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Anomalous spin–orbit torques in magnetic single-layer films


The spin Hall effect couples charge and spin transport1,2,3, enabling electrical control of magnetization4,5. A quintessential example of spin-Hall-related transport is the anomalous Hall effect (AHE)6, first observed in 1880, in which an electric current perpendicular to the magnetization in a magnetic film generates charge accumulation on the surfaces. Here, we report the observation of a counterpart of the AHE that we term the anomalous spin–orbit torque (ASOT), wherein an electric current parallel to the magnetization generates opposite spin–orbit torques on the surfaces of the magnetic film. We interpret the ASOT as being due to a spin-Hall-like current generated with an efficiency of 0.053 ± 0.003 in Ni80Fe20, comparable to the spin Hall angle of Pt7. Similar effects are also observed in other common ferromagnetic metals, including Co, Ni and Fe. First-principles calculations corroborate the order of magnitude of the measured values. This work suggests that a strong spin current with spin polarization transverse to the magnetization can be generated within a ferromagnet, despite spin dephasing8. The large magnitude of the ASOT should be taken into consideration when investigating spin–orbit torques in ferromagnetic/non-magnetic bilayers.

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Fig. 1: Illustrations of the AHE and ASOT.
Fig. 2: Symmetry of the ASOT.
Fig. 3: Dependence of ASOT on current density, angle, thickness and the interface.
Fig. 4: Anomalous spin–orbit torque modifies the net current-induced surface spin torques in a Py/Cu/Pt multilayer.

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Data availability

The MOKE measurement data are available at the Illinois Data Bank at The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

Code availability

The code to numerically simulate the MOKE response using the propagation matrix method is available at the Illinois Data Bank at


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The work carried out at the University of Denver is partially supported by the PROF and by the National Science Foundation under grant no. ECCS-1738679. W.W., D.G.C. and V.O.L. acknowledge support from the NSF-MRSEC under award no. DMR-1720633. T.W., Y.W. and J.Q.X. acknowledge support from the NSF under award no. DMR-1505192. V.P.A. acknowledges support under the Cooperative Research Agreement between the University of Maryland and the National Institute of Standards and Technology Center for Nanoscale Science and Technology, award 70NANB14H209, through the University of Maryland. The authors also thank M. Stiles and E. Jue for critical reading of the manuscript and X. Li for illuminating discussions.

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Authors and Affiliations



X.F. and H.O. conceived the idea and X.F., W.W. and T.W. designed the experiments. T.W. fabricated the sample. T.W., Y.W., W.W., A.R., A.D., T.J.S., D.B. and B.L.Z. patterned and characterized the samples. W.W. performed the MOKE measurements and W.W., X.F., V.O.L., D.G.C. and J.Q.X. analysed the data. V.P.A. and P.M.H. carried out the first-principles calculations. X.F., W.W., V.O.L., V.P.A. and P.M.H. prepared the manuscript. All authors commented on the manuscript.

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Correspondence to Virginia O. Lorenz or Xin Fan.

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Peer review information: Nature Nanotechnology thanks Chi-Feng Pai and other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Notes 1–10, Supplementary Figs. 1–10, Supplementary Table 1.

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Wang, W., Wang, T., Amin, V.P. et al. Anomalous spin–orbit torques in magnetic single-layer films. Nat. Nanotechnol. 14, 819–824 (2019).

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