additionally, the material undergoes an undetected lattice distortion below approximately 900 K. Building on these findings, Z. H. Zhu et al. employed resonant X-ray scattering (RXS) across the Ru L absorption edge to 2 investigate the magnetic ordering in both thin films and bulk crystals of rutile RuO [Z. 2 H. Zhu et al., Phys. Rev. Lett. 122, 017202 (2019)]. By analyzing polarization and azimuthal-angle dependencies of the magnetic Bragg signal, they confirmed collinear AFM spin order up to at least 400 K. Longitudinal scans of the magnetic ordering vector demonstrated that long-range magnetic order is retained in both bulk and thin-film samples at temperatures exceeding 400 K. Remarkably, these studies reveal that RuO₂ thin films maintain a stable AFM state even at 375 K, underscoring the robustness of antiferromagnetic correlations in RuO₂ across a broad temperature range.\nWe have included the results and discussion on this aspect in the revised manuscript. (Pages 13 and 14 in revised Supporting Information)\n[Comment 1-3]:\n[Response 1-6]\nThe method to derive the out-of-plane spin-splitter torque efficiency should not be reasonable. As I mentioned in my previous review report, the spin-splitter torque should be proportional to the current and should not have any x-intercept. Therefore, linear fit to the date in the region beyond the threshold should be invalid. Considering the fact that the bistable property almost disappears above the threshold, I think it is more reasonable to derive the out-of-plane spin splitter torque efficiency from a linear fit below the threshold.\nI would also mention that the data point above the threshold in Fig. 2c, in particular the ones for negative current, do not look to me “almost linear”.\nResponse 1-3: We sincerely thank the reviewer for the valuable comments and suggestions. As we replied in response 1-1, the threshold behavior for the SOT-induced loop-shift method is general and the fitting above the threshold current gives rise to the z-component of the SOT effective field. This is a general method that is widely adopted in the SOT area and not the major point of our current work, therefore, we think this point doesn’t affect the novelty of our work. In response, we have repeated several measurements of the anomalous Hall effect (AHE) loops for the RuO /Mo/CoFeB/MgO/Ta device to ensure both reliability and accuracy of the results. 2 As illustrated in Figs. R7a-7c measurements were performed with the pulsed current of 15 mA, 18 mA and 21 mA. For +I (blue line), the AHE curve shifts in the pulse positive x-direction, whereas for -I (orange line), an opposite shift is observed. pulse Additionally, the results presented in Fig. R7d are accompanied by error bars and exhibit an almost linear behavior above the threshold current of 18 mA. We have revised Fig. 2c in the main manuscript (Pages 10 and 12).\nFig. R7. a-c AHE loops for the RuO /Mo/CoFeB/MgO/Ta device under the pulsed current of 2 15 mA, 18 mA and 21 mA. +I (blue line) results in the AHE curve to the +x while -I pulse pulse (orange line) leads to the opposite shift. d. A summary of the shift (Heff) at different I . The z pulse threshold I to cause a shift in the AHE curve is about 18 mA. pulse\n[Comment 1-4]:\n[Response 1-7]\nThe fact that the current induces only a partial switching and their speculated reason should be described in the main text.\nResponse 1-4: We thank the reviewer for the valuable comments, which have contributed to the improvement of our manuscript. In the revised manuscript, we have included the detailed explanation of the partial switching behavior observed.\nAs shown below in the revised manuscript:\n“Indeed, the partial switching observed in our experiments is a known phenomenon in such systems, often attributed to thermal effects leading to partial demagnetization. Several studies have reported similar observation [M. X. Wang et al., Nat. Electronics. 1, 582 (2018)]. In our case, the local heating effects might have contributed to the partial demagnetization of magnetic domains. We believe that this technical/engineering point can be further optimized in future work, particularly by refining parameters such as anisotropy, device dimensions, pulse width, and others.”\n(Pages 17-18)\n[Comment 1-5]:\n[Response 1-8]\nI am not sure the authors properly understood the intention of my previous comment. If the same effect governs the results shown in Fig. 2 (anomalous Hall measurement) and those shown in Fig. 4 (tunnel junction measurement), the switching loop direction (CW or CCW) at H = 0 should be the same with either Hx < 0 or Hx > 0 for both measurements. However, still in the revised manuscript, the switching loop direction at H = 0 (CW) is the same with the one at H > 0 for Fig. 2, whereas for Fig. 4 that at H =0 (CCW) is the same with the one at H < 0.\nResponse 1-5: We sincerely thank the reviewer for their careful reading of our manuscript and for raising this important point regarding the switching loop directions in Figs 2 and 4. We apologize for not having performed more thorough experimental calibration in our previous response.\nWe have recalibrated the pulse current (I ) and sample positioning during the pulse current-induced magnetization switching. Firstly, the Al O (11̅02) substrate used in our 2 3 study features a chamfered edge, as shown in Fig. R8a, illustrating the epitaxial relationship between the epitaxial relationship between the Al O (11̅02) substrate and 2 3 the RuO (101) film with Al O [1̅101]//RuO [101], Al O [112̅0]//RuO [010]. Fig. R8b 2 2 3 2 2 3 2 depicts the lattice structure of the RuO (101) film (left) and the Al O (11̅02) substrate 2 2 3 (right). Then, we performed calibration on the samples c and e, aligning the I along pulse the Al O [112̅0]//RuO [010] direction (indicated by the blue arrows in Fig. R8a) to 2 3 2 measure the current-driven SST switching. The results are shown in Figs. R8d and 8f.\nFor both the RuO /Mo/CoFeB/MgO/Ta device and the RuO -pMTJ device, a switching 2 2 loop is observed even in the absence of H , when the I along the [010] direction, x pulse revealing the z-component of the SST. The polarity is found to be clockwise (CW). The measured R - I loops under positive in-plane magnetic fields H exhibit CW. xy pusle x Reversing the direction of H causes the polarity of the current-induced switching loop x also reverse with CCW. Therefore, the switching loop direction with CW at H = 0 to be x the same with H > 0 for both the RuO /Mo/CoFeB/MgO/Ta device and the RuO - x 2 2 pMTJ device.\nWe have corrected the polarity of the zero-field magnetization switching in RuO 2 presented for Fig. 4d in the main manuscript. (Page 16)\nFig. R8. a. Schematic representation of the epitaxial relationship between the Al O (11̅02) 2 3 substrate and the RuO (101) film with Al O [1̅101]//RuO [1̅01], Al O [112̅0]//RuO [010]. b. 2 2 3 2 2 3 2 Schematic diagram of the lattice structure of the RuO (101) film (left) and the Al O (11̅02) 2 2 3 substrate (right). c and d. Schematic illustration and switching curve of RuO /Mo/CoFeB/MgO/Ta multilayer under different external magnetic fields, from negative 2 to positive. e. and f. Schematic illustration and current-driven SST switching in the RuO -pMTJ 2 device under different magnetic fields.