Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Intrinsic spin Hall torque in a moiré Chern magnet

Nature Physics volume 19, pages 807–813 (2023)Cite this article

Subjects

Abstract

In spin torque magnetic memories, electrically actuated spin currents are used to switch a magnetic bit. Typically, these require a multilayer geometry including both a free ferromagnetic layer and a second layer providing spin injection. For example, spin may be injected by a non-magnetic layer exhibiting a large spin Hall effect, a phenomenon known as spin–orbit torque. Here we demonstrate a spin–orbit torque magnetic bit in a single two-dimensional system with intrinsic magnetism and strong Berry curvature. We study AB-stacked MoTe2/WSe2, which hosts a magnetic Chern insulator at a carrier density of one hole per moiré superlattice site. We observe hysteretic switching of the resistivity as a function of applied current. Magnetic imaging reveals that current switches correspond to reversals of individual magnetic domains. The real space pattern of domain reversals aligns with spin accumulation measured near the Hubbard band edges with high Berry curvature. This suggests that intrinsic spin or valley Hall torques drive the observed current-driven magnetic switching in both MoTe2/WSe2 and other moiré materials. The switching current density is substantially less than those reported in other platforms, suggesting that moiré heterostructures are a suitable platform for efficient control of magnetic order.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Current-driven switching in the AB-stacked 2L-MoTe2/WSe2 heterostructure.
Fig. 2: Nanoscale magnetic imaging.
Fig. 3: Imaging current-induced switching.
Fig. 4: Spin Hall effect.

Similar content being viewed by others

Data availability

The raw data that support the one-dimensional plots are available as Source Data files. All other data are available from Dryad46.

Code availability

All the software supporting the data processing pipeline is available at ref. 47.

References

  1. Chang, C.-Z., Liu, C.-X. & MacDonald, A. H. Colloquium: Quantum anomalous Hall effect. Rev. Mod. Phys. 95, 011002 (2023).

    Article  ADS  Google Scholar 

  2. Chen, G. et al. Tunable orbital ferromagnetism at noninteger filling of a moiré superlattice. Nano Lett. 22, 238–245 (2022).

    Article  ADS  Google Scholar 

  3. Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiré heterostructure. Science 367, 900–903 (2020).

    Article  ADS  Google Scholar 

  4. Polshyn, H. et al. Electrical switching of magnetic order in an orbital Chern insulator. Nature 588, 66–70 (2020).

    Article  ADS  Google Scholar 

  5. Li, T. et al. Quantum anomalous Hall effect from intertwined moiré bands. Nature 600, 641–646 (2021).

    Article  ADS  Google Scholar 

  6. Balents, L., Dean, C. R., Efetov, D. K. & Young, A. F. Superconductivity and strong correlations in moiré flat bands. Nat. Phys. 16, 725–733 (2020).

    Article  Google Scholar 

  7. Andrei, E. Y. et al. The marvels of moiré materials. Nat. Rev. Mater. 6, 201–206 (2021).

    Article  ADS  Google Scholar 

  8. Zhang, Y.-H., Mao, D., Cao, Y., Jarillo-Herrero, P. & Senthil, T. Nearly flat Chern bands in moiré superlattices. Phys. Rev. B 99, 075127 (2019).

    Article  ADS  Google Scholar 

  9. Zhang, Y., Devakul, T. & Fu, L. Spin-textured Chern bands in AB-stacked transition metal dichalcogenide bilayers. Proc. Natl Acad. Sci. USA 118, e2112673118 (2021).

    Article  Google Scholar 

  10. Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).

    Article  ADS  Google Scholar 

  11. He, W.-Y., Goldhaber-Gordon, D. & Law, K. T. Giant orbital magnetoelectric effect and current-induced magnetization switching in twisted bilayer graphene. Nat. Commun. 11, 1650 (2020).

    Article  ADS  Google Scholar 

  12. Su, Y. & Lin, S.-Z. Current-induced reversal of anomalous Hall conductance in twisted bilayer graphene. Phys. Rev. Lett. 125, 226401 (2020).

    Article  ADS  Google Scholar 

  13. Ying, X., Ye, M. & Balents, L. Current switching of valley polarization in twisted bilayer graphene. Phys. Rev. B 103, 115436 (2021).

    Article  ADS  Google Scholar 

  14. Pan, H., Xie, M., Wu, F. & Das Sarma, S. Topological phases in AB-stacked MoTe2/WSe2 topological insulators, Chern insulators, and topological charge density waves. Phys. Rev. Lett. 129, 056804 (2022).

