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## Creator

[Yutaro Takeuchi](https://orcid.org/0000-0002-5031-1347), [Yuma Sato](https://orcid.org/0000-0001-8205-6769), [Yuta Yamane](https://orcid.org/0000-0002-3306-2967), [Ju-Young Yoon](https://orcid.org/0000-0001-7447-3466), Yukinori Kanno, [Tomohiro Uchimura](https://orcid.org/0000-0001-8992-7782), [K. Vihanga De Zoysa](https://orcid.org/0000-0003-4212-4610), [Jiahao Han](https://orcid.org/0000-0002-3275-7687), [Shun Kanai](https://orcid.org/0000-0003-4689-1374), [Jun’ichi Ieda](https://orcid.org/0000-0001-6069-8533), [Hideo Ohno](https://orcid.org/0000-0001-9688-8259), [Shunsuke Fukami](https://orcid.org/0000-0001-5750-2990)

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[Electrical coherent driving of chiral antiferromagnet](https://mdr.nims.go.jp/datasets/9a9cc7b2-c218-4f57-83d4-7db2f876c9a0)

## Fulltext

1  Electrical coherent driving of chiral antiferromagnet Yutaro Takeuchi1,2,3*, Yuma Sato4,5, Yuta Yamane4,6*, Ju-Young Yoon4,5, Yukinori Kanno4,5, Tomohiro Uchimura4,5, K. Vihanga De Zoysa4,5, Jiahao Han1,4, Shun Kanai1,4,5,7,8,9, Jun’ichi Ieda10, Hideo Ohno1,4,7,11, and Shunsuke Fukami1,4,5,7,11,12* Affiliations:  5 1Advanced Institute for Materials Research, Tohoku University; Sendai, 980-8577, Japan. 2International Center for Young Scientists, National Institute for Materials Science; Tsukuba, 305-0047, Japan. 3Research Center for Magnetic and Spintronics Materials, National Institute for Materials Science; Tsukuba, 305-0047, Japan. 10 4Laboratory for Nanoelectronics and Spintronics, Research Institute for Electrical Communication, Tohoku University; Sendai, 980-8577, Japan. 5Graduate School of Engineering, Tohoku University; Sendai, 980-0845, Japan. 6Frontier Research Institute for Interdisciplinary Sciences, Tohoku University; Sendai, 980-8578, Japan 15 7Center for Science and Innovation in Spintronics, Tohoku University; Sendai, 980-8577, Japan 8Division for the Establishment of Frontier Sciences of Organization for Advanced Studies at Tohoku University; Sendai, 980-8577, Japan 9National Institutes for Quantum Science and Technology; Takasaki, 370-1292, Japan 20 10Advanced Science Research Center, Japan Atomic Energy Agency; Tokai, Ibaraki, 319-1195, Japan 11Center for Innovative Integrated Electronic Systems, Tohoku University; Sendai, 980-0845, Japan 12Inamori Research Institute for Science; Kyoto, 600-8411, Japan 25 * Corresponding author. Email: takeuchi.yutaro@nims.go.jp, yutaymn@tohoku.ac.jp, s-fukami@tohoku.ac.jp  Abstract: Electric current driving of antiferromagnetic states at radio or higher frequencies remains challenging to achieve.  Here we report all-electrical, gigahertz-range, coherent driving of 30 chiral antiferromagnet Mn3Sn nanodot samples. High coherence in multiple trials and threshold current insensitive to pulse width, in contrast to ferromagnets, are achieved in sub-nanosecond range, allowing 1,000/1,000 switching by 0.1-ns pulses at zero field. These features are attributed to the inertial nature of antiferromagnetic excitations. Our study highlights the potential of antiferromagnetic spintronics to combine high speed and high efficiency in magnetic device 35 operations.  2   Electrical manipulation of collective spin states is a central subject of magnetics and spintronics, and various physical schemes have been demonstrated mostly with ferromagnetic systems (1–3). The spin-orbit torque (SOT) (4–6), a relativistic phenomenon originating from the spin Hall effect (7) and/or Rashba-Edelstein effect (8) in magnetic heterostructures, has been 5 recently applied to antiferromagnets (9–11). One of the prospective advantages of antiferromagnets over ferromagnets is their potential for faster driving with higher efficiency owing to the exchange-enhanced intrinsic frequency (12) and the inertia in their dynamics (13). Ultrafast switching of ferromagnets has been recently reported; however, it required relatively large current densities and the assistance of external fields and thermal effects (14, 15). For 10 antiferromagnets, an electrical control was achieved by the staggered SOT (16), which emerges in locally noncentrosymmetric crystals (16–20). Later, the standard SOT in antiferromagnet/nonmagnet heterostructures was demonstrated to be capable of switching (21–27) and continuously rotating (28, 29) antiferromagnetic spin states. In pursuit of revealing the high-speed dynamics of antiferromagnets, earlier works reported switching of antiferromagnets by 15 picosecond laser pulses (30, 31) and an efficient excitation and ultrafast propagation of antiferromagnetic magnons (32–34). However, all-electrical switching of an antiferromagnet, required for electronic devices, has been limited in timescales longer than nanoseconds, where the results can be understood by an extrapolation from the DC-regime experiments. Despite the promising prospect for all-electrical switching of antiferromagnets with a combination of high speed and high 20 efficiency that cannot be reached with ferromagnets, its experimental exploration remains challenging. Here we show all-electrical driving of a chiral antiferromagnetic Mn3Sn nanodot by single electric pulses in GHz range, through coherent spin excitations in a single antiferromagnetic  3  domain. In contrast to ferromagnets, where fast electrical control at the timescale of 0.1 ns and beyond is challenging because of significant increase in the threshold current (35–39), we show that it is not the case for antiferromagnets. The markedly suppressed increase in the driving current in sub-nanosecond range, combined with a high coherence of the employed system, allows us to achieve 1,000/1,000 switching by 0.1-ns pulses at zero magnetic field. The observed advantage of 5 antiferromagnets over ferromagnets can be attributed to the universal inertial nature of antiferromagnetic dynamics, as indicated by our theoretical modeling. Sample structure and measurement layout for control of coherent rotation in chiral antiferromagnet Mn3Sn nanodot To realize a coherent control of the antiferromagnetic order, we fabricate Mn3Sn / heavy metal 10 heterostructure-based nanodot samples. The stack structure consists of W(2 nm) / Ta(3 nm) / Mn3Sn(20 nm) / MgO(1.3 nm) / Ru(1 nm), which is deposited on MgO(110) substrate by sputtering [Materials and Methods (40)]. We confirm (1100)-plane (M-plane) oriented, epitaxial Mn3Sn films where the kagome plane is perpendicular to the film plane (Fig. S1) (28, 41). The films are processed into Hall-bar devices, where a Mn3Sn nanodot is formed on a cross-shaped 15 W/Ta channel (Fig. 1A) (40). The nominal dot diameter D, channel width, and channel length are 200 nm, 250 nm, and 600 nm, respectively. An image of a fabricated nanodot sample taken by scanning electron microscopy is displayed in Fig. 1B. After defining the Hall-cross with a nanodot, coplanar waveguides are formed for high-frequency measurements. Our