\n[Comment 1-6]:\n[Response 1-9]\nTheir revision in line 64 on page 3, “ultrahigh-writing current”, is non-scientific and lacks a respect for researchers/engineers working on STT-MRAM considering the fact that STT-MRAM has been successfully commercialized whereas the present work shows magnetization switching only with a significant effect of the Joule heating.\nResponse 1-6: We sincerely appreciate the reviewer’s insightful comment. We recognize the importance of using precise and respectful language in scientific discussions. Yes, in STT-MRAM, the current density passes through the tunnel barrier, which contributes to the limitations on device endurance. In contrast, for SOT-MRAM, the writing current is injected via the heavy metal layer and does not directly pass through the tunnel barrier. In response, we have revised the term “ultrahigh-writing current” to “high-writing current” to more accurately reflect the current densities typically employed in STT-MRAM systems.\nAs shown on page 3: “One of the major challenges for STT-MRAM is that a high current density needs to pass through an ultrathin-tunnel barrier (~1 nm), and thus the endurance of the MTJ is limited”.\n[Comment 1-7]:\n[Response 1-10]\nThe authors’ explanation that “during the current driven switching measurement, the applied writing current provides a large external energy to induce the non-equilibrium dynamic magnetic switching process, and this writing energy is enough to overcome the energy barrier between two magnetization states. (…) Thus, these two aspects are different and not directly related.” does not sound to me physically sound, or at least fully supported. I think that for the case of spin-orbit torque or spin splitter torque, the current driven switching can be completed by overcoming an energy barrier whose height can be approximated by the one that needs to be overcome during the field-driven switching. If the authors stick to this scenario, they need more thorough and scientific explanations.\nResponse 1-7: Thank you for your insightful comments. We agree that the energy barriers in current (SOT/STT)-driven and field-driven switching should be equal. In field-driven switching, an external magnetic field modifies the Zeeman energy term, altering the energy landscape quasi-statically. In contrast, current-driven switching relies on spin-orbit torque (SOT) or spin-transfer torque (STT), which induces precessional and damping-like torques to overcome the energy barrier.\nIn this study, the thermal stability (Δ) refers to the ability of the MTJ to maintain either the low-resistance parallel (P) configuration or the high-resistance anti-parallel (AP) configuration during the K T room-temperature thermal fluctuation in the absence B of any external magnetic or electrical excitations/energy. This is determined by the energy barrier (E ) from the magnetic anisotropy that separates these two equilibrium B states. The thermal stability factor involves the passive retention of the magnetization state under natural conditions, focusing on how resistant the MTJ is to spontaneous switching due to room-temperature thermal energy.\n[Comment 1-8]:\nLast but not least, it is quite tough for reviewers to catch how the authors have reflected the reviewers’ comments to the manuscript, because it is not explicitly described in the response letter how the manuscript is revised. Accordingly, the reviewers need to go back and forth between the response letter and the manuscript. I would request that the authors describe in their response letter how they reflected the reviewers’ comments into the manuscript, if they have a chance to resubmit this manuscript.\nResponse 1-8: Thank you for your detailed review and valuable comments on our manuscript. We sincerely apologize for any inconvenience caused by the need to cross-reference between the response letter and the manuscript. We fully understand the challenge you described and have taken specific steps to address this issue in our revised submission. Firstly, for each comment, we have specified the exact locations in the manuscript where changes have been made (e.g., page number and line number), along with a brief description of the modifications. Then, at the end of the response letter, we have included a summary File of “Change list” of all the revisions made to the manuscript.\nWe hope that these modifications will facilitate a more straightforward review process.\nResponse: We appreciate your valuable insights. In response, we have carefully reviewed your comments and revised the manuscript accordingly. Additional data and clarifications have been incorporated to further enhance its overall quality.\nWe have cited the work from Fedchenko et al. [O. Fedchenko et al. Sci. Adv. 10, eadj4883 (2024)] in our revised manuscript, which provides the first experimental evidence of altermagnetism in RuO₂/TiO (110). (Page 5 in the main manuscript)\n[Comment 3-1]\n1) The authors present XAS/XMLD data at the Ru-M resonant edges, referring to 2,3 them as L edges. I would recommend that to be corrected. 2,3\nResponse 3-1: Thank you for your valuable feedback. We appreciate your suggestion and acknowledge the mistake in the manuscript regarding the edges. The XAS data should indeed refer to the Ru-M resonant edges, not the L edges. We have corrected 2,3 2,3 the reference to the Ru-M resonant edges in the revised manuscript. (Pages 7 and 9 2,3 in the main manuscript)\n[Comment 3-2]\n2) The [101] surface axes written in black of figure R7a,b ( and figure 1a on the main text) are wrong. The z is correct, but the x//[010] and y//[-101] are in the wrong directions in the figure. The long black dashed line along the z[101] axis in fig R7a is confusing because it overlaps with the yellow E-vector and is painted above the Ru purple atom, making the 3d view confusing. Some effort should be made to improve the readibilty of fig. R7 because the Js vectors labels are barely visible when printed. See attached sketch of to correct fig R1b.