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# Perpendicular full switching of chiral antiferromagnetic order by current

## Abstract

Electrical control of a magnetic state of matter lays the foundation for information technologies and for understanding of spintronic phenomena. Spin–orbit torque provides an efficient mechanism for the electrical manipulation of magnetic orders1,2,3,4,5,6,7,8,9,10,11. In particular, spin–orbit torque switching of perpendicular magnetization in nanoscale ferromagnetic bits has enabled the development of stable, reliable and low-power memories and computation12,13,14. Likewise, for antiferromagnetic spintronics, electrical bidirectional switching of an antiferromagnetic order in a perpendicular geometry may have huge impacts, given its potential advantage for high-density integration and ultrafast operation15,16. Here we report the experimental realization of perpendicular and full spin–orbit torque switching of an antiferromagnetic binary state. We use the chiral antiferromagnet Mn3Sn (ref. 17), which exhibits the magnetization-free anomalous Hall effect owing to a ferroic order of a cluster magnetic octupole hosted in its chiral antiferromagnetic state18. We fabricate heavy-metal/Mn3Sn heterostructures by molecular beam epitaxy and introduce perpendicular magnetic anisotropy of the octupole using an epitaxial in-plane tensile strain. By using the anomalous Hall effect as the readout, we demonstrate 100 per cent switching of the perpendicular octupole polarization in a 30-nanometre-thick Mn3Sn film with a small critical current density of less than 15 megaamperes per square centimetre. Our theory reveals that the perpendicular geometry between the polarization directions of current-induced spin accumulation and of the octupole persistently maximizes the spin–orbit torque efficiency during the deterministic bidirectional switching process. Our work provides a significant basis for antiferromagnetic spintronics.

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## Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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## Acknowledgements

We thank R. Uesugi, T. Matsuo, H. Tsai and S. Minami for discussions. This work was partially supported by JST-MIRAI Program (JPMJMI20A1), JST-CREST (JPMJCR18T3), JST-PREST (JPMJPR20L7), MEXT/JSPS-KAKENHI (15H05882, 15H05883, 15K21732, 19H00650, 20K21067, 21H04437, 22H00290), and Spintronics Research Network of Japan (Spin-RNJ). T.H. acknowledges support from the Hattori Hokokai Foundation. S.N. acknowledges support from the CIFAR as a Fellow of the CIFAR Quantum Materials Research Program. Institute for Quantum Matter, an Energy Frontier Research Center was funded by DOE, Office of Science, Basic Energy Sciences under Award (DE-SC0019331). The use of the facilities of the Materials Design and Characterization Laboratory at the Institute for Solid State Physics, and the Laboratory for Magnetic and Electronic Properties at Interface, the University of Tokyo, is acknowledged.

## Author information

Authors

### Contributions

T.H. and K.K. contributed equally to this work. S.N. conceived the project. S.N., T.H., K.K., Y.O. and S.M. planned the experiments. T.H., M.S., S.S., X.C. and S.M. developed the magnetic multilayered films. T.H. and D.N.-H. characterized fundamental properties of the films. K.K. and T.H. performed the electrical switching measurements. T.N. and R.A. planned the theoretical studies, performed numerical calculations and provided a theoretical explanation. T.H., K.K., T.N., S.M. and S.N. wrote the manuscript with input from R.A. and Y.O. All authors discussed the results and commented on the manuscript.

### Corresponding author

Correspondence to Satoru Nakatsuji.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Peer review

### Peer review information

Nature thanks Kyung-Jin Lee, Cheng Song and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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## Extended data figures and tables

### Extended Data Fig. 1 Structural analyses for the Mn3Sn stack.

a, Room-temperature spectra obtained by X-ray diffraction (XRD) measurements using the 2θ/ω-scan for the MgO(110)-substrate/W(7 nm)/Mn3Sn(30 nm)/MgO(5 nm) stack (red line) and the substrate (black line). The theoretical spectra for the D019-Mn3Sn and W are presented at the bottom panels. Ta is the post-annealing temperature (Methods). b, XRD patterns of the Φ-scan for the {$$02\bar{2}1$$} planes of the Mn3Sn layer, the {110} planes of the W layer, and the {200} planes of the MgO substrate. c, Surface topography of the MgO(110)-substrate/W(7 nm)/Mn3Sn(30 nm)/MgO(5 nm) stack obtained by atomic force microscopy. The stack has a smooth surface with a root-mean-square (RMS) roughness of 0.6 nm. The scan area is 5 µm × 5 µm. In panels a and b, vertical and horizontal axes are on logarithmic and linear scales, respectively.