    Article  ADS  Google Scholar 

  15. Devakul, T., Crépel, V., Zhang, Y. & Fu, L. Magic in twisted transition metal dichalcogenide bilayers. Nat. Commun. 12, 6730 (2021).

    Article  ADS  Google Scholar 

  16. Xie, Y.-M., Zhang, C.-P., Hu, J.-X., Mak, K. F. & Law, K. T. Valley-polarized quantum anomalous Hall state in moiré MoTe2/WSe2 heterobilayers. Phys. Rev. Lett. 128, 026402 (2022).

    Article  ADS  Google Scholar 

  17. Devakul, T. & Fu, L. Quantum anomalous hall Effect from inverted charge transfer gap. Phys. Rev. X 12, 021031 (2022).

    Google Scholar 

  18. Chang, Y.-W. & Chang, Y.-C. Quantum anomalous Hall effect and electric-field-induced topological phase transition in AB-stacked MoTe2/WSe2 moiré heterobilayers. Phys. Rev. B 106, 245412 (2022).

    Article  ADS  Google Scholar 

  19. Jiang, M. et al. Efficient full spin–orbit torque switching in a single layer of a perpendicularly magnetized single-crystalline ferromagnet. Nat. Commun. 10, 2590 (2019).

    Article  ADS  Google Scholar 

  20. Fan, Y. et al. Magnetization switching through giant spin–orbit torque in a magnetically doped topological insulator heterostructure. Nat. Mater. 13, 699–704 (2014).

    Article  ADS  Google Scholar 

  21. Nair, N. L. et al. Electrical switching in a magnetically intercalated transition metal dichalcogenide. Nat. Mater. 19, 153–157 (2020).

    Article  ADS  Google Scholar 

  22. Vasyukov, D. et al. A scanning superconducting quantum interference device with single electron spin sensitivity. Nat. Nanotechnol. 8, 639–644 (2013).

    Article  ADS  Google Scholar 

  23. Anahory, Y. et al. SQUID-on-tip with single-electron spin sensitivity for high-field and ultra-low temperature nanomagnetic imaging. Nanoscale 12, 3174–3182 (2020).

    Article  Google Scholar 

  24. Brandt, N. B., Chudinov, S. M., & Ponomarev, Ya. G. Semimetals 175–196 (Elsevier, 1988).

  25. Tschirhart, C. L. et al. Imaging orbital ferromagnetism in a moiré Chern insulator. Science 372, 1323–1327 (2021).

    Article  ADS  Google Scholar 

  26. Thiel, L. et al. Probing magnetism in 2D materials at the nanoscale with single-spin microscopy. Science 364, 973–976 (2019).

    Article  ADS  Google Scholar 

  27. Tao, Z. et al. Valley-coherent quantum anomalous Hall state in AB-stacked MoTe2/WSe2 bilayers. Preprint at https://arxiv.org/abs/2208.07452 (2022).

  28. Zhao, W. et al. Realization of the Haldane Chern insulator in a moiré lattice. Preprint at https://arxiv.org/abs/2207.02312 (2022).

  29. Lau, C. N., Bockrath, M. W., Mak, K. F. & Zhang, F. Reproducibility in the fabrication and physics of moiré materials. Nature 602, 41–50 (2022).

    Article  ADS  Google Scholar 

  30. Shao, Q. et al. Roadmap of spin–orbit torques. IEEE Trans. Magn. 57, 1–39 (2021).

    Article  Google Scholar 

  31. Hidding, J. & Guimarães, M. H. D. Spin–orbit torques in transition metal dichalcogenide/ferromagnet heterostructures. Front. Mater. 7, 594771 (2020).

    Article  Google Scholar 

  32. Kato, Y. K., Myers, R. C., Gossard, A. C. & Awschalom, D. D. Observation of the spin Hall effect in semiconductors. Science 306, 1910–1913 (2004).

    Article  ADS  Google Scholar 

  33. Lee, J., Mak, K. F. & Shan, J. Electrical control of the valley Hall effect in bilayer MoS2 transistors. Nat. Nanotechnol. 11, 421–425 (2016).

    Article  ADS  Google Scholar 

  34. Chen, G. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020).

    Article  ADS  Google Scholar 

  35. Deng, Y. et al. Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi2Te4. Science 367, 895–900 (2020).

    Article  ADS  Google Scholar 

  36. Zhou, H. et al. Half- and quarter-metals in rhombohedral trilayer graphene. Nature 598, 429–433 (2021).

    Article  ADS  Google Scholar 

  37. Zhou, H. et al. Isospin magnetism and spin-polarized superconductivity in Bernal bilayer graphene. Science 375, 774–778 (2022).