experimental setup for electrical driving of Mn3Sn is shown in Fig. 1C. We apply a pulse 20 voltage with the width of 0.1-10 ns using a pulse generator through an RF port of the bias tee. The state of the chiral spin structure in Mn3Sn is detected through the anomalous Hall effect (42) by measuring the voltage between the two Hall probes under a DC current of 100 μA, corresponding to the current density in W/Ta layer of 3.8 MA cm-2, applied to the DC port of the bias tee. The  4  output side of the waveguide is terminated by an oscilloscope with an impedance of 50 Ω, which is used to monitor the transmitted waveforms of the injected pulses. Shown in Fig. 1D is the captured transmitted waveform of the applied pulse with nominal width of 0.1 ns (details on the captured waveforms with various nominal pulse widths are summarized in Fig. S2). Notice that the pulse voltage is applied in the [1120] direction of the hexagonal Mn3Sn film, which is the 5 most effective configuration for the Slonczewski-like SOT to induce the chiral-spin rotation (28, 29). Figure 2A shows the Hall resistance RH vs. the out-of-plane magnetic field Hz in a Mn3Sn nanodot with D = 200 nm, where D is the nanodot diameter. Negative anomalous Hall resistance and binary state in the hysteresis loop are observed, consistent with our previous study on the 10 thermal stability of Mn3Sn nanodots (43), where the uniaxial perpendicular anisotropy and the exchange stiffness for the antiferromagnetic order have been determined as 370 Jm-3 and 3.5 pJm-1, respectively, leading to the domain wall width of ~ 300 nm. The switching field in the present study is evaluated to be about 350 mT (Fig. 2A). Hall resistance vs. applied current in Mn3Sn nanodot 15 Before performing all-electrical experiments in GHz range, we establish the field-free continuous rotation and field-assisted bipolar switching of the Mn3Sn nanodots in DC regime. Figure 2B shows RH vs. JHM in a Mn3Sn nanodot with D = 200 nm, where JHM denotes the current density flowing into the W/Ta heavy metal layers [Sections S3 and S4 of (40)]. The field Hx is also applied to the [1120] direction of Mn3Sn, i.e., parallel to the current. For μ0Hx = 0 mT, the 20 binary randomization of RH is observed above the threshold current density, regardless of the pulse current direction. This is attributed to the SOT-driven continuous rotation of the chiral antiferromagnetic order in Mn3Sn (28, 44). The randomization between the binary states shows that the predominant magnetic anisotropy is twofold with the easy axis normal  5  to the film (24, 29) and that the Mn3Sn nanodot has a single-domain structure (43). With finite Hx, a bipolar switching of RH is obtained, where the polarity of the hysteresis curve depends on the sign of Hx. This characteristic of the field-assisted switching is consistent with that reported in the previous studies on Hall bar devices (23–26, 29, 44) and can be explained as a result of the SOT-driven rotation being balanced by the external field that 5 prefers the uncompensated net magnetization of Mn3Sn pointing parallel to Hx. We then move onto experiments with short current pulses in the range of ns ~ sub-ns. We first check the field-assisted switching by the short current pulses. Shown in Fig. 2C are RH-JHM curves with the pulse width τ = 0.1 ns and μ0Hx = 300 mT;  the RH-JHM curves at μ0Hx = 300 mT with various τ are displayed in Fig. 2D. JHM is calculated from the peak amplitude of the transmitted 10 waveform. Bipolar switching is observed for all the τ down to 0.1 ns at JHM < 75 MAcm-2. In the following sections, the relationship between the pulse width and the threshold current density is extensively investigated. Switching probability vs. pulse width and amplitude For deeper investigation into the dynamics of the chiral-spin structure in Mn3Sn nanodots in the 15 GHz regime, we measure the switching probability P as a function of JHM, τ, and Hx by multiple applications of current pulses [see Section S5 of (40) and Fig. S5 for more details]. Here, P is defined as the ratio of the number of successful switching out of at least 50 attempts of pulse application for a given set of JHM, τ, and Hx. The antiferromagnetic ordering is initialized by applying 0.1-s pulse current with an amplitude of 42 MAcm-2 under μ0Hx = 300 mT. 20 Figures 3, A-D, show the P vs. JHM for τ = 0.1, 0.2, 0.3, and 1.0 ns, respectively, under μ0Hx = 0 and 300 mT. A general tendency for the case with μ0Hx = 300 mT is that P initially increases with JHM, reaches 1 and starts decreasing as JHM further increases. The range of JHM achieving P = 1 expands with a reduction of τ. This observation indicates that the antiferromagnetic order  6  acquires a lower probability to switch back to the original state with the shorter pulse widths. Under a longer and larger pulse, the chiral antiferromagnetic order experiences a larger driving force to rotate for a longer time, resulting in less predictability for the final state. For μ0Hx = 0 mT, non-deterministic behavior (P ~ 0.5) above a threshold is observed at τ = 1.0 ns as expected from Fig. 2B;  interestingly, there is a P = 1 range at τ = 0.1 and 0.2 ns, achieving all-electrical switching, 5 which at this timescale has been seen only in current-induced heat driven reversal of GdFeCo (45).  The dependencies of P on τ, JHM, and Hx are summarized by two-dimensional color maps in Fig. 3, E-H. In the regions where JHM is sufficiently large (the upper regions of the color maps), P oscillates with τ between relatively high values (switched regions) and relatively low values (switched-back regions). At μ0Hx = 0 mT (Fig. 3E), we confirm a periodic appearance of switched 10 and switched-back regions at least seven times as labeled by the arrows, indicating a highly coherent rotation of chiral-spin structure in the 50 trials. The oscillation of P becomes less appreciable as τ increases. The switched and switched-back regions are shifted toward the right side (longer τ) with decreasing JHM. As μ0Hx increases from 0 to 300 mT, the switched (switched-back) regions expand (shrink). This is because the in-plane magnetic field breaks the ±𝑥 symmetry, 15 assisting the “up” to “down” spin rotation (switching) and hindering the “down” to “up” rotation (switching-back). The switching and switching-back processes through the coherent chiral spin rotation are schematically illustrated in Fig. 3 I and J. It is theoretically predicted that the frequency of the SOT-driven chiral spin rotation increases with JHM (28). Exploiting this unconventional current 20 dependence of the antiferromagnetic dynamics, the switching and switching-back of the antiferromagnetic order can be all electrically controlled by current pulses with τ ~ (2N–1) τ180 and 2Nτ180, respectively, where N is a positive integer and τ180 is the time period for 180o rotation under the given JHM. In Fig. 3, E-H, the first, second, …, N-th switched (switched-back) regions