The Edelstein effect is the origin of the spin-orbit torque: a current-induced torque that is used for the electrical control of ferromagnetic and antiferromagnetic materials. This effect originates from the relativistic spin-orbit coupling, which necessitates utilizing materials with heavy elements. Here, we show that in magnetic materials with non-collinear magnetic order, the Edelstein effect and, consequently, a current-induced torque can exist even in the absence of the spin-orbit coupling. Using group symmetry analysis, model calculations, and realistic simulations on selected compounds, we identify large classes of non-collinear magnet candidates and demonstrate that the current-driven torque is of similar magnitude as the celebrated spin-orbit torque in conventional transition metal structures. We also show that this torque can exist in an insulating material, which could allow for highly efficient electrical control of magnetic order.

Aix Marseille Université CNRS CINaM Marseille France

Grupó de Investigación en Física Aplicada Departamento de Física Universidad del Norte Barranquilla Colombia

Institute of Physics Czech Academy of Sciences Cukrovarnická 10 162 00 Praha 6 Czech Republic

Zobrazit více v PubMed

Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P. Anomalous Hall effect. Rev. Mod. Phys.82, 1539 (2010).10.1103/RevModPhys.82.1539 DOI

Ritzinger, P. & Výborný, K. Anisotropic magnetoresistance: materials, models and applications. R. Soc. Open Sci.10, 230564 (2023). 10.1098/rsos.230564 PubMed DOI PMC

Sinova, J., Valenzuela, S. O., Wunderlich, J., Back, C. H. & Jungwirth, T. Spin Hall effect. Rev. Mod. Phys.87, 1213 (2015).10.1103/RevModPhys.87.1213 DOI

Soumyanarayanan, A., Reyren, N., Fert, A. & Panagopoulos, C. Spin-orbit coupling induced emergent phenomena at surfaces and interfaces. Nature539, 509 (2016). 10.1038/nature19820 PubMed DOI

Manchon, A. et al. Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems. Rev. Mod. Phys.91, 035004 (2019).10.1103/RevModPhys.91.035004 DOI

Sunko, V. et al. Maximal Rashba-like spin splitting via kinetic energy-driven inversion symmetry breaking. Nature549, 492 (2017). 10.1038/nature23898 PubMed DOI

Železný, J. et al. Unidirectional magnetoresistance and spin-orbit torque in NiMnSb. Phys. Rev. B104, 054429 (2021).10.1103/PhysRevB.104.054429 DOI

Pekar, S. & Rashba, E. I. Combined resonance in crystals in inhomogeneous magnetic fields. J. Exp. Theor. Phys.20, 1295 (1965).

Ramazashvili, R. Kramers degeneracy in a magnetic field and Zeeman spin-orbit coupling in antiferromagnetic conductors. Phys. Rev. B79, 184432 (2009).10.1103/PhysRevB.79.184432 PubMed DOI

Shindou, R. & Nagaosa, N. Orbital ferromagnetism and anomalous Hall effect in antiferromagnets on the distorted fcc lattice. Phys. Rev. Lett.87, 116801 (2001). 10.1103/PhysRevLett.87.116801 PubMed DOI

Martin, I. & Batista, C. D. Itinerant electron-driven chiral magnetic ordering and spontaneous quantum Hall effect in triangular lattice models. Phys. Rev. Lett.101, 156402 (2008). 10.1103/PhysRevLett.101.156402 PubMed DOI

Ndiaye, P. B., Abbout, A., Goli, V. M. L. D. P. & Manchon, A. Quantum anomalous Hall effect and Anderson-Chern insulating regime in the noncollinear antiferromagnetic 3Q state. Phys. Rev. B100, 144440 (2019).10.1103/PhysRevB.100.144440 DOI

Zhang, Y., Zelezny, J., Sun, Y., Brink, J. V. D. & Yan, B. Spin Hall effect emerging from a noncollinear magnetic lattice without spin-orbit coupling. N. J. Phys.20, 073028 (2018).10.1088/1367-2630/aad1eb DOI

Zelezný, J., Zhang, Y., Felser, C. & Yan, B. Spin-polarized current in noncollinear antiferromagnets. Phys. Rev. Lett.119, 187204 (2017). 10.1103/PhysRevLett.119.187204 PubMed DOI

Kimata, M. et al. Magnetic and magnetic inverse spin Hall effects in a non-collinear antiferromagnet. Nature565, 627 (2019). 10.1038/s41586-018-0853-0 PubMed DOI

Vasko, F. T. Spin splitting in the spectrum of two-dimensional electrons due to the surface potential. JETP Lett.30, 541 (1979).