    Article  ADS  Google Scholar 

  38. Gupta, V. et al. Manipulation of the van der Waals magnet Cr2Ge2Te6 by spin–orbit torques. Nano Lett. 20, 7482–7488 (2020).

    Article  ADS  Google Scholar 

  39. Wang, X. et al. Current-driven magnetization switching in a van der Waals ferromagnet Fe3GeTe2. Sci. Adv. 5, eaaw8904 (2019).

    Article  ADS  Google Scholar 

  40. Schmidt, G., Ferrand, D., Molenkamp, L. W., Filip, A. T. & van Wees, B. J. Fundamental obstacle for electrical spin injection from a ferromagnetic metal into a diffusive semiconductor. Phys. Rev. B 62, R4790–R4793 (2000).

    Article  ADS  Google Scholar 

  41. Vasyukov, D. et al. Imaging stray magnetic field of individual ferromagnetic nanotubes. Nano Lett. 18, 964–970 (2018).

    Article  ADS  Google Scholar 

  42. Uri, A. et al. Nanoscale imaging of equilibrium quantum Hall edge currents and of the magnetic monopole response in graphene. Nat. Phys. 16, 164–170 (2020).

    Article  Google Scholar 

  43. Uri, A. et al. Mapping the twist-angle disorder and Landau levels in magic-angle graphene. Nature 581, 47–52 (2020).

    Article  ADS  Google Scholar 

  44. Roth, A. et al. Nonlocal transport in the quantum spin Hall state. Science 325, 294–297 (2009).

    Article  ADS  Google Scholar 

  45. Young, A. F. et al. Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state. Nature 505, 528–532 (2014).

    Article  ADS  Google Scholar 

  46. Tschirhart, C.L. et al. Data for: Intrinsic spin Hall torque in a moiré Chern magnet. Dryad https://doi.org/10.25349/D9GP7F (2023).

  47. Tschirhart, C.L. et al. Data for: Intrinsic spin Hall torque in a moiré Chern magnet. Zenodo https://doi.org/10.5281/zenodo.7504768 (2023).

Download references

Acknowledgements

We acknowledge discussions with A. Macdonald, D. Ralph, K. Luo, V. Gupta, R. Jain, N. Chao Hu, B. Shen and Z. Tao. Work at UCSB was primarily supported by the Army Research Office under award W911NF-20-2-0166 and by the Gordon and Betty Moore Foundation EPIQS programme under award GBMF9471. Work at Cornell was funded by the Air Force Office of Scientific Research under award no. FA9550-19-1-0390. K.W. and T.T. acknowledge support from JSPS KAKENHI (grant nos. 19H05790, 20H00354 and 21H05233). E.R. and T.A. were supported by the National Science Foundation through Enabling Quantum Leap: Convergent Accelerated Discovery Foundries for Quantum Materials Science, Engineering and Information (Q-AMASE-i) award number DMR-1906325. C.L.T. acknowledges support from the Hertz Foundation and from the National Science Foundation Graduate Research Fellowship Program under grant 1650114.

Author information

Author notes

  1. These authors contributed equally: C. L. Tschirhart, Evgeny Redekop.

Authors and Affiliations

  1. Department of Physics, University of California at Santa Barbara, Santa Barbara, CA, USA

    C. L. Tschirhart, Evgeny Redekop, T. Arp, O. Sheekey & A. F. Young

  2. School of Applied and Engineering Physics, Cornell University, Ithaca, NY, USA

    Lizhong Li, Tingxin Li, Shengwei Jiang, Kin Fai Mak & Jie Shan

  3. International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan

    Takashi Taniguchi

  4. Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan

    Kenji Watanabe

  5. Departments of Physics and Electrical Engineering, University of Colorado Denver, Denver, CO, USA

    M. E. Huber

  6. Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY, USA

    Kin Fai Mak & Jie Shan

  7. Kavli Institute at Cornell for Nanoscale Science, Ithaca, NY, USA

    Kin Fai Mak & Jie Shan

Authors
  1. C. L. Tschirhart
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Evgeny Redekop
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lizhong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tingxin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Shengwei Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. T. Arp
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. O. Sheekey
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Takashi Taniguchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Kenji Watanabe
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. M. E. Huber
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Kin Fai Mak
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. Jie Shan
    View author publications

    You can also search for this author in PubMed Google Scholar

  13. A. F. Young
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

K.F.M., J.S. and A.F.Y. conceived the research project. T.T. and K.W. grew hexagonal boron nitride and highly oriented pyrolytic graphite, which served as the source material for graphite gates. M.E.H., C.L.T., T.A., O.S. and E.R. developed the nanoSQUID microscope. L.L., T.L. and S.J. prepared and tested the devices. C.L.T. and E.R. performed nanoSQUID and transport measurements. C.L.T., E.R. and A.F.Y. analysed the data. C.L.T., T.A., O.S. and E.R. prepared nanoSQUID tips for the measurements. C.L.T., E.R. and A.F.Y. wrote the paper, and all authors commented on the paper.