therefore  7  correspond to the coherent chiral spin rotation being completed one, three, …, 2N-1 (two, four, …, 2N) times. This is consistent with our numerical calculation considering the SOT-driven chiral-spin rotation in a single-domain antiferromagnet without any thermal assistance (Fig. S6). The calculation also shows that the switching characteristic is insensitive to the rise and fall times of the pulse (Fig. S7), indicating a minor impact of the thermally-assisted SOT (25, 26) in our 5 experiment. Notably, although the experimentally observed switching characteristic may appear to be similar to the ferromagnetic switching by a short electric-field pulse (46, 47), our scheme for the antiferromagnetic system does not require an external magnetic field. Next we demonstrate the reproducibility of the field-free switching based on the coherent driving of the chiral-spin structure. We repeat the write-and-read cycle 1,000 times at zero field, 10 where a writing current pulse of τ = 0.1 ns and JHM = 112 MA cm-2 is utilized. Figure 3K shows a portion of the data, with RH varying with the pulse number; the full results are shown in Fig. S8. It clearly manifests the full switching of the antiferromagnetic state taking place at each pulse application. We observe no error in the 1,000 attempts thanks to the high coherence of the chiral-spin dynamics. 15 Switching current density vs. pulse width We now study the switching in more detail, and start by examining the dependence of the switching current density JC on the pulse width τ. Here, JC (τ) is defined as the value of JHM at which P first reaches 0.5 at fixed τ. Figure 4A shows the measured τ dependence of JC for each Hx.  The presence of Hx diminishes JC because in the current configuration Hx assists the switching, as 20 discussed in the previous section. We find that reducing τ from 1 to 0.2 ns (0.1 ns) leads to an increase in JC by a factor of about 1.2 (1.4). This increasing rate is markedly lower than for ferromagnetic switching. For example, in a three-terminal magnetic tunnel junction comprising of Ta/W/CoFeB/MgO designed to be switched by both spin-orbit and spin-transfer torques, the  8  reduction of τ from 1 to 0.2 ns was reported to result in an increase in JC by a factor of about 2.6 (39). A similar significant increase in JC was also reported in a perpendicularly magnetized Pt/Co/AlOx nanodot (36), multilevel magnetization switching in exchange-biased Pt/Co/Ir-Mn (48), field-free SOT switching in a CoFeB/Ti/CoFeB nanodot (49), and SOT-driven domain wall motion in ferrimagnetic Co-Gd (50). In the case of ferromagnetic switching by the conventional 5 spin-transfer torque or the so-called Type-Y SOT switching (5, 6), the rate of JC increase is even higher (35, 37–39). A thorough comparison of the pulse width dependence of the switching current density reported in previous studies on ferromagnets and this work is shown in Fig. S9, showcasing a qualitative difference between the ferromagnets and chiral antiferromagnets. The physical mechanism behind the greater suppression of JC in Mn3Sn can be mainly attributed to the inertial 10 nature of the chiral spin rotation, a universal property of antiferromagnetic dynamics. This is discussed in more detail later in theoretical considerations. Rotation frequency vs. current density In this section, we evaluate the frequency frot of the chiral spin rotation in the Mn3Sn nanodots with respect to the applied current. For this purpose, we extract the P vs. τ at μ0Hx = 0 mT for 15 various JHM shown in Fig. 3E. In Fig. 4B, we show P vs. τ at JHM = 104 MA cm-2 as an example, where seven peaks are identified in the oscillation of P. We evaluate frot from the τ interval between the first and last peaks. Results of the P vs. τ evaluated in the same fashion for various JHM are summarized in Fig. S10. We note that, because of the inertial nature in antiferromagnetic dynamics that will be discussed later, frot may not be a quantitatively very accurate indicator of the actual 20 frequency of the chiral spin rotation. However, the JHM dependence of frot (Fig. 4C) displays an important physical feature:  frot increases with JHM, consistent with the theoretical prediction (28, 51). This tunability of the frequency with the current could lead to a different type of electrically tunable spintronic oscillators, in contrast to the conventional ones, where ferromagnetic resonance  9  is the basic working principle and thus the frequency of the spin dynamics is intrinsic to the system determined by material parameters such as the magnetic anisotropy (11, 46, 52, 53). Theoretical Considerations Now we theoretically show that the threshold current density with a given pulse width is almost universally lower in antiferromagnets than in ferromagnets in sub-ns regime, because of the inertial 5 nature of the former’s equation of motion. The magnetization of a ferromagnet obeys the Landau-Lifshitz-Gilbert (LLG) equation, a first-order differential equation in time. In contrast, the dynamics of the angular variable 𝜃 of the antiferromagnetic order parameter in the kagome plane is described by a second-order differential equation in time (54, 55), (𝛾𝐻 ) 𝜕 𝜃 = −𝛼𝜕 𝜃 −sin 2𝜃 − 𝛾𝐻 ; the left-hand-side is the inertial term with 𝛾 the gyromagnetic ratio and 𝐻  the 10 effective field associated with the antiferromagnetic exchange coupling. The three “forces” on the right-hand-side originate from, respectively, the damping torque on each sublattice magnetic moment with 𝛼  the Gilbert damping constant, the uniaxial anisotropy characterized by the effective field 𝐻 ,  and the SOT with 𝐻  the Slonczewski-like effective field. The antiferromagnetic dynamics are therefore mathematically described as a point mass moving in 15 potential hills arising due to the magnetic anisotropy. For successful antiferromagnetic switching, the point mass needs to be supplied with sufficient kinetic energy by the SOT to overcome the potential barrier, and the pulse width can be shorter than the time it takes for the point mass to pass through a peak of the potential (30, 31). In our present experiment, the observed antiferromagnetic advantage over ferromagnets can be attributed to the role that the 𝛼  term plays in the 20 antiferromagnet, i.e., a frictional force that resists the dynamics of 𝜃. Smaller 𝛼, therefore, can generally lead to faster and more energy-efficient driving of 𝜃, hence to smaller 𝐽 (𝜏). This is in  10  stark contrast to the ferromagnetic SOT-switching with the injected spin orthogonal to the magnetization (3,6), where 𝐽 (𝜏) depends little on 𝛼 (56). In Fig. 5, the 𝛼 dependence of 𝐽 (𝜏) obtained by numerical simulations are shown for three different τ, where we computed the dynamics of the magnetization (sublattice magnetic moments) for a ferromagnet (antiferromagnet). The details of the calculations are given in Sections S6 and 5 S11-14 of (40). For the antiferromagnet, the parameter values are chosen to reproduce our experimental results with Mn3Sn. To give a fair comparison between the two systems, for the ferromagnet we employed parameter values that give the same effective magnetic anisotropy energy and Slonczewski-like SOT as for Mn3Sn. For the unrealistically large 𝛼 = 1, 𝐽 (𝜏) takes similar values for the antiferromagnet and ferromagnet. As 𝛼  decreases, 𝐽 (𝜏)  for the 10 antiferromagnet is linearly reduced until it hits the minimum value to overcome the energy barrier (~64 MAcm-2), whereas for the ferromagnet it exhibits little dependence on 𝛼. As 𝛼 ≪ 1 for most magnetic materials of interest, 𝐽 (𝜏)  is significantly and almost universally smaller for antiferromagnets. The experimental 𝐽 (𝜏) is reproduced quantitatively by the simulation with 𝛼 =0.002 (Fig. S11).  