\nResponse 3-2: Thank you for your constructive feedback. We agree with the reviewer and apologize for the errors in the axes directions in the last revision (Fig. 1a in the main manuscript). Figs. R9a and 9b show the correct axes orientations with (101)-RuO 2 plane, with the coordinate system defined as the x-axis with [1̅01], the y-axis with [010] and the z-axis with [101]. We have revised the (101) surface axes of Fig. 1a in the manuscript. (Page 7)\nIn response to the reviewer’s suggestion, the figure has been simplified for better visualization, using both Fig. R9a and its front view in Fig. R9b. When the E is applied along the [010] direction [Fig. R9a, yellow arrow], it indeed generates a J along the s [100] direction. For the (101)-RuO film used in this study (represented by the orange 2 plane), the J along [100] can be decomposed into components: one perpendicular (J⊥, s s purple arrows) and one parallel (J∥, azure arrow) to the (101) plane, In Fig. R9b, the s front view of Fig. R9a, it can be observed that the perpendicular component (J⊥) aligns s with the [101] direction, with its magnitude being approximately J sin. The s visualization of the image has also been updated in the revised manuscript. (Pages 5 and 7)\nFig. R9. a. The crystal structure of RuO with spin orientations indicated (green and blue arrows) 2 with (001)-RuO plane and the coordinate system defined by the a[100], b[010] and c[001] axes 2 (red arrows). The (101) crystal plane highlighted in orange, with its coordinate by the x[1̅01], y[010] and z[101] axis (black arrows) in b. The applied E is along the axis with b[010]. b. The front view from a.  is the angle of the N to the z[101] axis.\n[Comment 3-3]\n3) The XMLD spectrum in figure 1h is barely visible and not clearly distinguishable from the base line and the noise. It should be magnified vertically, and possibly plotted on versus the right vertical axis, and shifted vertically to avoid overlap with the XAS. The XMLD of all the 3 measured surface orientations should be displayed on the same scale to allow visual quantitative comparison of the XMLD intensity.\nResponse 3-3: We sincerely appreciate the reviewer’s insightful suggestions to improve the clarity and comparability of the XMLD data in Figure 1h. Figure 1h in the revised manuscript has been revised to vertically magnify and shift the XMLD spectrum (plotted on the right axis), avoiding overlap with XAS, as shown in Figs. 10a and 10b. The figures have been revised. (Page 7 in the main manuscript, Page 3 in the supplementary materials)\nFig. R10. XAS spectra with  = 0 and 90 of Ru4+ M and M edge in a. 3 2 Al O (11̅02)//RuO (101) and b. MgO(001)//RuO (110). The XMLD signal is plotted 2 3 2 2 on the right axis. c. The XMLD intensity of Ru4+ M for (101)-, (110)- and (001)-RuO 3 2 samples at room temperature.\nTo further investigate and manipulate the Néel vector (N) in RuO , magnetic field 2 annealing was employed to align the Néel vector with the direction of the annealing field (H ), followed by characterization using X-ray magnetic linear dichroism FA (XMLD). Initially, the RuO (100) thin film was deposited on the TiO (100) substrate, 2 2 with its N oriented along the y[001] direction [Fig. 11a]. X-ray absorption spectroscopy (XAS) measurements were then performed at normal incidence under zero-field conditions. The polarization of the incident X-rays was set at  = 0° and 90°, defined by the angle between the electric field vector (E⃗⃗ ) and the substrate’s x-axis. The XAS spectra at the Ru4+ M and M edges for the (100)-oriented RuO film exhibited an 3 2 2 XMLD effect with a ratio of 6.5% [Fig. 11b]. Then, magnetic field annealing was performed on the sample by applying a 7 kOe field (H ) during cooling from 250°C FA to room temperature to reorient the N along the x[010] direction [Fig. 11c]. XMLD then changes the sign and reveale an effect ratio of -5.3% in Fig. 11d, in marked contrast to the unannealed sample [Fig. 11b]. These observations confirm that the field-induced reorientation of the Néel vector was successful and directly linked to the XMLD response.\nFor the (001)-oriented RuO₂ film show in Fig. R11e, an XMLD effect is absent.\nAll XMLD spectra are presented on the same scale in Fig. R11f, which enables direct visual comparison of their XMLD intensities. The figures have been updated accordingly. (Page 7 in the main manuscript, Pages 3-4 in the supplementary materials)\nFig. R11. Schematic of magnetic field annealing on (100)-RuO film with a. unannealed and b. 2 H // x[010]. H represents the annealing field. The b. and d: XAS spectra with  = 0 and FA FA 90 of Ru4+ M and M edges results corresponding to the configurations in a. and c. e. XAS 3 2 spectra at Ru4+ M and M edges for TiO (001)//RuO (001). The XMLD signal is plotted on the 3 2 2 2 right axis. f. The relative intensity of Ru4+ M for (100)-, (100)_FA- and (001)-RuO samples at 3 2 room temperature.\n[Comment 3-4]\n4) The fig 1i, presented in the caption as “The relative intensity of Ru4+ L3 for (110)-, (101)- and (001)-RuO ” is obscure: it is not clear what how the “relative intensity” is 2 defined. The definition of relative intensity is not presented (line 180). The same should be said for line 180-182: “Then, we extracted the relative intensity between phi = 0° and 90°, as summarized in Fig. 1i.”. The formula used to calculate the percentage XMLD intensity should be presented.\nResponse 3-4: Thank you for your valuable feedback and raising an important point. We have carefully considered your suggestions and have made the necessary revisions. The XMLD effect is present for both RuO (110) and RuO (101) films, with effect ratios 2 2 of 1.68% and 2.2%, respectively. The effect ratio is calculated using the following formula: Ratios (%) = 𝐼𝝓=0° - 𝐼𝝓=90° × 100%. 𝐼𝝓=0° + 𝐼𝝓=90° Then, we apologize for any confusion regarding the term “relative intensity”. In Figure 1i of the revised manuscript, the “relative intensity” has been revised to “XMLD intensity”. This refers to the raw XMLD signal, with data from different orientations plotted on a single coordinate system using a uniform y-axis scale, without any additional processing.\nBoth the formula and the refined phrasing have been explicitly added to the revised manuscript. (Page 9 in the main manuscript).\n[Comment 3-5]\n5) It is stated that “neither XMLD nor any x-ray absorption” is observed in the RuO2(001) film (line 183), which is impossible because, if the Ru is present in the film, the XAS signal cannot go to zero. The disappearance of the Ru XAS on the (001) surface declared by the authors casts doubt over the quality of the sample and on the understanding of the physical meaning of the experimental results. It is possible that the text describing the results might not be accurate and that I misunderstood the findings, however the authors should present the XAS/XMLD results of the three RuO 2 surface orientations to clarify this point and show that the XAS signal on the RuO (001) 2 does not disappear (while the XMLD does). If this request cannot be satisfied, I am afraid that the validity of the whole XAS/XMLD dataset cannot be trusted to support the present of magnetic order in the Ru film.\nResponse 3-5: We sincerely thank the reviewer for pointing out this critical concern. Yes, we agree with the reviewer’s comments. The phrasing in Line 183 (“neither XMLD nor any x-ray absorption”) was unintentionally misleading. We confirm that XAS signals are present for all three orientations, including RuO (001), as Ru atoms are 2 inherently part of the lattice. The absence of XMLD in RuO (001) does not imply a 2 lack of XAS, as shown in Fig. R12. The statement has been corrected to: “The (110)- and (101)-RuO films exhibit significant XMLD signals, while XAS signals are 2 detectable for all orientations including (110), (101), and (001)-RuO films. However, 2 the XMLD intensity is absent in the (001)-RuO films.” (Page 9) 2 In the revised supporting materials, we have included the XAS spectra for three orientations (101)-, (110)- and (001)-RuO , demonstrating their Ru4⁺ M edge 2 3,2 absorption. (Page 7 in the main manuscript and Page 3 in the supporting materials)\nFig. R12. XAS spectra with  = 0 and 90 of Ru4+ M and M edges in RuO (001) film. 3 2 2\n[Comment 3-6]\n6) To the best of my knowledge, there are not published data on RuO XMLD at the 2 M edges, therefore, the data presented in the paper are novel and interesting. The only 2,3 mention to similar data I could find are from a conference abstract titled “Detecting Altermagnetism in RuO by Angular-Dependent X-ray Magnetic Linear Dichroism” , 2 by Jun Okabayashi1, Zhenchao Wen, Hiroaki Sukegawa and Seiji Mitani. (https://pub.confit.atlas.jp/en/event/jsap2023a/presentation/21a-C501-5) Their results appear to be unpublished and I had no access to their results, but they might be useful as a term of comparison with the data presented in the paper under review, to support their claim of altermagnetic character of their films.\nResponse 3-6: Thank you for your insightful comment. We agree with you and believe the data presented in this paper are novel and contribute to the understanding of RuO 2 in this manuscript.\nWe appreciate your reference to the conference abstract titled “Detecting Altermagnetism in RuO by Angular-Dependent X-ray Magnetic Linear Dichroism” by 2 Jun Okabayashi et al. Unfortunately, we were unable to access their unpublished results, but we agree that their findings may serve as a valuable method. Additionally, we would like to mention the recent work by C. Song et al., “Probing the Néel order in altermagnetic RuO films by X-ray magnetic linear dichroism” [Y.-C. Zhang, et al., 2 Chinese Phys. Lett. 42, (2025)], which agrees with our studies.\nIn the revised manuscript, we have cited both Okabayashi et al.’s abstract [J. Okabayashi, et al., arXiv:2412.17016, (2023)] and C. Song et al.’s work [Y.-C. Zhang, et al., Chinese Phys. Lett. 42, (2025)] to acknowledge the potential relevance of their findings, which further support the claim of antiferromagnetic behavior in RuO films. 2 (Page 9 in the main manuscript)\n[Comment 3-7]\n7) Line 177: “It can be observed that the XMLD effect at the L3 edge in this structure is purely magnetic origin at the normal incidence of x-rays. “should be removed because it is not possible to attribute an XMLD signal purely to magnetic order in absence of a temperature scan, as stated before. Instead the author could claim that the XAS/XMLD data presentes are compatible with the presence of altermagnetic order.\nResponse 3-7: Thank you for your valuable feedback. We sincerely appreciate the reviewer’s critical observation regarding the attribution of the XMLD signal to magnetic order. We agree with the reviewer’s suggestion.\nWe have revised the manuscript to align with the reviewer’s suggestion: “It can be observed that the presented XMLD data are consistent with the presence of altermagnetic order in the RuO₂ film”. (Page 9 in the main manuscript)\n[Comment 3-8]\n8) Line 180-182: “Then, we extracted the relative intensity between phi = 0° and 90°, as summarized in Fig. 1i.”: it is not clear how the “relative intensity” is calculated and what the traces in figure 1i represents.\nResponse 3-8: We appreciate the reviewer’s request for clarification. As we replied in response 3-4, The XMLD effect is present for both RuO (110) and RuO (101) films, 2 2 with effect ratios of 1.68% and 2.2%, respectively. The effect ratio is calculated using the following formula: Ratios (%) = 𝐼𝝓=0° - 𝐼𝝓=90° × 100%. Then, we apologize for any 𝐼𝝓=0° + 𝐼𝝓=90° confusion regarding the term “relative intensity”. In Figure 1i, the “relative intensity” has been revised to “XMLD intensity”. This refers to the raw XMLD signal, with data from different orientations plotted on a single coordinate system using a uniform y-axis scale, without any additional processing.\nBoth the formula and the refined phrasing have been explicitly added to the revised manuscript. (Page 9 in the main manuscript)."}, {"round": 2, "reviewer_comments": {"reviewer_1": "I have carefully reviewed the authors’ response letter and revised manuscript and concluded that the editor should terminate the review process and reject this manuscript at this stage. The main reason for this assessment is that there are at least two inconsistencies in their results in the previous rounds and this round. For example, the results shown in Fig. S10b in the previous round and in Fig. S12a in the present round are vastly different. Also, some data in Fig. 2c in the previous round is out of the error bar of the present data in Fig. 2c. The authors do not give any explanation for these discrepancies, indicating that they submitted unreliable results either in the previous or present rounds. Accordingly, it is completely impossible for me to assess the scientific validity of this work. I also found some other critical errors in their analysis of their result, but I think there is no room to argue them because the inconsistencies in their presented results among the different rounds of review are already fatal enough.", "reviewer_2": "The authors have addressed all my point accurately and update the main text accordingly. I am satisfied with their response and I recommend the publications of their findings.\nI just have one final remark to do with regards to comment 3-2. The image in fig.1 has been improved, but in panel (b) the x-axis is actually along the [10-1] direction and not along the [-101] as stated in the figure).", "reviewer_3": "In this manuscript, the authors reported that the all-electrical field-free altermagnetic spin-splitting torque (SST)-driven switching of the perpendicular-magnetic tunnel junction (MTJ) in the 3-terminal altermagnetic SST- magnetic random-access memory (MRAM) device, with the tilted spin polarization and the transversal flow of the spin current. Spin splitting torque from altermagnets can be a promising technique for next-generation MRAM, and reducing the switching current density is important for MRAM applications. The manuscript is well written and scientifically sound after the revision process. Nevertheless, before I can recommend publication, several questions need to be addressed. My questions about this manuscript are as follows:\n(1) Spin-splitting torque switching in MTJ: The authors present experimental results demonstrating magnetization switching in MTJs using spin-splitting torque. However, only a single-device measurement is provided in the current version of the manuscript. It is critically important to include switching data from multiple MTJ devices to ensure reproducibility and statistical significance. Moreover, as in the Hall bar measurements, the authors should clearly demonstrate that switching does not occur when current is applied along the direction in which spin-splitting torque is absent. In addition, Figure 4d (y axis) should present the actual resistance values from the MTJ device, rather than normalized resistance change.