Edelstein, V. M. Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems. Solid State Commun.73, 233 (1990).10.1016/0038-1098(90)90963-C DOI

Aronov, A. G. & Lyanda-Geller, Y. B. Nuclear electric resonance and orientation of carrier spins by an electric field. JETP Lett.50, 398 (1989).

Šmejkal, L., Sinova, J. & Jungwirth, T. Emerging research landscape of altermagnetism. Phys. Rev. X12, 040501 (2022).

López-Moreno, S., Romero, A. H., Mejía-López, J., Muñoz, A. & Roshchin, I. V. First-principles study of electronic, vibrational, elastic, and magnetic properties of FeF2 as a function of pressure. Phys. Rev. B85, 134110 (2012).10.1103/PhysRevB.85.134110 DOI

Noda, Y., Ohno, K. & Nakamura, S. Momentum-dependent band spin splitting in semiconducting MnO2: a density functional calculation. Phys. Chem. Chem. Phys.18, 13294–13303 (2016). 10.1039/C5CP07806G PubMed DOI

Okugawa, T., Ohno, K., Noda, Y. & Nakamura, S. Weakly spin-dependent band structures of antiferromagnetic perovskite LaMO3 (M = Cr, Mn, Fe). J. Phys. Condens. Matter30, 075502 (2018). 10.1088/1361-648X/aa9e70 PubMed DOI

Šmejkal, L., González-hernández, R., Jungwirth, T. & Sinova, J. Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets. Sci. Adv.6, eaaz8809 (2020). 10.1126/sciadv.aaz8809 PubMed DOI PMC

Naka, M. et al. Spin current generation in organic antiferromagnets. Nat. Commun.10, 4305 (2019). 10.1038/s41467-019-12229-y PubMed DOI PMC

Hayami, S., Yanagi, Y. & Kusunose, H. Momentum-dependent spin splitting by collinear antiferromagnetic ordering. J. Phys. Soc. Jpn.88, 123702 (2019).10.7566/JPSJ.88.123702 DOI

Ahn, K.-h, Hariki, A., Lee, K.-w & Kuneš, J. Antiferromagnetism in RuO2 as d-wave Pomeranchuk instability. Phys. Rev. B99, 184432 (2019).10.1103/PhysRevB.99.184432 DOI

Yuan, L.-D., Wang, Z., Luo, J.-w, Rashba, E. I. & Zunger, A. Giant momentum-dependent spin splitting in centrosymmetric low-Z antiferromagnets. Phys. Rev. B102, 014422 (2020).10.1103/PhysRevB.102.014422 DOI

González-Hernández, R. et al. Efficient electrical spin-splitter based on non-relativistic collinear antiferromagnetism. Phys. Rev. Lett.126, 127701 (2021). 10.1103/PhysRevLett.126.127701 PubMed DOI

Yuan, L.-D., Wang, Z., Luo, J. W. & Zunger, A. Prediction of low-Z collinear and noncollinear antiferromagnetic compounds having momentum-dependent spin splitting even without spin-orbit coupling. Phys. Rev. Mater.5, 014409 (2021).10.1103/PhysRevMaterials.5.014409 DOI

Šmejkal, L., Sinova, J. & Jungwirth, T. Beyond conventional ferromagnetism and antiferromagnetism: a phase with nonrelativistic spin and crystal rotation symmetry. Phys. Rev. X12, 031042 (2022).

Egorov, S. A., Litvin, D. B. & Evarestov, R. A. Antiferromagnetism-induced spin splitting in systems described by magnetic layer groups. J. Phys. Chem. C125, 16147 (2021).10.1021/acs.jpcc.1c02653 DOI

Šmejkal, L., Hellenes, A. B., González-Hernández, R., Sinova, J. & Jungwirth, T. Giant and tunneling magnetoresistance in unconventional collinear antiferromagnets with nonrelativistic spin-momentum coupling. Phys. Rev. X12, 011028 (2022).

Ghosh, S., Manchon, A. & Železný, J. Unconventional robust spin-transfer torque in noncollinear antiferromagnetic junctions. Phys. Rev. Lett.128, 097702 (2022). 10.1103/PhysRevLett.128.097702 PubMed DOI

Hayami, S., Yanagi, Y. & Kusunose, H. Spontaneous antisymmetric spin splitting in noncollinear antiferromagnets without spin-orbit coupling. Phys. Rev. B101, 220403 (2020).10.1103/PhysRevB.101.220403 DOI

Hayami, S., Yanagi, Y. & Kusunose, H. Bottom-up design of spin-split and reshaped electronic band structures in antiferromagnets without spin-orbit coupling: procedure on the basis of augmented multipoles. Phys. Rev. B102, 144441 (2020).

