Electrical manipulation of spin splitting torque in altermagnetic RuO₂

In the field of information storage, nonvolatile magnetic random-access memory (MRAM) with high speed, high density and low dissipation plays a key role, and it requires efficient approaches, especially electrical ones, to recording data^1,2,3,4. During the past decades, great progress has been made in spintronics, and spin torques carrying angular momentum has replaced current-induced Oersted field as the state of the art for writing technology^5,6,7,8. The widely used spin torques include spin transfer torque (STT) and spin-orbit torque (SOT), and corresponding STT-MRAM and SOT-MRAM possess the strengths of lower power consumption, higher storage density and better reliability^9,10,11. On one hand, the STT usually has higher spin torque efficiency due to nonrelativistic ferromagnetic exchange splitting, but relevant devices are more fragile because of the writing current flowing directly through the magnetic tunneling junctions (MTJs)^12,13. On the other hand, for SOT-MRAM, although the writing current does not pass through MTJs, the spin torque efficiency is restricted by spin-orbit coupling (SOC) of spin source materials^14,15. Therefore, it will be much beneficial to the improvement of data writing technique if the advantages of both STT and SOT can be combined together.

Recently, a new spin splitting torque (SST) related with nonrelativistic altermagnetic spin splitting effect (ASSE) has been predicted theoretically in collinear antiferromagnets with crystal and spin-rotation symmetries (Supplementary Information Note S1), which are termed as altermagnets^{16,17,18,19,20,21}. This SOC-independent ASSE is able to generate nontrivial transverse spin current or out-of-plane polarized spin current with higher efficiency compared to other mechanisms, such as low crystal symmetry^22,23,24,25. Experimental evidence of SST has been reported in RuO₂ films with rutile crystal structure^26,27,28. The SST exhibits controllable spin polarization with its direction parallel to the Néel vector of the altermagnets, which can overcome the limitation of orthogonal relation among charge current, spin polarization and spin current. Not only does RuO₂ possess desirable electrical conductivity despite being a metallic oxide, but it also has relatively high Néel temperature above 300 K as well as feasible preparation techniques, which are in favor of being applied in spintronic devices operating at room temperature^{29,30,31,32,33}. While some recent studies raise doubts about the antiferromagnetism of RuO₂^34,35, there are some other latest papers pointing out that the properties of RuO₂ can be fragile and may depend on various synthesis conditions^36,37,38,39, which highlights the potential uncertainty in present measurements.

Most notably, the Néel vector of RuO₂ is reported to be along the [001] crystallographic axis, and hence various behaviors related with SST can be observed in RuO₂ films with different crystallographic orientations^29,30. For example, RuO₂(101) films with tilted Néel vector are not only able to generate SST with out-of-plane polarization in favor of field-free switching of the magnetization in adjacent magnetic layer^27,28, but they can also be utilized for spin detection⁴⁰. To extend the functionalities of altermagnetic spin sources, SST is expected to be manipulated, which will be achieved once the Néel vector can be controlled efficiently in altermagnets. Meanwhile, the effective control of Néel vector is likely to change the band structure of altermagnets, which will also enrich the new physics of altermagnetic materials⁴¹. Taking into account the difficulty of using extremely large magnetic field (usually dozens of Tesla) to overcome the anisotropic field of RuO₂, it is more applicable to adopt electrical approach as an alternative solution, which is also suitable for device integration^42,43.

In this work, we achieve the effective manipulation of Néel vector to tune SST in altermagnetic RuO₂ via electrical approach. More importantly, both (i) controllable Néel vector under electrical currents and (ii) Néel vector-dependent generation of spin current and SST are two crucial prerequisites to accomplish this task. As presented in Fig. 1a, a y-direction preset current (J_preset) flowing inside heavy metal (HM) layer generates SOT and switches the Néel vector (N) in RuO₂ layer to be along y-axis as well. The charge current (J_C) in RuO₂ layer produces SST with spin polarization parallel to N, which is along y-axis (σ_y). By comparison, if using another J_preset along x-axis at first, we can align N along x-axis and then obtain adjustable SST with x-direction spin polarization (σ_x) by applying J_C, as displayed in Fig. 1b.

a The y-direction J_preset flowing in subjacent HM layer generates SOT, leading to the alignment of N to be parallel with y-axis in RuO₂ layer, and the charge current in RuO₂ layer produces SST with σ_y. b The x-direction J_preset switches N to be along the x-direction, giving rise to tunable SST with σ_x.