Corresponding author

Correspondence to A. F. Young.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks Yonglong Xie and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Device schematic.

(a) Optical image of device. Bottom gate is outlined with a dashed line. (b) Schematic of region outlined with a black line in (a). Scan range shown in main text is outlined with dashed line. (c) AFM micrograph of device with contacts and top gate overlaid. (d) Optical image of WSe2 monolayer. (e) Optical image of top gate. (f) Optical image of MoTe2 bilayer attached to monolayer. (g) Optical image of top gate overlapping with WSe2 monolayer.

Extended Data Fig. 2 Electric field sensitivity.

(a) Scanning electron micrograph of nanoSQUID tip with nanometer-scale metal droplets between the superconducting contacts outlined in yellow. Inset shows equivalent circuit, with SQUID in parallel with Coulomb blockaded single electron transistor. (b) Differential conductance ðITip/ðVBG of nanoSQUID tip as a function of heterostructure gate voltage VBG with nanoSQUID positioned above gate. Blue, black, and red lines show three different measurements with different values of voltage applied to the tip (VTip). (c) Integrated current through nanoSQUID tip as a function of VBG. (d) 2D plot of ðITip/ðVBG as a function of both VBG and VTip (e) 2D plot of ITip as a function of both VBG and VTip, showing Coulomb blockade behavior of parasitic electric field sensitivity. Such simple single-electron-transistor-like behavior is rare in nanoSQUIDs; electric field sensitivity is ubiquitous, but usually corresponds to a complex and disordered network of quantum dots and tunnel junctions. (f) NanoSQUID scan of device containing both magnetism and strong electric fields. (g) NanoSQUID scan of same region in a regime with no magnetism. Note the lack of signal above the top gate and contacts, which screen out electric fields from the modulated bottom gate.

Extended Data Fig. 3 Absence of magnetization in ‘holes’.

(a) Magnetization of the device at VTG = -3.755 V and VBG = 7.994 V. (b) Magnetization phase diagrams spatially mapped to the positions where they are taken. (c) Magnetization phase diagram in the ‘hole’ highlighted by light-brown square in panel b. (d) Magnetization phase diagram in the region highlighted with dark-brown on b. The signal in c is negligibly small compared to the signal in the magnetized region d, confirming the absence of the magnetized state in the ‘hole’ for all values of applied gate voltages.

Extended Data Fig. 4 Disorder.

(a) AFM image of MoTe2/WSe2 device. Several types of disorder are evident; examples are outlined in b. There are circular features 10-15 nm in height (outlined in orange), oblong features 0.5 - 1.5 nm in height (outlined in white), jagged-edged features that are known to correspond to dust on the surface of the sample (outlined in blue), and a feature adjacent to a contact 5 - 10 nm in height (green). (c) Image of magnetization of Chern magnet with some identifiable features superimposed. The circular and oblong features destroy magnetism.

Extended Data Fig. 5 Quantization of chiral and helical edge states.

a. Schematic of our AB MoTe2/WSe2 device. b. Two-terminal resistance of device across region imaged here. Contact resistances are small relative to h/e2. c. Magnetic image of region inside dotted line in panel A at gate voltages marked with arrow in panel B. d. Schematic of continuous QAH region with chiral edge states superimposed. e. Schematic of the quantum spin Hall state, with helical edge states superimposed. While the quantum spin Hall state QSH state is invisible to magnetic imaging, we hypothesize that the region of uniformity for the QSH state is identical to the region of uniformity for the QAH state. This is expected under the assumption that the dominant source of long-range inhomogeneity are strains or rotations, as they are in other moiré systems (include citations: uri_mapping_2020). f. Two-terminal conductance through the QAH state. Resistance is approximately quantized, consistent with Landauer-Büttiker model of electronic transport through a single quantum channel. g. Two-terminal conductance through the QSH state. Resistance is approximately quantized and depends only on the number of floating metallic contacts in series, consistent with Landauer-Büttiker model of electronic transport through a pair of counter-propagating quantum channels that equilibrate at each contact (include citations: roth_nonlocal_2009, young_tunable_2014).

Extended Data Fig. 6 Current-induced degradation of quantized transport.