\n(2) Discrepancy in switching current between Hall bar and MTJ: The switching current in the Hall bar (12.15 ×106 A·cm-2) and the MTJ (2.1×106 A·cm-2) differs by more than one order of magnitude. The manuscript should provide a clear explanation for this difference. In my opinion, possible reasons might include reduced current shunting, changes in CoFeB magnetic properties, or device geometry effects - these possibilities should be addressed. A further discussion on the reason behind this is needed in the revised manuscript.\n(3) Minor comment: Please carefully review the manuscript. There are many typos throughout (e.g. Please capitalize the “x” in “x-ray” (i.e., write it as “X-ray”), The x in the x-axis label is inconsistently formatted italic in some instances and regular in others.)."}, "author_response": "Response：\nRegarding Fig. S10b (previous version) and Fig. S12a (current version):\nFig. R1. Left: previous round. Right: present round.\nWe would like to clarify that the data presented in the original manuscript (Fig. S10b in the original Supplementary Information) in Fig. R1, although unusual in shape, were indeed obtained from our experiments—we did not fabricate or manipulate the data in any way. At the time, we believed it to be a valid result, as the measurements were taken using the same device used elsewhere in the main manuscript, with the intention of estimating the R -I curve. However, based on the reviewer’s insightful xx pulse 1 comments, we have come to recognize the limitations and potential issues associated with that dataset.\nIn response to the 1st-round reviewer #1’s comment 1-2, we measured resistance using newly fabricated devices on the same sample in Fig. R2. The revised data (right data in Fig. R1), now shown in Fig. S12a of the updated supplementary information, displays the expected and more conventional behavior. After careful discussion and analysis, we believe the abnormal shape in the original data was likely caused by repeated measurements on a single device such as multiple applications of current or magnetic field—which may have led to cumulative degradation and affected its electrical performance.\nIn contrast, the updated results were obtained from fresh devices located at different positions on the same sample, which we believe more accurately reflect the intrinsic behavior of the RuO₂/Mo/CoFeB multilayer system. Therefore, we have replaced the earlier data in the revised manuscript with these improved measurements to ensure the reliability and accuracy of the results.\nAs illustrated in Fig. R2, the thin film sample contains multiple uniformly distributed devices, which are available for experimental measurements. After performing multiple measurements with device ①, additional measurements can be carried out using new devices such as ②, ③, ④, ⑤, and so on.\nFig. R2. Microscopic picture of the pattern Hallbar device with the RuO /Mo/CoFeB 2 multilayer. The red squares with ①, ②, ③, ④, ⑤… indicate devices located at different positions on the same sample.\nFig. R3. Left: previous round. Right: present round with repeat measurements.\nAs shown in Fig. R3, the differences between the previous and current data shown in Fig. 2c arise from improvements in response to the 1st-round reviewer #1’s comment 1-3. Specifically, we increased the number of repeated measurements to enhance the statistical reliability of the data. As a result, the error bars in the revised figure are smaller, and the data points exhibit slight shifts due to improved averaging.\n[Comment]:\nThe authors have addressed all my point accurately and update the main text accordingly. I am satisfied with their response and I recommend the publications of their findings.\nI just have one final remark to do with regards to comment 3-2. The image in fig.1 has been improved, but in panel (b) the x-axis is actually along the [10-1] direction and not along the [-101] as stated in the figure).\nResponse：Thank you very much for your positive evaluation and helpful comments.\nWe are glad that our revisions have addressed your concerns and that you are satisfied with the updated manuscript.\nRegarding your final remark on comment 3-2, we appreciate your careful observation. We have corrected the x-axis label in Fig. 1(b) to accurately indicate the [101̅] direction instead of [1̅01], as shown in Fig. R4. The figure and its caption have been updated accordingly in the revised manuscript. We sincerely appreciate your valuable feedback throughout the review process. (Page 7)\nFig. R4. a. The crystal structure of RuO with spin orientations indicated (green and blue arrows) 2 with (001)-RuO plane and the coordinate system defined by the a[100], b[010] and c[001] axes 2 (red arrows). The (101) crystal plane highlighted in orange, with its coordinate by the x[101̅], y[010] and z[101] axis (black arrows) in b. The applied E is along the axis with b[010]. b. The front view from a.  is the angle of the N to the z[101] axis.\n[Comments]:\nIn this manuscript, the authors reported that the all-electrical field-free altermagnetic spin splitting torque (SST)-driven switching of the perpendicular-magnetic tunnel junction (MTJ) in the 3-terminal altermagnetic SST- magnetic random-access memory (MRAM) device, with the tilted spin polarization and the transversal flow of the spin current. Spin splitting torque from altermagnets can be a promising technique for next- generation MRAM, and reducing the switching current density is important for MRAM applications. The scientific quality of the manuscript has clearly improved after the revision. Nevertheless, before I can recommend it for publication, several critical issues need to be addressed. My specific questions regarding the manuscript are as follows:\nResponse: We appreciate your valuable insights. In response, we have carefully reviewed your comments and revised the manuscript accordingly. Additional clarifications have been incorporated to further enhance its overall quality.\n[Comment 3-1]:\n(1) Change in resistance data: The resistance data presented in the original manuscript (Fig. S10b in the original SI) exhibit an abnormal shape that is not typically observed in standard devices. In contrast, the revised data (Fig. S12a in the revised SI) show a more conventional and expected behavior. This raises a critical question: why did the authors choose to present the abnormal data in the initial submission, despite having fabricated multiple devices during the course of their research? While I would like to believe this was simply an honest mistake, it is clear that this process has significantly undermined the credibility of the authors’ data. I believe a proper explanation is necessary. In particular, providing validation from a larger number of samples would be helpful in addressing this concern.