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Growth and fundamental characterizations of film samples

According to the physical picture of ASSE (Supplementary Information Note S1), RuO₂(100) can generate SST by applying charge current while RuO₂(110) cannot, though the Néel vector lies in plane for both cases. To investigate SST manipulation in altermagnetic RuO₂, we need to achieve controllable Néel vector in RuO₂ films with in-plane easy axis. Hence we deposited Pt/RuO₂ film samples on Al₂O₃(0001) and MgO(100) substrates, respectively. The X-ray diffraction (XRD) patterns indicate that RuO₂ has strong (100) and (110) texture in Al₂O₃/Pt/RuO₂ and MgO/Pt/RuO₂ samples respectively, and they exhibit fine crystallization (Supplementary Information Note S2, Fig. S2). The straight lines of magnetic field-dependent magnetization (M-H) curves measured by superconducting quantum interference device (SQUID) at 300 K (Supplementary Information Note S2, Fig. S3) can be accounted for by the diamagnetism of substrates, and there is negligible net magnetization in Pt/RuO₂(100) or Pt/RuO₂(110). Besides, the temperature-dependent magnetization (M-T) curves measured by SQUID reveal the Néel temperature of RuO₂ films on Al₂O₃ and MgO substrates to be 400 ~ 450 K (Supplementary Information Note S2, Fig. S4). The Al₂O₃/Pt/RuO₂ and MgO/Pt/RuO₂ film samples with desirable crystal quality and magnetization can be used for further depositing comparable Py layers, which are also the basis for conducting following experiments on various device samples (Supplementary Information Note S3).

Current-induced Néel vector switching of RuO₂

First we investigate current-induced switching of Néel vector in altermagnetic RuO₂ by electrical transport measurement at room temperature. We fabricated eight-terminal devices of Pt(5 nm)/RuO₂(15 nm) on Al₂O₃ and MgO substrates. As shown in the inset of Fig. 2a, each device has a pair of vertical (I_write1) and horizontal (I_write2) channels with the width of 20 μm. After applying each writing current pulse with different magnitude along one certain channel, the change of transverse Hall resistance (ΔR_Hall) is plotted in Fig. 2a for RuO₂(100) (red square) and RuO₂(110) (blue diamond). When we increase the magnitude of applied current pulses, no remarkable ΔR_Hall signals can be observed until it reaches threshold value, corresponding with the current densities of 5.3 × 10¹¹A m^–2 and 4.8 × 10¹¹A m^–2 in Pt layer (J_Pt), for Pt/RuO₂(100) and Pt/RuO₂(110) samples respectively^28,44. Considering the characteristics of the power source used in our experiments, we further calibrate the actual threshold values to be 2.4 × 10¹¹A m^–2 and 1.9 × 10¹¹A m^–2 for Pt/RuO₂(100) and Pt/RuO₂(110) samples respectively (Supplementary Information Note S4). These critical values can be taken as reference to conduct the following experiments. The slight discrepancy of critical switching current densities is mainly caused by the different anisotropy when the films were deposited on different substrates.

a ΔR_Hall as a function of current density in the Pt layer, with each data point being collected after applying one pulse current. The inset shows the schematic of eight-terminal device for electric transport measurement, where the read current and voltage paths are mutually perpendicular and are aligned 45° to the two writing channels. b Pulse number dependence of ΔR_Hall of Pt/RuO₂(100) (red square) and Pt/RuO₂(110) (blue diamond) devices under critical switching current densities. Ru M-edge XMLD results of Pt/RuO₂ devices for c RuO₂(100) and d RuO₂(110). From top to bottom: before applying writing currents (Original), after applying a group of five writing currents along vertical (I_write1) channel and along horizontal (I_write2) channel.

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Then we use critical switching currents to test each Pt/RuO₂ device for three cycles: a group of five successive pulse currents with the same amplitude are applied alternatively along the two orthogonal channels. Figure 2b displays ΔR_Hall of RuO₂(100) (red square) and RuO₂(110) (blue diamond) as a function of pulse numbers. For the two Pt/RuO₂ devices, the obvious ΔR_Hall is observed after applying the first pulse current, and it increases gradually regarding the second to the fifth pulses. By comparison, no apparent ΔR_Hall signals can be detected in Pt or RuO₂ devices when 1 ms-wide current pulses are applied (Supplementary Information Note S5). Significantly, previous literature has reported that thermal artifacts could be observed in electrical Hall resistance measurements under specific circumstances⁴⁵. Hence to study the Joule heating caused by applied current pulses⁴⁶, we meticulously conducted both experiment measurement and finite element simulation, and the results distinctly demonstrate that the temperature of device samples remains under the Néel temperature from start to finish (Supplementary Information Note S6). Therefore, the recorded ΔR_Hall of Pt/RuO₂ devices can be attributed to current-induced Néel vector switching. The Hall resistance measurements preliminarily prove the in-plane Néel vector switching with 90° in altermagnetic RuO₂, and partial switching of domains is likely to exist here^47,48,49,50.

To further verify the in-plane Néel vector switching in altermagnetic RuO₂ films, we performed the measurement of Ru M-edge X-ray magnetic linear dichroism (XMLD) at room temperature. By this synchrotron radiation test technique which is sensitive to in-plane Néel vector, we can reveal the distribution of Néel vector in RuO₂(100) and RuO₂(110) and its dependence on writing currents^51,52,53. Considering the compatibility with the size of detecting spot (80 × 80 μm²) for XMLD measurement, we fabricated the eight-terminal devices with 100 μm-wide writing channels for Pt(5 nm)/RuO₂(15 nm) in which the crystalline orientations of RuO₂ are (100) and (110). The detecting light is focused on the intersection area of the device, and the signals of linearly polarized X-ray absorption spectroscopy (XAS) are collected (Supplementary Information Note S7, Fig. S12 and Fig. S13). The peak position of XAS curves near 462 eV corresponds to the M₃ 3p_3/2 binding energy of Ru element. The XMLD results presented in Fig. 2c and Fig. 2d are obtained by the difference of linearly vertical (V) and horizontal (H) polarized XAS signals.

Before applying writing currents, we collected XMLD signals of the initial state of both devices. Due to non-epitaxial growth mode, twin crystal structure with different in-plane alignment of Néel vector exists in RuO₂ films²⁶. Hence the in-plane Néel vectors without uniaxial orientation cancel out each other, leading to no peaks or valleys in XMLD results for the initial state of both switching devices, which is presented by the (black circle) curves at the top of Fig. 2c and Fig. 2d. For each eight-terminal device, writing currents are applied by following two schemes: a group of successive five pulse currents flow through either the vertical channel (I_write1) or the horizontal channel (I_write2). The nominal values of J_Pt are 5.4 × 10¹¹A m^–2 and 4.9 × 10¹¹A m^–2 for Pt/RuO₂(100) and Pt/RuO₂(110) devices, respectively. To ensure the repeatability of testing results, we have measured sufficient switching devices after applying writing currents. Noticeably, spikes appear in the XMLD signals after applying writing currents, as evidenced by the representative peaks and valleys in middle (red square) and bottom (blue diamond) curves in Fig. 2c,  d. After I_write1 flows through the vertical channel of Pt/RuO₂(100) and Pt/RuO₂(110) devices, the XMLD curves undergo zero-negative-positive-zero trace as photon energy increases, as displayed by two (red square) curves in the middle of Fig. 2c and Fig. 2d. Meanwhile, after we applied I_write2 to these devices, the distinct XMLD signals can be seen in the two (blue diamond) curves at the bottom of Fig. 2c,  d.

It is reasonable to deduce that after we used writing currents which reached the threshold, the Néel vector is capable of being switched towards the direction of charge current in Pt/RuO₂ devices. In contrast to their counterparts in the middle, the two curves at the bottom of Fig. 2c,  d reveal that the XMLD signals exhibit a zero-positive-negative-zero tendency with increasing photon energy, which indicates the reversed polarity of XMLD signals after we rotated the direction of writing currents with in-plane 90°. Of note that there is a delay time from the application of current pulses to the measurement of XAS (or XMLD) signals. We have prolonged the delay time to make another test and observed the same phenomenon in XMLD patterns, which proves the stability of XMLD measurement results (Supplementary Information Note S7, Fig. S14). Therefore, the onefold orientation of Néel vector after applying writing currents is determined by the direction of applied charge currents, which results from SOT-induced Néel vector switching. The above XMLD measurements of Ru M-edge support the current-induced switching of Néel vector with in-plane 90° in altermagnetic RuO₂, which is an important basis for manipulating SST because of the close relation between SST and the state of Néel vector. The XMLD data are compatible with the presence of antiferromagnetic order³⁹, besides the previous evidence by transport measurements such as the anomalous Hall effect and SST^26,27,28,42.