(a) R xy as a function of AC current. Red and black lines correspond to rising and falling magnetic field. Quantization of R xy is degraded by increased AC current. (b) Differential R xy measured using AC current and variable DC current ISD. Red and black lines correspond to positive and negative magnetic fields, respectively. These measurements were performed at VTG = -3.756 V, VBG = 7.943 V.

Extended Data Fig. 7 Tuning fork imaging of static magnetization of domains.

The two columns show the analysis pipeline used to generate Fig. 3c (left column) and Fig. 3d (right column). (a) Static background measured at I = 0 nA. Signal includes both ð BTF as well as electric field and mechanical signals. (b) ð BTF measured at I = +670 nA. (c) Difference in ð BTF obtained by subtracting data in panel a from data in panel b. (d) Magnetic field difference ð Bz corresponding to fringe magnetic fields from the current-switched domain. This is obtained by integrating ð BTF with respect to in-plane coordinates along the vector ð r indicated in the inset (i). Because the magnitude of ð r is not known precisely, we present the data in arbitrary units. (e) Change in magnetization ð mz corresponding to the current switched domain for I = +670 nA. (f-j) The same as a-e, but for I = -670 nA.

Extended Data Fig. 8 Magnetic field dependence of domain dynamics.

Magnetic field dependence of domain dynamics (a) ð BI measured for the domain on the left side of the device as a function of ISD and magnetic field at fixed VBG = 8.2 V. (b) Differential two-terminal resistance ð VSD/ð ISD as a function of ISD and B measured simultaneously with data in panel a. ð VSD/ð ISD at 200 mT has been subtracted from all other values to highlight small variations. Red markers identify minima of ð BI from panel a. Some variations in ð VSD/ð ISD coincide with and thus likely correspond to domain wall motion measured locally in panel a. Other variations may correspond to nucleation and pinning of magnetic domains walls at other locations. (c) ð B_I measurement with large ð ISD=89 nA, and fixed ISD=-175 nA. (d) Illustration of the voltages applied for panels c (gray) and f-h (red, green, and black). The large AC voltage applied in panel c allows us to visualize the full range of domain wall positions for -86 nA >ISD>-264 nA; smaller AC excitations applied in panels e (and f-h) allow us to resolve individual domain wall pinning sites within this range. (e) Dependence of ð BI on ISD measured at three separate positions near the left edge of the device. Domains are pinned at these positions at slightly different values of ISD. (f-h) Real space visualizations of the domain wall positions for the three peak values shown in panel e. The peaks correspond with weak features visible in transport data presented in panel b.

Extended Data Fig. 9 Detail of current-driven domain dynamics I.

(a) Schematic of measurement configuration 1, corresponding to current injected through the top contact with the bottom contact grounded. NanoSQUID is positioned near the left edge of the device. (b) Differential resistance ðVSD/ðISD as a function of ISD and VBG for measurement configuration 1. (c) ð BI measured on the left side of the device as a function of ISD and VBG. This measurement was performed simultaneously with the measurement shown in b. (d) Measurement configuration 2, corresponding to current injected through the bottom contact with the top contact grounded. NanoSQUID is positioned near the right edge of the device. The ISD DC sign convention is consistent between measurement configurations 1 and 2. (e) Differential resistance ð VSD/ð ISD as a function of ISD and VBG for measurement configuration 2. (f) ð BI measured on the right side of the device as a function of ISD and VBG. This measurement was performed simultaneously with measurement shown in e.

Extended Data Fig. 10 Detail of current-driven domain dynamics II.

(a) Differential two-terminal resistance ð VSD/ð ISD. The data are the same as shown in Fig. 3a and Extended Data Fig. 9b, ISD<0 . This dataset uses measurement configuration 1 from Extended Data Fig. 9a. (b) Differential two-terminal resistance ð VSD/ð ISD. The data are the same as shown in Fig. 3b. This dataset uses measurement configuration 2 from Extended Data Fig. 9b and Extended Data Fig. 9e, ISD>0 . (c-h) ð BI in response to AC current ð ISD and DC current ISD, for different values of ISD and ð ISD. The intervals corresponding to the AC modulated current are indicated in panels a and b.

Supplementary information

Supplementary Information

Supplementary Figs. 1–7.

Evolution of magnetization through the magnetic Chern insulator gap over a two-dimensional region.

Source Data Fig. 1

Magnetic transport data.

Source Data Fig. 3

NanoSQUID one-dimensional scans.

Source Data Fig. 4

NanoSQUID two-dimensional scans.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tschirhart, C.L., Redekop, E., Li, L. et al. Intrinsic spin Hall torque in a moiré Chern magnet. Nat. Phys. 19, 807–813 (2023). https://doi.org/10.1038/s41567-023-01979-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-023-01979-8

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing