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Magnetic and magnetic inverse spin Hall effects in a non-collinear antiferromagnet

A Publisher Correction to this article was published on 22 January 2019

This article has been updated


The spin Hall effect (SHE)1,2,3,4,5 achieves coupling between charge currents and collective spin dynamics in magnetically ordered systems and is a key element of modern spintronics6,7,8,9. However, previous research has focused mainly on non-magnetic materials, so the magnetic contribution to the SHE is not well understood. Here we show that antiferromagnets have richer spin Hall properties than do non-magnetic materials. We find that in the non-collinear antiferromagnet10 Mn3Sn, the SHE has an anomalous sign change when its triangularly ordered moments switch orientation. We observe contributions to the SHE (which we call the magnetic SHE) and the inverse SHE (the magnetic inverse SHE) that are absent in non-magnetic materials and that can be dominant in some magnetic materials, including antiferromagnets. We attribute the dominance of this magnetic mechanism in Mn3Sn to the momentum-dependent spin splitting that is produced by non-collinear magnetic order. This discovery expands the horizons of antiferromagnet spintronics and spin–charge coupling mechanisms.

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Fig. 1: Device structure and experimental setup for spin-accumulation detection.
Fig. 2: Spin-accumulation signal.
Fig. 3: Spin pumping and MISHE.
Fig. 4: Model calculation of angular variation for the MSHE.

Data availability

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

Change history

  • 22 January 2019

    In this Letter, the formatting of some of the crystallographic axes was incorrect. This has been corrected online.


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This work is partially supported by CREST (grant numbers JPMJCR15Q5 and JPMJCR18T3), the Japan Science and Technology Agency, Grants-in-Aid for Scientific Research (16H02209, 25707030), Grants-in-Aids for Scientific Research on Innovative Areas (15H05882, 15H05883, 26103001, 26103002) and the Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers (R2604) from the Japanese Society for the Promotion of Science. H.C. and A.H.M. were supported by SHINES, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Basic Energy Sciences, under award SC0012670.

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Authors and Affiliations



Y. Otani and S.N. planned the experimental project, and M.K., Y. Omori, M.I., T.T., S.S., P.K.M. and K.K. fabricated the devices. M.K., S.S. and K.K. performed the experiments and collected data. H.C. and A.H.M. performed the theoretical analyses. M.K., H.C., K.K., S.N., A.H.M. and Y. Otani wrote the manuscript, and M.K., K.K. and H.C. prepared the Methods section and the figures. All authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to Yoshichika Otani.

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Extended data figures and tables

Extended Data Fig. 1 Switching field of microfabricated Mn3Sn signle crystals.

a, External-magnetic-field dependence of AHE resistance in the spin-accumulation device. The resistance jump around ±2,000 Oe corresponds to the magnetization reversal of the microfabricated Mn3Sn crystal. The observed AHE resistance is much smaller than that expected in the bulk samples because the AHE signal in this device arises from the slight tilting of the sample’s basal plane from the crystallographic kagome plane. b, External-magnetic-field dependence of d.c. voltage under the application of an a.c. current in the spin-pumping device. The sharp voltage jumps around ±1,200 Oe correspond to the magnetization reversal field Hc of Mn3Sn.

Extended Data Fig. 2 Comparison of FMR-induced d.c. voltage signals in NiFe/Mn3Sn bilayer and NiFe single layers.

External-magnetic-field dependence of d.c. voltage signal under FMR excitation. The green and blue lines are symmetric and asymmetric voltage contributions, respectively. The voltage signals are normalized by the asymmetric voltage amplitude. The symmetric voltage contribution in the NiFe/Mn3Sn bilayer (left) is considerably enhanced compared with that of the Ni80Fe20 single layer (right); Py, permalloy.

Extended Data Fig. 3 Frequency and angular dependence of spin-pumping experiment.

a, Frequency dependence of the ratio between symmetric (Vsym) and asymmetric (Vanti) voltage contributions for f = 10–13 GHz. The value of Vsym/Vanti is independent of the microwave frequency. b, Magnetic-field-angle dependence of symmetric voltage signals at several microwave frequencies.

Extended Data Fig. 4 Toy model for MSHE and MISHE calculations.

Left, bilayer kagome toy model mimicking the (0001) surface of Mn3Sn. Right, band structure of the toy model with Λ = 0.1t, J = 1.5t and λR = 0.2t. The horizontal axis shows the wavevector k nomalized by the lattice constant a.

Extended Data Fig. 5 Angular dependence of interband contribution of current-induced spin density.

Interband contribution to the current (along x) induced spin density for the toy model in equation (19) with Λ = 0.1t, J = 1.5t and λR = 0.2t. Only the first half of the rotation (anticlockwise, from 0 to π) is shown. The second half is related to the first through time reversal.

Extended Data Fig. 6 Calculated intraband contribution of time-dependent current induced by magnetization precession.

Intraband contribution to the time-dependent current induced by precessing magnetization for the model described by equations (12) and (23) with Λ = 0.2t, J = 0, λR = 0.2t, θ = 0.1, |Δ| = 0.5t, EF = 2t and kBT = 0.1t (EF, Fermi energy; kB, Boltzmann constant).

Extended Data Fig. 7 Calculated intraband contribution of time-dependent current induced by magnetization precession without spin–orbit interaction.

Intraband contribution to the time-dependent current induced by precessing magnetization for the model described by equations (12) and (23) without spin–orbit coupling. The other parameters are Λ = 0.2t, J = 0.6t, θ = 0.1, |Δ| = 0.5t, EF = 2t and kBT = 0.1t.

Extended Data Fig. 8 Model calculation of angular dependence for MISHE.

MISHE versus in-plane magnetic-field direction, calculated using the same geometry as the experiment. The parameters are Λ = 0.1t, J = 1.5t, λR = 0.2t, EF = 0 and kBT = 0.1t (for faster convergence of numerical integration over the Brillouin zone).

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Kimata, M., Chen, H., Kondou, K. et al. Magnetic and magnetic inverse spin Hall effects in a non-collinear antiferromagnet. Nature 565, 627–630 (2019).

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