Manipulation of spin splitting torque in RuO₂

To study the electrical control of spin splitting torque related to spin current generation in altermagnetic RuO₂, we fabricated Pt/RuO₂(100)/Py and Pt/RuO₂(110)/Py devices for spin torque ferromagnetic resonance (ST-FMR) measurements, where the thickness of each layer is indicated by Pt(5 nm)/RuO₂(10 nm)/Py(15 nm). It is worth noting that this well-established ST-FMR technique is particularly appropriate for detecting and analyzing spin currents with various spin polarizations (σ_x, σ_y and σ_z)^24,27,54,55.

Figure 3a illustrates the setup of ST-FMR measurement to characterize the SST in Pt(5 nm)/RuO₂(10 nm)/Py(15 nm) devices at room temperature. A radio-frequency (RF) charge current flowing through the RuO₂ layer is converted into transverse spin current, and then it is injected into the adjacent Py layer. According to the physical picture of ASSE (Supplementary Information Note S1), the spin-current generation is contributed by ASSE together with spin Hall effect (SHE) in Pt/RuO₂(100)/Py, while it is solely due to SHE in Pt/RuO₂(110)/Py. Under the applied magnetic field, the oscillating spin current exerts spin torques on ferromagnetic Py layer leading to magnetization precession. The external magnetic field is swept with φ_H (angle between charge current and applied magnetic field), which can be regarded the same as φ_M (angle between charge current and magnetization in Py) because of the relatively small in-plane anisotropy of Py.

a The measurement setup of ST-FMR. b A typical ST-FMR spectrum consisted of antisymmetric (V_A, red curve) and symmetric (V_S, blue curve) signals under φ_H = 45° after applying writing currents of 60 mA. The analysis of spin torques with various polarization directions by fitting the angle-dependent V_S results after applying writing currents of (c) 60 mA and (d) 150 mA. All data in panels (b, c, d) are obtained by measuring Pt/RuO₂(100)/Py device under 6 GHz and 19 dBm. The |V_σx/V_σy| data points of (e) Pt/RuO₂(100)/Py and f Pt/RuO₂(110)/Py devices are displayed in terms of different applied writing currents. The |V_σx/V_σy| indicates the ratio of dampinglike torques with x-direction polarization (σ_x) to those with y-direction polarization (σ_y). The data points with error bars in panels (e and f) are fitted by B-spline curves, and the insets refer to the state of SST before and after Néel vector switching in Pt/RuO₂(100)/Py and Pt/RuO₂(110)/Py devices.

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Figure 3b displays a typical ST-FMR spectrum of Pt/RuO₂(100)/Py device after applying a group of writing currents (I_write) of 60 mA, and it is measured with φ_H = 45° under the excitation of 6 GHz and 19 dBm microwave current. As shown in Fig. 3b (with more data of the same type shown in Supplementary Information Note S8, Fig. S15), the (black) dots are measured DC voltage data, and corresponding fitted V_mix curve (green one) can be decomposed into both symmetric (V_S, blue one) and antisymmetric (V_A, red one) Lorentz line shapes. From the voltage signals, we can see that the amplitude of V_A (red line) is comparatively much larger than that of V_S (blue line), for the Oersted field plays a remarkable role in the former resulting from the shunting effect.

Each time after applying a group of five successive writing currents with the same magnitude to Pt/RuO₂/Py devices, we conducted an angle-dependent ST-FMR measurement to characterize the SST in altermagnetic RuO₂. The magnetic field was applied in the plane of tested samples, and the angle between the Pt/RuO₂/Py devices and magnetic field was defined as φ_H. We swept φ_H with a step size of 15° under 6 GHz and 19 dBm microwave currents. Of note is that RuO₂(100) and RuO₂(110) studied in the present case can only generate in-plane spin polarizations (σ_x and σ_y). Besides, V_S and V_A are related with in-plane and out-of-plane current-induced spin torques respectively (Supplementary Information Note S8, Table S2). Therefore, we are able to analyze spin torques with in-plane polarization directions in Pt/RuO₂(100)/Py device by trigonometric function fitting, according to the acquired V_S data. The fitting results after applying I_write = 60 mA and I_write = 150 mA (nominally) are presented in Fig. 3c,  d, which are below and above the critical switching current density, respectively. As depicted by (purple and orange) curves in Fig. 3c,  d, prominent \({S}_{{{{\rm{DL}}}}}^{X}\) can be observed in the latter, while \({S}_{{{{\rm{DL}}}}}^{Y}\) remains almost the same under the two circumstances.

Notably, both SST (by ASSE) and SOT (by SHE) give rise to σ_y, but σ_x can only be attributed to SST. Therefore, we extract the ratios of \({S}_{{{{\rm{DL}}}}}^{X}\) to \({S}_{{{{\rm{DL}}}}}^{Y}\) from the angle-dependent measurements as |V_σx/V_σy| in terms of the writing currents. Correspondingly, the data points of |V_σx/V_σy| connected by B-spline lines are presented in Fig. 3e,  f for Pt/RuO₂(100)/Py and Pt/RuO₂(110)/Py, respectively. Taking into account the multiple steps of data fitting with possible propagation of fitting errors, error bars are also displayed accompanying the final data points in Fig. 3e,  f. As the magnitude of writing currents rises, the |V_σx/V_σy| for Pt/RuO₂(100)/Py fluctuates within a reasonable range, and then it increases abruptly at I_write = 130 mA, as displayed in Fig. 3e. Under this situation, the corresponding nominal writing current density is about 5.1 × 10¹¹A m^–2, which reaches the nominal threshold writing current density to trigger Néel vector switching. This result is further verified by repeated experiment (Supplementary Information Note S8, Fig. S16), whose critical value of current densities is also in accordance with the previous results measured by SOT switching experiments. Hence this current-induced Néel vector switching in RuO₂ layer leads to the alignment of Néel vector to be along x-axis (being parallel to the direction of writing currents). Considering the potential partial switching of Néel vector, further improvement of switching ratio of domains will probably enhance the value of |V_σx/V_σy| to a larger extent. By contrast, Fig. 3f shows that there is no apparent enhancement for the σ_x component in Pt/RuO₂(110)/Py as the writing currents increase, and typical angular-dependent ST-FMR results of Pt/RuO₂(110)/Py (Supplementary Information Note S8, Fig. S17) are also different from those of Pt/RuO₂(100)/Py shown in Fig. 3c,  d.

In view of the situation where the Néel vector lies in plane, RuO₂(100) films have higher spin torque efficiency than RuO₂(110) films do because of the existence of SST in the former, and the resultant spin torque conductivity surpasses that of many heavy metals and topological insulators, which are potential candidates for efficient spin sources^10,14,26,56. However, the spin polarization directions of SST are unable to be changed in previous studies. To address this issue, a feasible solution is to manipulate the Néel vector in altermagnets by electrical currents. Once the writing currents meet the threshold, the SST can be tuned by applying charge currents in altermagnetic RuO₂(100) layer along x-axis: its spin polarization direction is parallel to the switched Néel vector, which is shifted from σ_y to σ_x (Fig. 3e). After the Néel vector is switched in RuO₂(100), the proportion of σ_x enhances but σ_y still dominates, which can be ascribed to conventional spin Hall effect. By comparison, no SST can be generated in (110)-oriented RuO₂ by applied charge currents, according to the physical picture of ASSE mechanism (Fig. 3f). Hence the generated transverse spin current comes entirely from the conventional SHE depending on spin-orbit coupling, and the spin torques regarding different in-plane coordinate axes cannot be tuned, which is irrelevant to the Néel vector switching in RuO₂(110).