### Extended Data Fig. 2 RHEED and TEM images for the Mn3Sn stack.

a, In situ RHEED images of (bottom) the MgO (110) substrate after annealing at 800 °C for 10 min, (middle) the W layer annealed at 800 °C for 10 min and (top) the Mn3Sn layer deposited at 260 °C. The incident electron beam is parallel to the MgO [001]-direction. b, Cross-sectional TEM image of the MgO(110)-substrate/W(7 nm)/Mn3Sn(30 nm) stack at room temperature. c, High-resolution electron image for the Mn3Sn layer in the real space. Inset: Simulation image for Mn3Sn. Pink and light blue spheres represent Mn and Sn atoms in the Mn3Sn unit cell (yellow diamond), respectively. d, Electron diffraction patterns of the film (left) and the simulated patterns (right) in the reciprocal space for Mn3Sn (pink), W (orange), and MgO (yellow).

### Extended Data Fig. 3 Structural information of the MBE-grown Mn3Sn film on the MgO substrate.

a, Schematics of the interatomic arrangements in the MgO (110) substrate and Mn3Sn ($$01\bar{1}0$$) film plane. b, Crystal structure of the kagome plane in Mn3Sn. Interatomic distances and angles are obtained from the structural information of the bulk Mn3Sn with the lattice constants a = 5.665 Å and c = 4.531 Å43. c, Room-temperature spectra obtained by the X-ray diffraction (XRD) measurements using the 2θ/ω-scan for the ($$02\bar{2}0$$), ($$20\bar{2}0$$) and ($$\bar{2}200$$) planes of Mn3Sn in the MBE-grown MgO(110)-substrate/W(7 nm)/Mn3Sn(30 nm)/MgO(5 nm) stack. d, Schematics for the in-plane atomic arrangement in the Mn3Sn layer of the MBE-grown film. The interatomic distances d1 and d2 and the angle θ12 are experimentally obtained. The distance d3 and the length of the altitude parallel to the x-direction din are calculated from d1, d2, and θ12. The uniaxial tensile strain ε (pink arrows) parallel to the [$$2\bar{1}\bar{1}0$$] direction is schematically illustrated.

### Extended Data Fig. 4 Anomalous Hall conductivity of the Mn3Sn layer and estimate of the magnetic anisotropy using angular dependence of the anomalous Hall effect.

a, Magnetic field dependence of the Hall conductivity in the Mn3Sn (30 nm) layer of the MgO(110)-substrate /W(7 nm)/Mn3Sn(30 nm)/MgO(5 nm) stack at 300 K (Method). The Hall conductivity of the Mn3Sn layer in the W/Mn3Sn conducting layer is estimated using the experimentally obtained resistivity of the W(7 nm)/Mn3Sn(30 nm) layer and W(7 nm) layer (Methods). b, Angular (θ) dependence of the Hall voltage normalized by the voltage obtained at θ = 0 for the MBE-grown Mn3Sn stack under 1 T (red circles) at 300 K. The blue solid curve corresponds to the angular dependence expected in the sample with the anisotropy field for the 2-fold magnetic anisotropy field K2/Mr = 1.5 ± 0.1 T, 4-fold magnetic anisotropy field K4/Mr = 0.5 ± 0.1 T, and 6-fold magnetic anisotropy field K2/Mr = 0.4 ± 0.1 T, which are obtained by using the equation (K2/2)sin2θM + (K4/4)sin4θM + (K6/6)sin6θM − μ0MrHsin(θθM) = 0. Here K2/4/6, μ0H, Mr, θ and θM denote the 2-/4-/6-fold magnetic anisotropic energy, external magnetic field, remnant (spontaneous) magnetization, magnetic field angle, and angle of the magnetic order parameter (the polarized direction of the cluster magnetic octupole) (see Methods). Inset: Schematic illustration of the measurement set-up for the W/Mn3Sn devices. The purple and green arrows represent the directions of the magnetic field H and current I, respectively. θ and θM are the polar angle of the magnetic field and of the polarized direction of the cluster magnetic octupole (orange arrow) in the z–x plane, respectively.