Because the discussion here is based on the fundamental inertial nature of 15 antiferromagnetic dynamics, it holds true with any driving forces including spin-transfer torque (1, 35, 39) and electric field-induced driving (46, 47). Furthermore, it was found that 𝐽 (𝜏) monotonically increases with 𝐻  (Fig. S12). We also find that 𝐽 (𝜏) for the antiferromagnet is insensitive to 𝐻  (Fig. S13), confirming that the exchange-enhanced effect has a minor impact here. Dependencies of  𝐽 (𝜏) on some other micromagnetic parameters are also shown in Fig. S13, 20 demonstrating that our conclusions are quantitatively robust against changes in those parameters. Simulated antiferromagnetic dynamics in time domain with several different pulses are given in Fig. S14. Discussion and Outlook  11  In this work, we show a GHz-range electrical coherent driving of a chiral antiferromagnet under the spin-orbit torque using Mn3Sn nanodots. The results were consistently described by coherent dynamics of the chiral-spin structure with an electrically tunable rotation frequency. Using this scheme, we demonstrate a highly reproducible, field-free GHz switching of the chiral antiferromagnet. We also show that the driving current for the antiferromagnet is much less 5 sensitive to the pulse width in the high-speed regime, owing to the inertial spin dynamics that is universal to antiferromagnets in general. 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Ohno, S. Fukami, Electrical coherent driving of chiral 30 antiferromagnet, NIMS Materials Data Repository (MDR); https://doi.org/10.48505/nims.5415   17  Acknowledgments:  We thank Y. Nakano, T. Tanno, I. Morita, R. Ono, M. Musha, H. Kodaira, F. Shibata, S. Kasai, and S. Mitani for their technical supports and helpful discussions.   Funding:  JSPS Kakenhi Grant No. 19H05622 (SF, JI, SK) 5 JSPS Kakenhi Grant No. 21J23061 (JYY) JSPS Kakenhi Grant No. 22K14558 (YT) JSPS Kakenhi Grant No. 22KK0072 (YY, YT) JSPS Kakenhi Grant No. 22KF0035 (SF, JH) JSPS Kakenhi Grant No. 23KJ0216 (TU) 10 JSPS Kakenhi Grant No. 24KJ0432 (YS) JSPS Kakenhi Grant No. 24K16999 (JH) JSPS Kakenhi Grant No. 24H00039 (SF, YT, YY, SK, JI) JST PRESTO Grant No. JPMJPR24H6 (YT) JST PRESTO Grant No. JPMJPR21B2 (SK) 15 MEXT Initiative to Establish Next-Generation Novel Integrated Circuits Centers (X-NICS) Grant No. JPJ011438 (SF) Iketani Science and Technology Foundation No. 0331108-A (YY, YT, JYY) Iketani Science and Technology Foundation No. 0361247-A (YT, YY) Casio Science and Technology Foundation No. 39-11 and 40-4 (YT) 20 Seiko Instruments Advanced Technology Foundation, Research Grants 2024 (YT) Research Institute of Electrical Communication, Cooperative Research Projects (SF) Author contributions:  Conceptualization: YT, YY, SF Methodology: YT, YY, SF 25 Software: YT, YS, YY Validation: YT, YS, YY Formal analysis: YT, YS, YY, SF Investigation: YT, YS, YY, YK Resources: YT, YS, YY, JYY, YK, TU, KVDZ, SK, HO, SF 30 Data curation: YT, YS, YY Writing – original draft: YT, YY, JH, JI, SF Writing – review & editing: YT, YS, YY, JYY, YK, TU, KVDZ, JH, SK, JI, HO, SF Visualization: YT, YS, YY, SF Supervision: HO, SF 35 Project administration: YT, YY, HO, SF Funding acquisition: YT, YS, YY, JYY, TU, JH, SK, JI, HO, SF  Competing interests: Authors declare that they have no competing interests. Data and materials availability: All of the data needed to evaluate the conclusions in this 40 work are available in the main text or the supplementary materials and have also been deposited to the NIMS Materials Data Repository (MDR) (58). Supplementary Materials Materials and Methods Supplementary Text 45  18  Figs. S1 to S14    19  Figure legends: Fig. 1. Sample layout and measurement system.  The system is used for electrical control of coherent antiferromagnetic chiral-spin rotation in Mn3Sn nanodot. (A) Illustration of Hall device with a Mn3Sn nanodot and a W/Ta channel. (B) Scanning electron microscopy image of a fabricated Hall device. (C) Schematic of the Hall device, coplanar waveguide, and measurement 5 system. (D) A transmitted waveform of the applied pulse of 0.1 ns. The measurement is performed at room temperature. Fig. 2. Field- and SOT-induced switching of a Mn3Sn nanodot. (A) RH-HZ curve of prepared Mn3Sn nanodot. (B), (C) In-plane magnetic field dependence of RH-JHM curves for pulse width τ of 100 ms and 0.1 ns, respectively. (D) RH-JHM curves for various τ. Both RH-H and RH-JHM 10 curves are measured for Mn3Sn nanodot with a nominal diameter of 200 nm. The measurement is performed at room temperature. Fig. 3. Switching probability and field-free switching. (A)-(D) P versus JHM for various τ. (E)-(H) 2D mapping of P versus JHM and τ for various in-plane magnetic field Hx. The red and blue arrows above (E) point at switched and switched-back regions through coherent chiral-spin 15 rotation, respectively. The numbers without (with) the prime symbol denote 180o coherent chiral spin rotation being completed one, three, …, 2N-1 (two, four, …, 2N) times.  (I), (J) schematic illustration of switching and switching-back process through controlling the coherent chiral-spin rotation of Mn3Sn by short current pulse of τ ~ (2N+1) τ180t and 2Nτ180, respectively.  and τ180 denote  the angle of the antiferromagnetic order parameter in the kagome plane and the time 20 period for 180o rotation under the given JHM, respectively. (K) Pulse number dependence of Hall  20  resistance in Mn3Sn nanodot at zero magnetic field. Here, current pulse JHM = 112 MA cm-2 and τ = 0.1 ns is applied to the Hall devices. The measurement is performed at room temperature. Fig. 4. Relationship among pulse width, amplitude and switching properties. (A) τ dependence of switching current density JC for various Hx. (B) P vs. τ for JHM = 104 MA cm-2. (C) Current dependence of chiral-spin rotation frequency frot. No magnetic field is applied for (B) 5 and (C). More details on frot , including the definition of the error bars, are found in  Section S10 of (40). Fig. 5. Numerical calculation of switching current. (A)-(C) Calculated switching current density versus Gilbert damping constant in chiral antiferromagnet and ferromagnet for  = 1, 0.1, and 0.01 ns, respectively. 