\nResponse 3-1: Thank you for your valuable and critical comment. We would like to state that the data presented in the original manuscript (Fig. S10b in the original SI), in Fig. R5, although unusual in shape, were indeed obtained from our initial experiments. At that time, we believed it to be a valid result, as the measurements were taken using 5 the same device used elsewhere in the main manuscript, with the intention of estimating the R -I curve. However, based on the reviewer’s insightful comments, we have xx pulse come to recognize the limitations and potential issues associated with that dataset.\nIn response, we measured resistance using newly fabricated devices on the same sample, as shown in Fig. R6. The revised data, now shown in Fig. S12a of the updated supplementary information, displays the expected and more conventional behavior. After careful discussion and analysis, we believe the abnormal shape in the original data was likely caused by repeated measurements on a single device such as multiple applications of current or magnetic field—which may have led to cumulative degradation and affected its electrical performance.\nIn contrast, the updated results were obtained from fresh devices located at different positions on the same sample, which we believe more accurately reflect the intrinsic behavior of the RuO₂/Mo/CoFeB multilayer system. Therefore, we have replaced the earlier data in the revised manuscript with these improved measurements to ensure the reliability and accuracy of the results.\nFig. R5. Left: previous round. Right: present round.\nAs illustrated in Fig. R6, the thin film sample contains multiple uniformly distributed devices, which are available for experimental measurements. After performing multiple measurements with device ①, additional tests can be carried out using new devices such as ②, ③, ④, ⑤, and so on.\n[Comment 3-2]\n(2) Interpretation of experimental and simulation results using single- and multidomain models: In my view, the authors’ interpretation of their data (Fig. 2c and Fig. S19) involves a logical inconsistency. Both the experimental and simulation results exhibit two distinct regimes; however, they differ in slope behavior across the boundary. The experimental data show a zero slope in the low-current regime and a finite slope in the high-current regime, whereas the simulation results show a small but finite slope in the low-current regime and a larger slope in the high-current regime. Despite this discrepancy, the authors estimate the magnitude of the z-component of the spin-orbit torque using a single-domain model applied to the high-current regime. However, in their rebuttal, they state that magnetization reversal in the high-current regime occurs via a multi-domain process, while the single-domain reversal takes place in the low- current regime. This implies that the authors applied a single-domain model to analyze a regime in which multi-domain behavior dominates, which is conceptually inconsistent. That said, the overall trends observed are similar to those reported in other studies, as the authors have noted. Therefore, I recommend that the authors revise their explanation and provide a unified and physically consistent model that encompasses both regimes.\nIn our the RuO₂/Mo/CoFeB/MgO/Ta system, when measured on (101)-oriented RuO with a spin polarization component along the z-axis (), the damping-like torque 2 z is given by  =   m  , where m is the unit vector of the magnetization along z z z z z direction.\nFor the collinear spin polarization versus magnetization, like spin transfer torque- induced magnetization switching, under a small current (I) and in the absence of thermal fluctuations, σ and m are collinear, resulting in zero spin torque, consequently, z z with zero current-induced effective field. As a result, magnetization precession does not occur. Therefore, the hysteresis loops remain unaffected by the spin torque under these conditions. As the current increases, thermal fluctuations become non-negligible. The magnetization vector m begins to precess and deviates from its equilibrium position, z leading to a nonzero torque. This gives rise to a finite z-component of the torque and generates an effective out-of-plane field (H ) at low current density. When current- z induced spin torque becomes sufficiently large to overcome the magnetic damping of the system, the current-induced magnetization precession has a significantly increasement, resulting a sharply increased shift for the R -H hysteresis loops as a xy z function of current (current-induced effective field H ), appearing beyond a certain z threshold, as reported by S. C. Baek, et al., Nat. Mater. 17, 509 (2018), Lee, K. J. et al. J. Appl. Phys. 95, 7423 (2004) and Z. Li et al., Phys. Rev. 68, 024404 (2003).\nIn the revised manuscript, we have provided further details and included citations to relevant references. (Page 10)\nFurther, we thank the reviewer for pointing out this discrepancy in Fig. 2c and Fig. S19, as shown in Fig. R7. As noted, the experimental data shows a zero slope in the low-current regime, while the simulation shows a small but finite slope. This difference arises primarily because our simulations were performed at zero temperature, where the spin polarization has a small but non-zero out-of-plane (z-axis) component, leading to a finite slope even at low currents. In contrast, under experimental (room temperature) conditions, thermal fluctuations can average out such small deflections, resulting in an effectively zero slope in the low-current regime. Including temperature effects would significantly increase the computational cost and runtime due to the use of a disk-shaped model in our simulations.\nWe have added a discussion of this discrepancy (Fig. 2c and Fig. S19) in Supplementary Information. (Page 22 in Supplementary Information)\n[Comment 3-3]\n(3) Discrepancy in switching current between Hall bar and MTJ: The switching current in the Hall bar (12.15×106 A·cm-2) and the MTJ (2.1×106 A·cm-2) differs by more than one order of magnitude. The manuscript should provide a clear explanation for this difference. In my opinion, possible reasons might include reduced current shunting, changes in CoFeB magnetic properties, or device geometry effects - these possibilities should be addressed. A further discussion on the reason behind this is needed in the revised manuscript.\nResponse 3-3: We sincerely thank the reviewer for their valuable comments. The 9 reviewer has correctly pointed out the significant discrepancy in the switching current density (Jc) between the Hall bar (12.15 × 10⁶ A·cm⁻²) and the magnetic tunnel junction (MTJ) device (2.1 × 10⁶ A·cm⁻²). We fully agree that a clear explanation of this difference is necessary. The potential causes suggested by the reviewer—reduced current shunting, changes in the magnetic properties of the CoFeB layer, and device geometry effects—are highly insightful and indeed relevant to the observed results.