### Extended Data Fig. 5 Magneto-optical Kerr effect (MOKE) and MOKE images of the MBE-grown Mn3Sn film.

a, Field dependence of the polar magneto-optical Kerr rotation angle θK for the MgO(110)-substrate/W(7 nm)/Mn3Sn(30 nm)/MgO(5 nm) stack at room temperature. The field is applied along the perpendicular direction (|| z). b, Evolution of the AF domains as a function of a field perpendicular to the MgO(110)-substrate/W(7 nm)/Mn3Sn(30 nm)/MgO(5 nm) film plane at μ0H = 0 mT(i), 120 mT(ii), and 300 mT(iii). Black and grey regions correspond to the positive and negative values of the polar MOKE signal, respectively.

### Extended Data Fig. 6 Electrical and optical observation of the perpendicular full switching in the MBE-grown Mn3Sn film.

a,b, Field (a) and write current (b) dependence of the switching rate of the Hall signal VH/|ΔVHfield| at room temperature in the MgO(110)-substrate/W(7 nm)/Mn3Sn(30 nm)/MgO(5 nm) stack obtained with the post-annealing temperature Ta = 700 °C. The bias magnetic field of 0.1 T and the write/read current are applied along the x direction. c,d, Magneto-optical Kerr effect (MOKE) images of the W/Mn3Sn device obtained in the field (c) and write current (d) sweep measurements. Black and grey regions correspond to the positive and negative values of the polar MOKE signal, respectively. Wch (Wprobe) is the channel (probe) width of the Hall bar.

### Extended Data Fig. 7 Magnetic properties of the MBE-grown Mn3Sn film.

a, Field dependence of the magnetization M at 300 K measured in the perpendicular direction of the MgO(110)-substrate/W(7 nm)/Mn3Sn(30 nm)/MgO(5 nm) stack. b, Magnified view of the field dependence of M presented in the panel a. c, Temperature dependence of the remnant M of the MgO(110)-substrate/W(7 nm)/Mn3Sn(30 nm)/MgO(5 nm) film at T = 150-300 K, which is measured from 300 K to 150 K on cooling after the demagnetization process (a field of μ0H = 7 T is applied perpendicular to the film surface and subsequently the field is decreased down to 0 T at 300 K).

### Extended Data Fig. 8 Experimental conditions and bias field dependence of the electrical switching of the chiral AF order of Mn3Sn.

a, Sequence used for the electrical switching measurements. A 100-ms-pulse write current Iwrite followed by a d.c. read current of Iread = 0.2 mA is applied, where a wait time of 600 ms is inserted after turning off the write current and before measuring the Hall voltage VH. b, Bias-field dependence of the switching volume fraction ΔVHcurrent/|ΔVHfield| of the W/Mn3Sn devices at room temperature. Here ΔVHcurrent and ΔVHfield are the magnitude of the current- and field-induced switching of the Hall voltage, respectively. The field is applied along the x direction parallel to the electrical current. c, Angular (φ) dependence of the switching volume fraction ΔVHcurrent(φ)/|ΔVHfield| for the W/Mn3Sn devices with γ = +40 degrees. ΔVHcurrent(φ) is estimated under the bias field with the azimuthal angle φ. The vertical broken lines indicate φ = 130 and 310 degrees.