10  Fig. 1, Takeuchi et al.Fig. 2, Takeuchi et al.A BC D−1000 −500 0 500 1000−0.2−0.10.00.10.2RH (Ω)µ0Hz (mT)RH (Ω)µ0Hx (mT) -300 0 300τ = 100 ms0.1 Ω−60 −40 −20 0 20 40 60JHM (MA cm-2)−100 −50 0 50 100RH (Ω)JHM (MA cm-2)0.1 Ωτ = 0.1 ns µ0Hx = 300 mTµ0Hx = -300 mT−100 −50 0 50 100−0.2−0.10.00.10.2RH (Ω)JHM (MA cm-2)τ (ns) 0.1 0.2 0.3 0.5 1.0 10.0µ0Hx = 300 mTFig. 3, Takeuchi et al.Fig. 4, Takeuchi et al.AB C0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1020406080100120JC (MA cm-2)τ (ns)µ0Hx (mT) 0  100 200  3000.0 0.2 0.4 0.6 0.8 1.00.00.51.0Pτ (ns)6TRot60 70 80 90 100 110 12002468101214f rot (GHz)JHM (MA cm-2)Fig. 5, Takeuchi et al.A B C10−3 10−2 10−1 100101102103104105106JC (MA cm-2)α Chiral antiferromagnet  Ferromagnet τ = 1 ns10−3 10−2 10−1 100ατ = 0.1 ns τ = 0.01 ns10−3 10−2 10−1 100α  1     Supplementary Materials for  Electrical coherent driving of chiral antiferromagnet  Yutaro Takeuchi, Yuma Sato, Yuta Yamane, Ju-Young Yoon, Yukinori Kanno, Tomohiro Uchimura, K. Vihanga De Zoysa, Jiahao Han, Shun Kanai, Jun’ichi Ieda, Hideo Ohno, and Shunsuke Fukami  Corresponding author: takeuchi.yutaro@nims.go.jp (Y.T.); yutaymn@tohoku.ac.jp (Y.Y.); s-fukami@tohoku.ac.jp (S.F.);   The PDF file includes:  Materials and Methods Supplementary Text Figs. S1 to S14 References   2  Materials and Methods Samples The stack was deposited on MgO(110) single crystal substrate by magnetron sputtering. The MgO film layer was deposited by radio-frequency magnetron sputtering and other layers were deposited by DC magnetron sputtering. Mn3Sn film is deposited through the co-sputtering of Mn and Sn targets. The deposited stack consists of, from the substrate side, W(2 nm) / Ta(3 nm) / Mn3Sn(20 nm) / MgO(1.3 nm) / Ru(1 nm). MgO was deposited at room temperature, whereas W, Ta, Mn3Sn, and Ru were deposited at 400 oC on a heated stage. The base pressure of sputtering chambers was less than 1.0×10-6 Pa. The film was annealed at 500 oC for an hour in a vacuum after the deposition. The Mn composition in the Mn3Sn layer is obtained to be 76.8% by inductively coupled plasma-mass spectrometry. The prepared stack was processed into nanodot Hall devices. First, the dot was patterned by electron beam lithography and Ar ion milling. During the milling, we monitored the secondary ion mass spectra and stopped the milling when the Sn signal from the Mn3Sn layer disappeared. After the milling, Ta(3 nm) / Ru(1 nm) was deposited using DC magnetron sputtering to protect W(2 nm) / Ta(3 nm) underlayers from oxidation. Next, the W / Ta / Ru channel was formed by electron beam lithography and Ar ion milling. Then, electrodes made of Cr(5 nm) / Au(100 nm) film, attached to the channel, were formed using electron beam lithography and liftoff. Finally, the coplanar waveguide and contact pads for probing Hall voltage, made of Cr(5 nm) / Au(100 nm), were formed using photolithography and liftoff. After fabricating Hall dot devices, we captured their images using a scanning electron microscope (Fig.1B of the main text). The standard deviation between the actual and nominal device sizes is obtained to be about 15 nm.  Experimental Setup The structure properties of the prepared stack were characterized by the X-ray diffraction measurement using a Bruker X-ray diffractometer.  A Cu-Kα1 X-ray was used in the diffractometer with a wavelength of 1.54056 Å. All electrical measurements were performed at room temperature using a probing station with the measurement circuit depicted in Fig. 1C. The out-of-plane or in-plane magnetic field can be applied by electromagnets in the probing station. A current source (Yokogawa; Model GS200) was used to apply DC current into the channel and the Hall voltage was measured by a nano-voltmeter (Keithley; Model 2182A). A DC current with a magnitude of 100 μA was supplied when measuring the Hall voltage of the nanodot device. Short pulse voltages of 0.1-10 ns were applied from a pulse generator (Agilent; Model 81134). Transmitted waveforms of the injected pulse are monitored through an oscilloscope (Agilent; Model DSOX93204A) with an internal impedance of 50 . After the electrical switching of Mn3Sn, a pulse current of 0.1 s was applied from the current source to initialize the spin ordering.  Supplementary Text S1. Structure properties of Mn3Sn film To characterize the structure properties of the prepared stack, we perform the X-ray diffraction (XRD) measurement using a Bruker X-ray diffractometer. Figure S1A shows the obtained pattern of out-of-plane XRD measurement in the blanket film. The (1100) and (3300) super lattice peaks D019-Mn3Sn are observed in addition to the (2200) and (4400) fundamental peaks, indicating the (1100) (M-plane) orientation of D019-ordered phase, which is consistent with previous studies (28, 41). The  scan patterns for MgO substrate and the Mn3Sn layer are   3  shown in Fig.S1B, indicating the epitaxial growth of M-plane ordered Mn3Sn. The epitaxial relationship can be described as MgO(110)[001] ∥ Mn3Sn(1100)[0001].  S2. Transmitted waveforms of sub-ns ~ ns pulse voltage To evaluate the magnitude of applied pulse current flowing into the nanodot Hall bar device, transmitted waveforms of the pulse are measured by the oscilloscope. Figure S2 shows measured waveforms for various nominal pulse widths  and input voltage in the pulse generator. We confirm that the amplitude of transmitted pulse voltage VOSC decreases at shorter . The magnitude of pulse current I can be obtained as VOSC/ROSC, where ROSC (= 50 ) denotes the internal impedance of the oscilloscope.  S3. Evaluation of shunt current in nanodot device We prepared nanoscale Hall devices with W(2 nm) / Ta(6 nm) / Ru(1 nm) channels and nanodots consisting of W(2 nm) / Ta(3 nm) / Mn3Sn(20 nm) / MgO(1.3 nm) / Ru(1 nm). Figure S3A is the schematic illustration of the prepared device. We note that Ta(3 nm) / Ru(1 nm) films are deposited after milling Mn3Sn nanodots. To evaluate the current density flowing into W(2 nm)/Ta(3 nm) layers under Mn3Sn nanodots, we consider an electric circuit as shown in Fig.S3B. Here, RCh denotes the resistance of channel regions, RDot the resistance of dot, and RInt the resistance of intersection regions of W/Ta/Ru channel and Hall probe. Considering the parallel resistance model, the conductance of each region can be approximately estimated as 1𝑅 ~𝑤𝑙𝑡𝜌+𝑡𝜌+𝑡𝜌, (S1A) 1𝑅~𝑡𝜌+𝑡𝜌+𝑡𝜌, (S1B) 1𝑅 ~𝑤𝑙𝑡𝜌+𝑡𝜌+𝑡𝜌, (S1A) where 𝑤  is the width of X region, 𝑙   the length of X region, 𝑡  the thickness of Y layer in X region, and 𝜌  the resistivity of Y layer. Here, we assume the square-shaped dot with the effective length of √𝐷 . Following this assumption, 𝑤  and 𝑙  can be expressed as √ and √, respectively. Here, the resistivities of each layer are assumed as W = 60.2 cm, Ta = 122.8 cm, Mn3Sn = 333.3 cm, and Ru = 36.2 cm (28) to evaluate the device resistance. The procedure for evaluating the resistivities of W, Ta, and Mn3Sn is given in Supplementary Text 4. Due to the oxidation of Ta layer after milling Mn3Sn nanodot, we assume that 3-nm-thick Ta layer is insulated in the W(2 nm) / Ta(6 nm) / Ru(1 nm) channel and intersection regions. Using eqs. (S1A), (S1B), and (S1C), we evaluate the shunt current density flowing W/Ta layer in the dot region.  