\nWe have added a detailed discussion of this issue, focusing on the following three aspects:\n1. Current shunting in the MTJ structure: The MTJ stack consists of multiple conductive layers that can shunt part of the charge current. In contrast, the Hall bar device is typically based on a single magnetic layer with minimal current shunting.\n2. Changes in the magnetic properties of the CoFeB layer: Differences in device structure and fabrication processes can change the magnetic properties of the CoFeB layer—such as anisotropy and interface quality—affecting the switching current.\n3. Device geometry effects: The RuO₂(12)/Mo(2)/CoFeB(0.85)/MgO(1.2)/Ta(2) multilayer (thicknesses in nanometers) is patterned into a pillar structure with a diameter of 8 μm, while the MTJs are circular pillars with diameters of 250 nm. This difference in geometry influences current distribution, edge effects, and thermal behavior, all of which impact switching performance.\nWe have added a detailed discussion of these factors in the revised manuscript (Page 17).\n[Comment 3-4]\n(4) Minor comment: Please carefully review the manuscript. There are many typos throughout (e.g. Please capitalize the “x” in “x-ray” (i.e., write it as “X-ray”), The x in the x-axis label is inconsistently formatted italic in some instances and regular in others.).\nResponse 3-4: Thank you very much for pointing out these minor issues. We have 10 carefully reviewed the entire manuscript and corrected all typos and inconsistencies. Specifically, we have capitalized “X-ray” where appropriate and ensured consistent formatting of the “x” in all axis labels. These changes have been highlighted in red in the revised manuscript. We greatly appreciate your careful attention to detail which has contributed to improving the clarity and professionalism of our work.\n11"}, {"round": 3, "reviewer_comments": {"reviewer_3": "I would like to express my gratitude to the authors for the significant effort they have made in addressing my questions. Many of my concerns have been resolved; however, I still cannot fully dispel my doubts regarding the temperature measurements derived from device resistance.\n(1) Change in resistance data: I suggest that the authors measure a larger number of devices to ensure data reliability. How many devices are fabricated on each sample, and what is the approximate device yield? For instance, if there are 200 devices in total with a 50% yield, then at least 100 are measurable, and in that case I believe the authors should provide resistance - current (R - I ) curves for at least half of them (i.e., ~50 pulse devices). To justify their present explanation, measurements from a larger number of devices appear essential. Ideally, if repeated measurements could show that the initially reported R - I behavior evolves consistently into the revised result, this would pulse provide the most convincing evidence. Moreover, I encourage the authors not only to show resistance measurements across multiple devices, but also to include repetitions of their other key data (for example, the SST efficiency in RuO /Mo/CoFeB, charge- 2 spin conversion efficiency, and the critical switching current density). If these values are collected across devices and displayed with error bars, the scientific validity of the work would be greatly strengthened and would compensate for the earlier issues.\nGiven that this manuscript concerns the altermagnetic properties of RuO , which is a 2 topic of considerable present interest, I believe scientific rigor is especially important. If the authors can provide additional data from a larger number of devices as suggested, this manuscript will achieve the required level of rigor and will also provide greater benefit to the readers.\n(2) Minor comment: I would like to note that the content corresponding to Supplementary Note 10 is not explicitly mentioned in the main text. I request that the authors insert sentences in the manuscript that properly call out each Supplementary Note. In particular, at line 274, Supplementary Notes 9-14 are cited collectively in support of a single statement, even though Notes 9 and 10 concern Mo/CoFeB/MgO. Additionally, at line 388, when discussing micromagnetic simulation, Supplementary Note 10 is incorrectly cited. These issues should be corrected."}, "author_response": "Response：Thank you for your valuable comments and suggestions on our manuscript. We greatly appreciate your feedback and have carefully considered your points. Below are our responses to the two issues you raised.\n[Comment 3-1]:\n(1) Change in resistance data: I suggest that the authors measure a larger number of devices to ensure data reliability. How many devices are fabricated on each sample, and what is the approximate device yield? For instance, if there are 200 devices in total with a 50% yield, then at least 100 are measurable, and in that case I believe the authors should provide resistance - current (R - I ) curves for at least half of them (i.e., ~50 pulse devices). To justify their present explanation, measurements from a larger number of devices appear essential. Ideally, if repeated measurements could show that the initially reported R - I behavior evolves consistently into the revised result, this would pulse provide the most convincing evidence. Moreover, I encourage the authors not only to show resistance measurements across multiple devices, but also to include repetitions of their other key data (for example, the SST efficiency in RuO /Mo/CoFeB, charge- 2 spin conversion efficiency, and the critical switching current density). If these values are collected across devices and displayed with error bars, the scientific validity of the work would be greatly strengthened and would compensate for the earlier issues.\nGiven that this manuscript concerns the altermagnetic properties of RuO , which is a 2 topic of considerable present interest, I believe scientific rigor is especially important. If the authors can provide additional data from a larger number of devices as suggested, this manuscript will achieve the required level of rigor and will also provide greater benefit to the readers.\nResponse 3-1: We sincerely thank the reviewer for this constructive suggestion. Following the reviewer’s advice, we have performed additional measurements on multiple devices fabricated on the same film to verify the reliability and reproducibility of our data. As shown below:\n1. The resistance-current (R -I ) data: xx pulse\nWe have measured the R -I behavior of 24 different devices (Devices 1-24) xx pulse on one sample of the RuO₂/Mo/CoFeB multilayer. In Fig. R1, all these devices display characteristic parabolic dependence, and their R -I curves are highly consistent xx pulse with one another. The resistance variation among these devices is within ±1 Ω under applied same I , confirming the reproducibility of our measurements and indicating pulse that the observed R -I behavior is an intrinsic behavior of the RuO₂/Mo/CoFeB xx pulse multilayer. Furthermore, to account for potential variations across different devices, we included error bars in the R -I data. As shown in Fig. R2a, the R -I data of the xx pulse xx pulse tested devices were averaged and analyzed with standard deviation. When I pulse increases from 0 mA to 21 mA (the maximum current applied during current-induced magnetization switching in the RuO /Mo/CoFeB multilayer), the resistance R 2 xx increases from 1170.5 Ω to 1180 ± 1 Ω. These results demonstrate the high uniformity and consistency of different devices fabricated on one sample.