It has been studied that magnetic moment-dependent spin torques can be produced by magnetic SHE (e.g., in Mn₃Sn) or antiferromagnetic SHE (e.g., in Mn₂Au), abbreviated as MSHE or AFM-SHE respectively^25,57. Therefore, altermagnetic materials including RuO₂ with ASSE offers a new way to generate the spin torques besides the above two counterparts. Meanwhile, the electric field control of Néel vector in collinear antiferromagnet Mn₂Au with AFM-SHE is also able to tune the Néel spin-orbit torque (NSOT), which is different from the case in non-collinear Mn₃Sn^57,58. Sharing the similarity of Néel vector-dependent generation of spin torques, the tunable spin polarization of SST is parallel with the Néel vector in altermagnetic RuO₂ while that of NSOT is perpendicular to the Néel vector in Mn₂Au. Furthermore, compared to Mn₂Au relying on multi-step Rashba-like mechanism, our RuO₂ depends on nonrelativistic altermagnetic spin splitting to generate spin current and spin splitting torque with tunable polarization and higher efficiency.

In summary, we successfully achieve the electrical manipulation of altermagnetic RuO₂ to tune the spin splitting torque, which is accomplished based on (i) controllable Néel vector of RuO₂ and (ii) Néel vector-dependent generation of spin current and SST due to ASSE. By applying electrical writing currents, the Néel vector in altermagnetic RuO₂ with in-plane easy axis is switched by 90°. This current-induced switching is evidenced by electrical transport measurements of transverse Hall resistance and it is also manifested unambiguously by XMLD results in terms of the writing currents (and their directions). Moreover, the spin polarizations of SST along different coordinate axes are analyzed by the angular dependence of ST-FMR voltage signals, and it proves distinctly that the SST can be tuned based on the control of Néel vector in altermagnetic RuO₂. The effective manipulation of spin splitting torque in RuO₂ via a feasible electrical approach not only provides important additional piece of information for understanding the altermagnetism of RuO₂, but it is also beneficial to expanding the potential applications of altermagnetic spin sources with controllable SST as the efficient writing technology in the field of information storage involving MRAM.

Sample preparation

By DC magnetron sputtering method, two groups of Pt(5 nm)/RuO₂(15 nm) film samples were prepared on single-crystal Al₂O₃(0001) and MgO(100) substrates, and single Pt(5 nm) and RuO₂(15 nm) films were also deposited directly on the two substrates. The Pt layers were deposited by sputtering Pt target with Ar flow of 20 at 773 K under a base pressure below 5 × 10^–5Pa, and then they were annealed at 973 K for 1 hour. The RuO₂ layers were in-situ deposited by sputtering Ru target with Ar:O₂ flow of 20:5 at 773 K. The deposition rates of Pt and RuO₂ films were 0.69 nm/min and 3.3 nm/min, respectively. For ST-FMR measurement, we deposited Pt(5 nm)/RuO₂(10 nm)/Py(15 nm) film samples on Al₂O₃(0001) and MgO(100) substrates. After depositing Pt and RuO₂ layers with the parameters introduced above, we in-situ sputtered Py target with Ar flow of 20 at room temperature with the deposition rate of 1.33 nm/min. Also, the Pt(5 nm)/RuO₂(10 nm)/Py(15 nm) film samples were in-situ covered by 1 nm-thick Ru to prevent them from oxidation.

Sample characterization

Crystal quality and phase composition were analyzed by X-ray diffraction (XRD) characterization utilizing a Rigaku Smartlab instrument with Cu-Kα radiation (wavelength = 0.154 nm). The working voltage and working current were 40 kV and 150 mA, respectively. The scanning rate was 10°/min for each XRD pattern. Magnetic field dependence of magnetization (M-H) curves were measured via a superconducting quantum interference device (SQUID) from Quantum Design at room temperature. Temperature dependence of magnetization (M-T) curves were measured via the same SQUID instrument from 300 to 600 K. Photographs of three kinds of devices were taken by a Nikon ECLIPSE LV150NL optical microscope.

Fabrication of devices

By standard photolithography and Ar-ion milling techniques, the deposited Pt(5 nm), RuO₂(15 nm) and Pt(5 nm)/RuO₂(15 nm) films on single-crystal Al₂O₃(0001) and MgO(100) substrates were patterned into eight-terminal devices. The width of two orthogonal writing channels was 20 μm (for electrical transport measurement) or 100 μm (for XAS and XMLD measurement), and the two diagonal detecting paths were 5 μm wide. By standard photolithography and Ar-ion milling techniques, the deposited Pt(5 nm)/RuO₂(10 nm)/Py(15 nm)/Ru(1 nm) films on Al₂O₃(0001) and MgO(100) substrates were patterned into stripes whose length and width were 50 μm and 20 μm, respectively. Then the Cr(10 nm)/Cu(80 nm) electrode was deposited on the stripes via electron-beam evaporation method.