S4. Evaluation of the layer resistivities   4   To evaluate the layer resistivities in the stacks, we measure the sheet resistance of blanket films by a four-probe method.  We prepared three series of stacks consisting of, from substrate side, W(tW)/MgO(1.3 nm)/Ru(1 nm) (Series A), W(2 nm)/Ta(tTa)/MgO(1.3 nm)/Ru(1 nm) (Series B), and W(2 nm)/Ta(3 nm)/Mn3Sn(tMn3Sn)/MgO(1.3 nm)/Ru(1 nm) (Series C) by magnetron sputtering, where tW, tTa, and tMn3Sn denote the layer thicknesses of W, Ta, and Mn3Sn, respectively. All films are deposited on MgO(110) substrate. The dependencies of the sheet conductance GS on the layer thicknesses for series A, B, and C are summarized in Fig.4S. The resistivities are determined through the linear fitting of GS versus the layer thicknesses. We obtain the layer resistivities as W = 60.2 cm, Ta = 122.8 cm, and Mn3Sn = 333.3 cm, which are used to estimate the shunt current in the nanodot devices.  S5. Measurement of switching probability in Mn3Sn nanodot In Fig.3A-H, the results of SOT-induced switching probability P as a function of current density JHM, pulse width , and in-plane magnetic field Hx are displayed. Here, we describe the procedure for measuring P in chiral-antiferromagnetic Mn3Sn nanodot. First, the antiferromagnetic chiral-spin structure is initialized to low RH state by applying pulse current with  of 100 ms and JHM = 42 MA cm-2 under 0Hx = 300 mT, followed by measuring Hall resistance RH under DC current density of 3.8 MA cm-2. The 100 ms-pulse and DC current is generated from the current source connected to the DC port of the bias-tee (see also Fig.1C of the main text). Next, current pulse with the opposite polarity is applied to induce the switching under applied 0Hx of 0, 100, 200, or 300 mT. Then, RH is measured to check whether the spin structure of Mn3Sn nanodot is switched. We repeat the measurement at least 50 times for each JHM, , and Hx to evaluate P. Figure S5A-C show the distributions of RH versus JHM after the injection of single pulse with  of 0.10, 0.15, and 1.0 ns, respectively, under no external magnetic field. RH exhibits the binarized states of high and low resistance. Figure S5D displays the histogram of measured RH after initialization, which confirms that there are no initialize errors. The two-dimensional color maps of Fig. 3E-H are displayed with linearly interpolated values of experimental P versus JHM and .  S6. Calculation of chiral antiferromagnetic dynamics and switching phase diagram We model Mn3Sn by a three-sublattice antiferromagnet, with each of the magnetic sublattices A, B and C carrying a common saturation magnetization 𝑀 . The classical unit vector mA represents the sublattice magnetization direction in the sublattice A, and similarly defined are mB and mC. Now we introduce antiferromagnetic order parameters (54). 𝒏 =𝒎 + 𝒎 − 2𝒎3√2,        𝒏 =−𝒎 + 𝒎√6. When |𝒎| = |𝒎 + 𝒎 + 𝒎 | ≪ 1, i.e., the sublattice magnetizations make a nearly perfect triangular structure, it can be shown directly from the above definitions that  𝒏 ∙ 𝒏 ≃ 0 and |𝒏 | ≃ |𝒏 | ≃√. As 𝒚 ∙ 𝒏 × 𝒏 < 0 for the inverse triangular spin structure in Mn3Sn, it suffices to track either  𝒏  or 𝒏  for describing the time evolution of the antiferromagnetic order. In the simulation below, we start from an initial state with  𝒏 ∥ +𝒛, and the magnetic state is considered as “switched” if 𝒏 ∥ −𝒛 is reached after an electric current pulse is applied and then turned off. We assume spatial homogeneity in the magnetic structure and the magnetic energy density given by   5  𝑢 = 𝐽 (𝒎 ∙ 𝒎 + 𝒎 ∙ 𝒎 + 𝒎 ∙ 𝒎 ) − 𝐷𝒚 ∙ (𝒎 × 𝒎 + 𝒎 × 𝒎 + 𝒎 × 𝒎 )          −𝐾 ∑ 𝒆 ∙ 𝒎, , − ∑ 𝒆 ∙ 𝒎, , ,   where 𝐽  (> 0) is the antiferromagnetic exchange coupling constant, 𝐷(> 0) is the homogeneous Dzyaloshinskii-Moriya coupling constant, 𝐾(> 0) is the magnetic anisotropy constant originating from the local crystalline symmetry with 𝒆  being the unit vector along the easy axis for 𝒎 , and 𝐾 (> 0) phenomenologically describes the uniaxial anisotropy for 𝒏  along the z direction with 𝒆  the unit vector representing the corresponding easy axis for 𝒎 . Here we set the x, y and z axes along [1120], [0001] and [1100], respectively, of Mn3Sn. The explicit expressions of 𝒆  and 𝒆  are; 𝒆 = (cos , 0, sin ) , 𝒆 = (cos , 0, sin ) , 𝒆 = (1, 0, 0) , 𝒆 =(cos , 0, −sin ), 𝒆 = (− cos , 0, −sin ), and 𝒆 = (0, 0, 1).  The sublattice magnetizations 𝒎  (𝜂 = 𝐴, 𝐵, 𝐶) are assumed to obey coupled Landau-Lifshitz-Gilbert (LLG) equations, 𝜕𝒎𝜕𝑡= −𝛾𝒎 × 𝑯 + 𝛼𝒎 ×𝜕𝒎𝜕𝑡− 𝛾𝒎 × 𝒎 × 𝑯 , where 𝛾  is the gyromagnetic ratio, 𝛼  is the Gilbert damping constant, 𝑯 = −𝒎 is the effective magnetic field acting on 𝒎 , and 𝑯 =ℏ𝒚 is the current-induced Slonczewski-like effective field with 𝜗 and 𝑑 denoting, respectively, the spin Hall angle of the heavy metal layer and the film thickness of the Mn3Sn layer. The factor  in 𝑯  reflects the sublattice symmetry where the spin current injected into Mn3Sn is transferred equiprobably to each of the three magnetic sublattices.  It is challenging to experimentally measure some of the parameters, such as the local anisotropy K and the DMI constant D. However, there are theoretical relations that these parameters must satisfy (55). First, in order for the inverse triangular spin structure to be stable, the relation 𝐽 ≫ 𝐷 ≫ 𝐾 has to be satisfied. Second, the uncompensated small magnetization m is given by |𝒎| ≈ 𝑀 𝐾 𝐽⁄ . These relations greatly narrow down the ranges of values that K and D can take, while 𝐽  and 𝐾  have been experimentally evaluated in Mn3Sn nanodots (43), and 𝑀  can be estimated from the magnetic moment caried by each Mn atom. Based on these reasonings, we employ the following parameter values; 𝛾 = 1.76 × 10  HzT-1, 𝑀 = 0.55 T, 𝐽 = 6.2 ×10  Jm-3, 𝐷 = 6 × 10  Jm-3, 𝐾 = 3.8 × 10  Jm-3, 𝐾 = 3.4 × 10  Jm-3, 𝛼 = 0.002,  𝑑 = 20 nm, and 𝜗 = 0.033. In the calculations shown in Fig. 5 of the main text, we use the same parameter values as here, except for 𝛼 (we examine the 𝛼 dependence of 𝐽 (𝜏) in Fig. 5).  We investigate the current-driven dynamics of Mn3Sn by numerically solving the Landau-Lifshitz-Gilbert equations. Displayed in Fig. S6 is the calculated switching phase diagram against the pulse amplitude JHM and width . We find a quantitatively good agreement with the experimental result in Fig. 3E. Because of the absence of thermal effects in the calculation, the boundaries between the switched and switched-back regions are sharply defined, i.e., deterministic switching/switching-back with given (JHM, ).     