\nThe revised data, including error bars, have been provided in the updated Supplementary Information (Pages 16 and 17 in the Supplementary Information).\n2\nFig. R2. The R as a function of the amplitude of I for the RuO /Mo/CoFeB multilayer. xx pusle 2\n4\n2. The critical switching current density:\nFollowing the reviewer’s recommendation, we performed measurements about the critical switching current density on the RuO (101)/Mo/CoFeB multilayer. As shown 2 in Fig. R3a, the anomalous Hall effect (AHE) measurement confirms that the heterostructure exhibits strong perpendicular magnetic anisotropy (PMA). Fig. R4 presents the R -I loops measured from 6 different devices (Device 1-6) on the same xy pulse sample under various in-plane magnetic fields (H ) applied along the [1̅01] direction. x A full switching loop is observed even in the absence of H , indicating the presence of x a z-component of the spin-splitting torque (SST) in addition to the conventional y- torque. Then, Fig. R3b presents the all current-induced magnetization switching loops of 6 Devices measured without H . The R -I loops nearly coincide across all x xy pulse devices, indicating highly uniform switching behavior, with a critical switching current density of 12.15 × 106 (±0.1) A cm-2.\nThe performed measurements of current-induced magnetization switching loops have been provided in the updated Supplementary Information (Pages 9 and 10 in the Supplementary Information).\nFig. R3. a. AHE loop for the sample with the out-of-plane magnetic field (H ). b. Current-induced z magnetic switching without H for Devices 1 to 6. x\n3. The SST efficiency:\nWe further evaluated the SST efficiency by measuring multiple Devices 1-3, shown in Fig. R5. The hysteresis loops of R as a function of the H were recorded xy z under different I . In Fig. R5, the R -H loops nearly overlap for pulse currents of pusle xy z ±8, ±11, ±15 and ±16 mA. In contrast, a clear loop shift appears when applying pulse currents of ±18, ±19, ±20, and ±21 mA. The loop centers move toward positive (negative) fields for positive (negative) pulse currents, respectively, indicating the emergence of a current-induced out-of-plane effective field Heff, generated by SST. By z averaging the absolute values of the extracted slopes, the out-of-plane SST efficiency is determined to be 1.02  10-6 Oe A-1cm2. Furthermore, the processed results in Fig. R6 include error bars within ±0.12 Ω, which demonstrates the consistency among different devices on one sample and confirms the robustness of our experimental data. (Pages 5 and 6 in revised Supporting Information)\n4. The charge–spin conversion efficiency:\nWe measured Devices 1-4 to evaluate the charge–spin conversion efficiency in the RuO /Mo/CoFeB/MgO/Ta stack, as shown in Fig. R7. Harmonic measurements were 2 performed on the RuO /Mo/CoFeB/MgO/Ta stack. The left panels of Fig. R7a-d display 2 the typical dependence of the first (V ) and second (V ) harmonic Hall voltages on the ω 2ω in-plane longitudinal magnetic field. From the current dependence of damping-like effective (H ), in the right panels of Fig. R7a-d, the average in-plane ST efficiency DL (SST+SOT) is determined to be 0.824  10-6 Oe A-1cm2, corresponding to a charge-spin conversion efficiency of 0.052. Fig. R7 presents the current density dependence of the H , obtained from multiple measurements from the Devices 1-4. The error bar DL represents the standard deviation, indicating the statistical reliability of the results.\nWe have updated the results with error bar in the revised Supporting Information. (Page 11 in revised Supporting Information)\n9\n4\n3\n) e O ( 2 L D H 1 0 0.8 1.6 2.4 3.2 4.0 4.8 J (106 A cm-2) e\nFig. R8. Current density dependence of the H obtained from multiple measurements from Devices DL 1-4. Error bars denote the standard deviation across multiple measurements.\n[Comment 3-2]\n(2) Minor comment: I would like to note that the content corresponding to Supplementary Note 10 is not explicitly mentioned in the main text. I request that the authors insert sentences in the manuscript that properly call out each Supplementary Note. In particular, at line 274, Supplementary Notes 9-14 are cited collectively in support of a single statement, even though Notes 9 and 10 concern Mo/CoFeB/MgO. Additionally, at line 388, when discussing micromagnetic simulation, Supplementary Note 10 is incorrectly cited. These issues should be corrected.\nResponse 3-2: We appreciate the reviewer’s careful reading and constructive suggestion. In the revised manuscript, we have carefully checked all the citations of the Supplementary Notes to ensure that each Supplementary Note is explicitly mentioned in the main manuscript. In particular:\n“Furthermore, the R -I loops were measured for several devices on the same xy pusle sample under different H along the [1̅01] direction, confirming the consistent behavior x and robustness of the devices (Supplementary Note 6).” (Pages 11 and 12).\n“We then estimated the Joule heating during current-induced magnetization switching. The results show that, even at the maximum I applied in the pulse RuO /Mo/CoFeB multilayer, the RuO thin films preserve a stable antiferromagnetic 2 2 configuration (Supplementary Note 10). For continued investigation, the details and the 10 stack of RuO (12)/Pt(1.2)/Co(0.7)/Pt(1.2)/SiO (3) (number in nanometers) are 2 2 designed to verify the z-torque spin current generated by RuO (101) film 2 (Supplementary Note 11). MOKE imaging was performed on RuO (12)/Pt(1.2)/Co(0.7)/Pt(1.2)/SiO (3) in the absence of a magnetic field to uncover 2 2 magnetization switching under pulsed current (Supplementary Note 12). The dependence of H on I and harmonic measurements were caried out to reveal the z pulse z-component of the spin polarization and the effective charge-spin conversion induced by the altermagnetic (101)-RuO (Supplementary Note 13).” (Pages 13 and 14). 2\nIn the discussion of micromagnetic simulation:\n“We perform the micromagnetic simulations based on Landau-Lifshitz-Gibert (LLG) equation with including SST term (the details see Supplementary Note 14)” (Page 20)."}, {"round": 4, "reviewer_comments": {"reviewer_3": "I would like to express my gratitude to the authors for their tremendous efforts in alleviating my concerns. Therefore, I am pleased to recommend the publication of this manuscript."}, "author_response": ""}]

Decision letter