### Extended Data Fig. 9 Theoretical consideration for the electrical switching of the chiral AF order in Mn3Sn.

a, configuration-(a): the kagome plane is perpendicular to the current I and parallel to the electrically injected carrier spin polarization p (thick red arrows in the W layer) (kagome I || p). b, configuration-(b): the kagome plane is parallel to I and perpendicular to p (kagome || I p). c, configuration-(c): the kagome plane is parallel to the current I and parallel to the electrically injected carrier spin polarization p (kagome || I || p). d, Schematics for the current-induced switching of the chiral AF order in the configuration-(b) (kagome || I p) with the in-plane compressive strain (δ > 0 and ε < 0). Orange arrows represent the polarization direction of the cluster magnetic octupole. Large (small) green and purple arrows represent the electric current I || x (spin torque (Tcurrent) associated with the spin current with the polarization p, leading to the chiral spin rotation) and bias magnetic field H || z (spin torque (Tfield) associated with H), respectively. Here p is parallel to the spin moments of the spin current (antiparallel to the spin angular momentum). θM is the angle of the polarized direction of the cluster magnetic octupole. e-f, In-plane angle θM of the polarization direction of the cluster magnetic octupole as a function of time t in the W/Mn3Sn bilayer calculated numerically using the LLG equation in the configuration-(b), where the kagome plane is parallel to the current I and the magnetic field H, and perpendicular to the electrically injected carrier spin polarization p (Figs. 3, Methods, Extended Data Figure 9b). I with the current density Jwrite in the W layer is applied for 1 ns < t < 2 ns. A positive Jwrite is applied in (i) and (ii), and negative Jwrite is applied in (iii) and (iv) (See detailed configurations in Fig. 3b). The magnetic field is set to be 0.1 T. e, Perpendicular (chiral spin) switching of the chiral AF order under |Jwrite| = 64 MA cm−2 (corresponding to the region-(B) in Fig. 3c). f, Chiral spin rotation only for one ((ii) for Jwrite > 0 and (iii) for Jwrite < 0) of the initial states under |Jwrite| = 73.5 MA cm−2 (region-(C) in Fig. 3c). g, Chiral spin rotation for both initial states under |Jwrite| = 77.5 MA cm−2 (region-(D) in Fig. 3c). Inset: Magnified view of the in-plane angle θM of the octupole moment as a function of time.

### Extended Data Fig. 10 Experimental characterization of the electrical switching of the chiral AF order in Mn3Sn at zero-bias field.

a, Volume fraction of the electrically controllable Hall signal VH/|ΔVHfield| versus write current Iwrite for the W/Mn3Sn devices at zero magnetic field and room temperature. Each panel shows the result of the different switching experiment in the Hall bar with the channel width Wch = 8 μm at room temperature. b, Histogram showing the distribution in the switching rate of the electrically controllable Hall signal ΔVH/|ΔVHfield| in the N = 20 measurements. c, Fluctuation of the switching Hall signal due to SOT, σswitch and σSOT as a function of the Hall cross-area S−1/2 obtained in the zero-field switching experiments using the W/Mn3Sn devices with various channel widths (Wch = 4–32 µm). σSOTzero (red circles) is given by the standard deviation of (ΔVHcurrent − <ΔVHcurrent >)/|ΔVHfield| and σSOT (blue squares) is given by the standard deviation of (VH − <VH>)/|ΔVHfield| (Methods). Thick straight lines are the linear fitting results obtained by the equation σSOTzero and σSOT $$\approx \sqrt{{S}_{{\rm{domain}}}/S}$$. d, Domain images obtained by the polar MOKE microscopy for the device with Wch = 32 µm in the zero-field switching experiments. Each panel shows an image obtained after a different switching experiment. Grey and black regions correspond to the positive and negative values of the polar MOKE signal.

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Higo, T., Kondou, K., Nomoto, T. et al. Perpendicular full switching of chiral antiferromagnetic order by current. Nature 607, 474–479 (2022). https://doi.org/10.1038/s41586-022-04864-1

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• DOI: https://doi.org/10.1038/s41586-022-04864-1