6  S7. Pulse-shape dependence of the switching current density Here we numerically investigate impacts of the pulse shape on JC(). The same parameter values as in S6 are used, and the results are shown in Fig. S7. We take the pulse shapes so as the total amount of the spin angular momentum injected into Mn3Sn to be kept unchanged, to examine the effects purely originating from the pulse shape.  S8. Dependence of switching on writing pulse number As shown in Fig.3K of the main text, we demonstrate a part of the field-free switching 1,000 times by single pulse current through the control of coherent chiral-spin rotation in Mn3Sn nanodot. This section describes the result of all-electrical switching 1,000 times in the same nanodot device. The pulse current of  = 0.1 ns and JHM = 112 MA cm-2 is applied under 0Hx = 0 mT as well as Fig.4A of the main text. Figure S8 shows the pulse number dependence of measured RH for pulse number ranges of 1 to 1,000. We confirm the binary switching 1,000 times in succession by single pulses with no write error, which had not been realized in previous studies using antiferromagnet-based devices.  S9. Switching current versus pulse width: Comparison with other ferromagnetic and ferrimagnetic systems The SOT-induced switching current density JC versus pulse width in Mn3Sn nanodot  shows a small increase rate of about 1.4 times by reducing  from 1 to 0.1 ns [Fig.4A of the main text]. Here, we show the results of a quantitative comparison of switching current IC versus  between chiral antiferromagnet and ferromagnet-based devices studied in previous works. Figure S9 shows  dependence of the switching current IC normalized by IC at  ~ 1 ns in chiral antiferromagnetic Mn3Sn nanodot and other ferromagnetic nanoscale devices and ferrimagnetic wire (35–38, 49, 50) Type-X (39) and type-Y (37–39) denote in-plane magnetized ferromagnet (FM) / heavy metal (HM) systems whose magnetic easy axes are orthogonal and parallel to the generated spin accumulation vector, respectively. Type-Z (36, 49) represents FM/HM system with an out-of-plane magnetic easy axis.  is an angle between the current direction and magnetic easy axis (38). Therefore,  = 0o and 90o correspond to Type-X and Type-Y systems, respectively. SOT+STT denotes the combined systems using both SOT and spin-transfer torque (STT) induced by spin-polarized current from another magnetic layer. In the chiral antiferromagnet-based SOT device, the increase of IC/IC(~ 1 ns) by reducing  shows smaller values than other ferromagnet systems owing to the inertial nature of antiferromagnetic excitations.  S10. Determination of the rotation frequency in chiral antiferromagnet from switching probability To obtain the chiral-spin rotation frequency frot, we estimate the rotation period and number of oscillation peaks in evaluated switching probability P versus pulse width . Figure S10 shows  dependence of P for different current densities JHM. The P curves exhibit damped oscillation behavior with respect to . We then estimate the  distance between the first and last peaks of the oscillation. By reducing JHM from 104 to 77 MAcm-2, the number of observed peaks decreases from 7 to 3, corresponding to the estimated  distance of 12180 and 4180, respectively, where 180 is half value of the period of coherent chiral-spin rotation. Then we evaluate the JHM dependence of frot as shown in Fig.4C in the main text.   7  We also note that the oscillation speed appears to slightly increase with . It may be attributed to the effect of thermal activation and variation of the pulse shape with .  Accordingly, the error bars in Fig. 4C are provided to represent the lower and upper limits of frot, where the lower (upper) limit is estimated from the second and first (the last and the second to the last) peaks.  S11. Dependencies of the switching current density on micromagnetic parameters Here we numerically investigate the dependencies of the current-driven Mn3Sn dynamics on 𝐾 , 𝐽 , 𝐷, and 𝐾. In the following, the same parameter values as in S6 are used, unless otherwise stated. First, we show 𝐽 (𝜏) in Fig. S11, where 𝐽 (𝜏) is defined as the value of 𝐽  at which 180-degree switching is observed with the given 𝜏 . For a comparison, numerical results for two ferromagnetic cases (FM-1 and FM-2) and our experimental results are also shown in Fig. S11; For FM-1 we take similar parameter values to Mn3Sn to clarify fundamental differences between the two systems, while FM-2 assumes parameter values more relevant to realistic ferromagnetic materials (details of the ferromagnetic simulation are given in S14). Figure S12A shows 𝐽 (𝜏 = 0.1ns) and 𝐽 (𝜏 = 0.01ns) as functions of 𝐾  for Mn3Sn. The results for FM-1 are shown for a comparison in Fig. S12B. Given in Fig. S12C are the results in the DC limit, i.e. 𝐽 (𝜏 → ∞), for Mn3Sn. Note that, in the DC limit, what we actually observe is not 180-dgree switching but the continuous chiral spin rotation. It is seen that  𝐽 (𝜏) increases monotonically with 𝐾 , as expected. In Fig. S13, we demonstrate the 𝐽 , 𝐷, and 𝐾 dependencies of 𝐽 (𝜏). A general tendency is that, as 𝜏 is decreased, the dependencies of 𝐽 (𝜏) on the micromagnetic parameters become more appreciable. With the pulse as short as  𝜏 = 0.001  ns, however, the dependencies on the parameters are still negligible.  S12. Numerical calculation of antiferromagnetic order dynamics in time domain  In Fig. S14, we show numerical results for the evolution of n1z (the definition of the antiferromagnetic order vector 𝒏  is given in S6) in time, under several different pulse amplitudes JHM.  Here, the pulse length  is fixed to 0.1 ns. Note that the length of the vector 𝒏  is ≈ 1 √2⁄ , as can be straightforwardly shown from its definition. The threshold current densities JC( =0.1ns) for 180-degree and 360-degree rotations are ≈89 MAcm-2 and ≈152 MAcm-2, respectively. It is seen that, except for when JHM ≈ JC, switching is completed at around 0.1 ns after the pulse application.  S13. Connection between simulation and analytical model We briefly touch upon the relation between the coupled LLG equations for the sublattice magnetizations 𝒎  and the equation of motion for the antiferromagnetic order discussed in the main text. With the aid of the assumptions |𝒎| ≪ 1 and 𝑚 ≪ 1 ∀𝜂, the order parameter 𝒏  can be approximately described by a single parameter 𝜃 as 𝒏 =√(sin 𝜃 , 0, cos 𝜃). In the absence of external magnetic field, the closed equation of motion for 𝜃 can be derived at the first order of 𝒎 as in the main text (55). with 𝐻 =  and 𝐻 = .  S14. Numerical calculation of ferromagnetic dynamics   8  For a ferromagnet, we solve the LLG equation of the same form as in the last section, but for the single magnetization 𝒎 instead of the sublattice magnetizations 𝒎 . The magnetic energy density is assumed to consist only of the uniaxial magnetic anisotropy; 𝑢 = −𝐾 𝑚 . The current-induced Slonczewski-like effective field is now given by 𝑯 =ℏ𝒚. In Fig. 5 of the main text, we adopt 𝑀 = 0.55  T, 𝐾 = 3.4 × 10  Jm-3, 𝑑 = 20  nm, 𝜗 = 0. 