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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Dyakonov, M. I. & Perel, V. I. Possibility of orientating electron spins with current. Sov. J. Exp. Theor. Phys. Lett. 13, 467–469 (1971).
Hirsch, J. E. Spin Hall effect. Phys. Rev. Lett. 83, 1834–1837 (1999).
Kato, Y., Myers, R. C., Gossard, A. C. & Awschalom, D. D. Observation of the spin Hall effect in semiconductors. Science 306, 1910–1913 (2004).
Wunderlich, J., Kaestner, B., Sinova, J. & Jungwirth, T. Experimental observation of the spin-Hall effect in a two-dimensional spin–orbit coupled semiconductor system. Phys. Rev. Lett. 94, 047204 (2005).
Sinova, J. et al. Spin Hall effects. Rev. Mod. Phys. 87, 1213–1260 (2015).
Saitoh, E. et al. Conversion of spin current into charge current at room temperature: inverse spin-Hall effect. Appl. Phys. Lett. 88, 182509 (2006).
Kimura, T., Otani, Y., Sato, T., Takahashi, S. & Maekawa, S. Room-temperature reversible spin Hall effect. Phys. Rev. Lett. 98, 156601 (2007).
Liu, L. et al. Spin-torque switching with the giant spin Hall effect of tantalum. Science 336, 555–558 (2012).
Jungwirth, T. et al. Spin Hall effect devices. Nat. Mater. 11, 382–390 (2012).
Nakatsuji, S. et al. Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature. Nature 527, 212–215 (2015).
Freimuth, F. et al. Spin-orbit torques in Co/Pt(111) and Mn/W(001) magnetic bilayers from first principles. Phys. Rev. B 90, 174423 (2014).
Hals, K. M. D. & Brataas, A. Spin-motive forces and current-induced torques in ferromagnets. Phys. Rev. B 91, 214401 (2015).
Freimuth, F., Blügel, S. & Mokrousov, Y. Direct and inverse spin-orbit torques. Phys. Rev. B 92, 064415 (2015).
Chen, H., Niu, Q. & MacDonald, A. H. Anomalous Hall effect arising from noncollinear antiferromagnetism. Phys. Rev. Lett. 112, 017205 (2014).
Suzuki, M.-T., Koretsune, T., Ochi, M. & Arita, R. Cluster multipole theory for anomalous Hall effect in antiferromagnets. Phys. Rev. B 95, 094406 (2017).
Chien, C. L. & Westgate, C. R. The Hall Effect and its Applications (Plenum, 1980).
Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P. Anomalous Hall effect. Rev. Mod. Phys. 82, 1539–1592 (2010).
Tian, Y., Ye, L. & Jin, X. Proper scaling of the anomalous Hall effect. Phys. Rev. Lett. 103, 087206 (2009).
Morota, M. et al. Indication of intrinsic spin Hall effect in 4d and 5d transition metals. Phys. Rev. B 83, 174405 (2011).
Tserkovnyak, Y., Brataas, A. & Bauer, G. E. W. Enhanced Gilbert damping in thin ferromagnetic films. Phys. Rev. Lett. 88, 117601 (2002).
Harder, M., Cao, Z. X., Gui, Y. S., Fan, X. L. & Hu, C.-M. Analysis of the line shape of electrically detected ferromagnetic resonance. Phys. Rev. B 84, 054423 (2011).
Vasko, F. T. & Raichev, O. E. Quantum Kinetic Theory and Applications (Springer, New York, 2005).
Culcer, D., Sekine, A. & MacDonald, A. H. Inter-band coherence response to electric fields in crystals. Phys. Rev. B 96, 035106 (2017).
Aronov, A. G. & Lyanda-Geller, Y. B. Nuclear electric resonance and orientation of carrier spins by an electric field. JETP Lett. 50, 431–434 (1989).
Edelstein, V. M. Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems. Solid State Commun. 73, 233–235 (1990).
Garate, I. & MacDonald, A. H. Influence of a transport current on magnetic anisotropy in gyrotropic ferromagnets. Phys. Rev. B 80, 134403 (2009).
Železný, J., Zhang, Y., Felser, C. & Yan, B. Spin-polarized current in noncollinear antiferromagnets. Phys. Rev. Lett. 119, 187204 (2017).
Ikhlas, M. et al. Large anomalous Nernst effect at room temperature in a chiral antiferromagnet. Nat. Phys. 13, 1085–1090 (2017).
Fukuma, Y. et al. Giant enhancement of spin accumulation and long-distance spin precession in metallic lateral spin valves. Nat. Mater. 10, 527–531 (2011).
Narita, H. et al. Anomalous Nernst effect in a microfabricated thermoelectric element made of chiral antiferromagnet Mn3Sn. Appl. Phys. Lett. 111, 202404 (2017).
Shiomi, Y. et al. Spin–electricity conversion induced by spin injection into topological insulators. Phys. Rev. Lett. 113, 196601 (2014).
Birss, R. R. Symmetry and Magnetism (North-Holland, Amsterdam, 1966).
Taniguchi, T., Grollier, J. & Stiles, M. D. Spin-transfer torques generated by the anomalous Hall effect and anisotropic magnetoresistance. Phys. Rev. Appl. 3, 044001 (2015).
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.
Extended data figures and tables
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.
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.
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.
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.
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).