Electrical transport measurement

The two diagonal detecting paths of Pt(5 nm), RuO₂(15 nm) and Pt(5 nm)/RuO₂(15 nm) devices were connected to a Keitheley 2400 current source offering a reading current of 1 mA and a Keitheley 2182 nanovoltmeter recording transverse Hall voltage signals. A Keysight 2901 power source was adopted to output current pulses, which was also able to monitor the real-time resistance change of tested devices. A group of five successive pulse currents with the same amplitude were applied along the horizontal channel (red arrow I_write1 in the inset of Fig. 2a), and then another group of writing currents were applied along the vertical channel (blue arrow I_write2 in the inset of Fig. 2a), which constituted a testing cycle. After applying each current pulse, the calculated gap value of Hall resistance with respect to the initial value before applying this group of current pulses is defined as the ΔR_Hall.

XAS and XMLD measurements

XAS and XMLD measurements in total-electron-yield mode were carried out at the beam line BL08U1A in the Shanghai Synchrotron Radiation Facility at 300 K. We used this technique to probe into the in-plane distribution of Néel vector in altermagnetic RuO₂. The XMLD curves were the differences of linearly vertical (V) and horizontal (H) polarized XAS signals. The detecting light was perpendicular to the sample plane, and the spot with the size of 80×80 μm² was focused on the intersection of eight-terminal devices.

ST-FMR measurement

We adopted ST-FMR technique to characterize generated spin current and spin splitting torque with different polarizations in altermagnetic RuO₂. The sample holder was connected to a Ceyear 1465 F microwave source (0.1 ~ 40 GHz) via a bias-T which a Keitheley 2182 nanovoltmeter was also linked to. External magnetic field was swept along φ_H (0° ≤ φ_H ≤ 360°) with step size of 15°, and microwave current with 19 dBm and 6 GHz was flowing through the stripe. Meanwhile, the direct current (DC) voltage signals resulting from the anisotropic magnetoresistance (AMR) rectification of Py were recorded by the nanovoltmeter, which were consisted of symmetric and antisymmetric Lorentz line shapes, with the expression V = V_SL_S + V_AL_A. As for L_A = ΔH(H-H_res)/[(H-H_res)² + ΔH²] and L_S = (ΔH)²/[(H-H_res)² + ΔH²], ΔH, H_res and H represent line width, resonance field and external magnetic field, respectively. For the spin torques due to in-plane spin polarizations, the angular dependence of V_S and V_S could be described by the following equations^23,26:

where \({S}_{{{{\rm{DL}}}}}^{X}\) and \({S}_{{{{\rm{DL}}}}}^{Y}\) were the coefficients of dampinglike (DL) torques, and \({A}_{{{{\rm{FL}}}}}^{X}\) and \({A}_{{{{\rm{FL}}}}}^{Y}\) were those of fieldlike (FL) torques, with \({A}_{{{{\rm{FL}}}}}^{Y}\) also including the contribution by Oersted field torque.

Finite element simulations

We utilized finite element simulations for analyzing the temperature rise due to applied current pulses in Pt/RuO₂ devices. The simulated structures were Sub./Pt(5 nm)/RuO₂(15 nm) where Sub. referred to single-crystal Al₂O₃(0001) and MgO(100) substrates. Meanwhile, both writing channels of the simulated devices were 20 μm wide, which was in line with the device structure in electrical transport measurement. For the two Pt/RuO₂ devices, we applied a group of five 1 ms-wide current pulses with critical value, and the interval between two successive pulses was 10 s. The thermal parameters of RuO₂, including thermal conductivities (0.50 W cm^–1 K^–1) and specific heat capacities (56.42 J mol^-1 K^-1), were obtained from literature^59,60, and those of Pt, Al₂O₃ and MgO were acquired directly from the build-in database of simulation software. The simulated results (Supplementary Information Fig. S11) could be classified as two categories: (i) time-dependent temperature variation, and (ii) space-dependent temperature distribution. For category (i), the monitoring space point was located at the center of the Pt/RuO₂ switching devices (distance = 0 μm). For category (ii), the monitoring time point was in the middle of one current pulse (t = 0.5 ms).