033, 𝛾 = 1.76 ×10  HzT-1, and 0|𝐻 | = 1 μT. The same parameter values and 𝛼 = 0.002 are used for FM-1 in Fig. S11 and S12 ( 𝐾  is varied in the latter). For FM-2 in Fig. S11, 𝑀 = 1.093  T, 𝐾 =4.35 × 10  Jm-3, 𝑑 = 0.6 nm, 𝜗 = 0.4, 𝛼 = 0.002, 𝛾 = 1.76 × 10  HzT-1, and 0|𝐻 | = 91 mT (36).      9   Fig. S1. Structure properties of W(2 nm) / Ta(3 nm) / Mn3Sn(20 nm) / MgO(1.3 nm) heterostructure. (A) Out-of-plane XRD pattern of the prepared stack. (B)  scan patterns for MgO{100} and Mn3Sn{2201}.   20 30 40 50 60 70 80 90Intensity (arb.unit)2q (deg)Mn3Sn(1100)Mn3Sn(2200)Mn3Sn(4400)MgO(220)0 90 180 270 360Intensity (arb.unit) (deg)MgO{100}Mn3Sn{2201}A B  10   Fig. S2. Transmitted waveforms of applied pulse voltages. (A)-(L) Time dependence of transmitted voltage VOSC for various pulse width. The nominal amplitude of pulse voltage is 800 mV.   −0.2 0.0 0.2 0.4020406080VOSC (mV)0.1 ns−0.2 0.0 0.2 0.40.125 ns−0.2 0.0 0.2 0.40.15 ns−0.2 0.0 0.2 0.40.2 ns−0.5 0.0 0.5 1.0020406080VOSC (mV)0.3 ns−0.5 0.0 0.5 1.00.4 ns−0.5 0.0 0.5 1.00.5 ns−0.5 0.0 0.5 1.00.6 ns−1 0 1 2020406080VOSC (mV)Time (ns)0.7 ns−1 0 1 2Time (ns)0.8 ns−1 0 1 2Time (ns)0.9 ns−1 0 1 2Time (ns)1.0 nsA B C DE F G HI J K L  11   Fig. S3. Evaluation of shunt current in nanodot device. (A) Sample layout of the prepared nanodot Hall device. (B) The modelled electrical circuit for evaluation of the current density flowing into heavy metal layers under Mn3Sn nanodot.   LChWProbeWChDA BRCh RChRIntRDotRInt  12    Fig. S4. Evaluation of layer resistivities. (A) tW, (B) tTa, and (C) tMn3Sn dependence of the sheet conductance GS in the prepared stacks. The symbols denote the experimental data and the green solid lines are the best fitting lines.    A B C0 1 2 3 40246810GS (mS)tW (nm)W(tW) / MgO(1.3 nm) / Ru (1 nm) W(2 nm) / Ta(tTa) / MgO(1.3 nm) / Ru (1 nm)W(2 nm) / Ta(3 nm) /Mn3Sn(tMn3Sn) / MgO(1.3 nm) / Ru(1 nm)0 1 2 3 4 5 60246810GS (mS)tTa (nm)0 10 20 30 40 50051015202530GS (mS)tMn3Sn (nm)  13    Fig. S5. Measurement of switching probability P versus JHM and . (A)-(C) Distributions of Hall resistance RH versus JHM after the injection of single pulse with  of 0.10, 0.15, and 1.0 ns, respectively, under no external magnetic field. (D) The histogram of measured RH after initialization of Mn3Sn nanodot.  40 50 60 70 80 90 100 110−0.2−0.10.00.10.2RH ()JHM (MA cm-2) = 0.10 ns 40 50 60 70 80 90 100 110−0.2−0.10.00.10.2RH ()JHM (MA cm-2) = 0.15 ns 40 50 60 70 80 90 100 110−0.2−0.10.00.10.2RH ()JHM (MA cm-2) = 1.0 ns −0.14 −0.13 −0.12 −0.110100200300400CountRH () = 100 ms JHM = 42 MA cm-20Hx = 300 mTA BC D  14   Fig. S6. Calculated switching phase diagram in chiral antiferromagnet at zero field. The black circles represent the switching current densities, numerically obtained with given pulse lengths (for 180o, 360o, 540o, … switching from below). The red and blue regions represent the switched and unswitched/switched-back regions, respectively.  0.1 0.3 0.5 0.7 0.95060708090100J HM (MA cm-2) (ns)A  15   Fig. S7. Calculated pulse-shape dependence of the switching current densities. (A) The shape of the pulse current employed in the simulation here, with the rise and fall times . The calculated switching phase diagrams for (B)  = 0 and (C)  = 30 ps, where the red and blue regions correspond to the switched and unswitched/switched-back regions, respectively. The white regions are uncalculated regions. (D) The ratio of JC() with  = 30 ps to JC() with  = 0, for 180-degree switching.    0.1 0.3 0.5 0.7 0.90.1 0.3 0.5 0.7 0.95060708090100(ns) = 0 psJ HM (MA cm-2)(ns) = 30 ps0.1 0.3 0.5 0.7 0.90.900.951.001.051.10J C()| = 30 ps / JC()| = 0 ps (ns)B CJ0JHM0.5JHM /2/2AD  16   Fig. S8. Dependence of switching on writing pulse number (A)-(E) Pulse number dependence of measured RH for pulse number ranges of 1-200, 201-400, 401-600, 601-800, and 801-1000, respectively.    ABCDE0 20 40 60 80 100 120 140 160 180 200−0.2−0.10.00.10.2RH () = 0.1 ns, JHM = 112 MA cm-2, 0Hx = 0 mT600 620 640 660 680 700 720 740 760 780 800−0.2−0.10.00.10.2RH ()400 420 440 460 480 500 520 540 560 580 600−0.2−0.10.00.10.2RH ()200 220 240 260 280 300 320 340 360 380 400−0.2−0.10.00.10.2RH ()800 820 840 860 880 900 920 940 960 980 1000−0.2−0.10.00.10.2RH ()Pulse number  17    Fig. S9. Switching current versus pulse width.  dependence of the IC normalized by IC at  = 1 ns in chiral antiferromagnetic Mn3Sn nanodot and other nanoscale ferromagnetic and ferrimagnetic systems.   a0.1 1 10012345I C/IC( ~ 1 ns) (ns)Chiral antiferromagnet (This work)100 mT 200 mT 300 mTFerromagnets and ferrimagnetsSOT: Type-Z (36) SOT: Type-Y (37)SOT: Type-Y (38) SOT:  = 30o (38)SOT+STT: Type-X (39) SOT+STT: Type-Y (39)SOT: Field-free Type-Z (49) STT (35) DW motion of ferrimagnet (50)  18   Fig. S10. Determination of the rotation frequency in chiral antiferromagnet from switching probability.  dependence of P for various JHM.     0.00.51.0P12180 121800.00.51.0P10180 101800.00.51.0P8180JHM = 104 MA cm-2 JHM = 100 MA cm-261800.0 0.2 0.4 0.6 0.8 1.00.00.51.0P (ns)4180JHM = 96 MA cm-2 JHM = 93 MA cm-2JHM = 89 cm-2 JHM = 85 MA cm-2JHM = 81 MA cm-2 JHM = 77 MA cm-20.0 0.2 0.4 0.6 0.8 1.0 (ns)4180  19     Fig. S11. Numerical calculation of switching current density: Comparison between chiral antiferromagnet and ferromagnet. Calculated JC versus  in Mn3Sn, FM-1, and FM-2, and the experimental JC in Mn3Sn with different in-plane magnetic fields are shown by open symbols.   a10−2 10−1 100 101101102103104105J C (MA cm-2) (ns)Calculation Mn3Sn  FM-1 FM-2Experiment 0 mT100 mT   20     Fig. S12. Numerical calculation of switching current density: Dependencies on global magnetic anisotropy energy density. Calculated JC versus KZ for various  in (A) Mn3Sn and (B) FM-1. (C) The DC limit (𝜏 → ∞) for Mn3Sn.   A BC102 103 104 105101102103104105J C (MA cm-2)KZ (J m-3) (ns) 0.01 0.1Mn3Sn102 103 104 105101102103104105J C (MA cm-2)KZ (J m-3) (ns) 0.1 1 10FM-1102 103 104 105101102103104105J C (MA cm-2)KZ (J m-3)Mn3SnDC limit  21    Fig. S13. Numerical calculation of switching current density: Dependencies on micromagnetic parameters. Calculated JC versus  , varying (A) the exchange coupling constant Jex, (B) Dzyaloshinskii-Moriya coupling constant D, and (C) the local magnetic anisotropy K.   A B C10−3 10−2 10−1 100 101101102103104J C (MA cm-2) (ns)Jex (J m-3) 6.2×107 6.2×10810−3 10−2 10−1 100 101 (ns)D (J m-3) 6.0×106 1.8×10710−3 10−2 10−1 100 101 (ns)K (J m-3) 3.8×105 3.8×104  22    Fig. S14. Numerical calculation of antiferromagnetic order dynamics in time domain. (A) Current pulse shape employed in the simulation here, with the fixed width of 0.1 ns. (B)-(H) Calculated n1z versus t, under various pulse amplitudes.  A BC DE FG HJHM0 −1.0−0.50.00.51.0n 1zJHM = 89 MA cm-2−1.0−0.50.00.51.0n 1zJHM = 96 MA cm-2−1.0−0.50.00.51.0n 1zJHM = 108 MA cm-2−1.0−0.50.00.51.0n 1zJHM = 120 MA cm-2−1.0−0.50.00.51.0n 1zJHM = 132 MA cm-20.0 0.1 0.2 0.3−1.0−0.50.00.51.0n 1zt (ns)JHM = 144 MA cm-20.0 0.1 0.2 0.3−1.0−0.50.00.51.0n 1zt (ns)JHM = 151 MA cm-2