Hellenes, A. B., Jungwirth, T., Sinova, J. & Šmejkal, L. Unconventional p-wave magnets. Preprint at http://arxiv.org/abs/2309.01607 (2023).

Bihlmayer, G., Noël, P., Vyalikh, D. V., Chulkov, E. V. & Manchon, A. Rashba-like physics in condensed matter. Nat. Rev. Phys.4, 642–659 (2022).

Brinkman, W. F. & Elliott, R. J. Theory of spin-space groups. Proc. R. Soc. A294, 343–358 (1966).

Litvin, D. B. & Opechowski, W. Spin groups. Physica76, 538–554 (1974).10.1016/0031-8914(74)90157-8 DOI

Krempaský, J. et al. Altermagnetic lifting of Kramers spin degeneracy. Nature626, 517–522 (2024). 10.1038/s41586-023-06907-7 PubMed DOI PMC

Hajlaoui, M. et al. Temperature dependence of relativistic valence band splitting induced by an altermagnetic phase transition. Adv. Mater.36, 2314076 (2024). PubMed

Železný, J. et al. Spin-orbit torques in locally and globally non-centrosymmetric crystals: antiferromagnets and ferromagnets. Phys. Rev. B95, 014403 (2017).10.1103/PhysRevB.95.014403 DOI

Bonbien, V. & Manchon, A. Symmetrized decomposition of the Kubo-Bastin formula. Phys. Rev. B102, 085113 (2020).10.1103/PhysRevB.102.085113 DOI

Kurebayashi, H. et al. An antidamping spin-orbit torque originating from the Berry curvature. Nat. Nanotechnol.9, 211 (2014). 10.1038/nnano.2014.15 PubMed DOI

Li, H. et al. Intraband and interband spin-orbit torques in noncentrosymmetric ferromagnets. Phys. Rev. B91, 134402 (2015).10.1103/PhysRevB.91.134402 DOI

Hanke, J.-P., Freimuth, F., Niu, C., Blügel, S. & Mokrousov, Y. Mixed Weyl semimetals and dissipationless magnetization control in insulators. Nat. Commun.8, 1479 (2017). 10.1038/s41467-017-01138-7 PubMed DOI PMC

Železný, J. et al. Relativistic Néel-order fields induced by electrical current in antiferromagnets. Phys. Rev. Lett.113, 157201 (2014). 10.1103/PhysRevLett.113.157201 PubMed DOI

Zhang, X., Liu, Q., Luo, J.-w, Freeman, A. J. & Zunger, A. Hidden spin polarization in inversion-symmetric bulk crystals. Nat. Phys.10, 387 (2014).10.1038/nphys2933 DOI

Zhang, Y., Okamoto, S. & Xiao, D. Spin-Nernst effect in the paramagnetic regime of an antiferromagnetic insulator. Phys. Rev. B98, 035424 (2018).10.1103/PhysRevB.98.035424 DOI

Železný, J. Linear response symmetry. Bitbucket https://bitbucket.org/zeleznyj/linear-response-symmetry (2024).

Freimuth, F., Blügel, S. & Mokrousov, Y. Spin-orbit torques in Co/Pt(111) and Mn/W(001) magnetic bilayers from first principles. Phys. Rev. B90, 174423 (2014).10.1103/PhysRevB.90.174423 DOI

Kurz, P., Bihlmayer, G., Hirai, K. & Blügel, S. Three-dimensional spin structure on a two-dimensional lattice: Mn/Cu(111). Phys. Rev. Lett.86, 1106 (2001). 10.1103/PhysRevLett.86.1106 PubMed DOI

Kato, Y., Martin, I. & Batista, C. D. Stability of the spontaneous quantum Hall state in the triangular Kondo-lattice model. Phys. Rev. Lett.105, 266405 (2010). 10.1103/PhysRevLett.105.266405 PubMed DOI

Endoh, Y. & Ishikawa, Y. Antiferromagnetism of γ iron manganes alloys. J. Phys. Soc. Jpn.30, 1614 (1971).10.1143/JPSJ.30.1614 DOI

Gardner, J. S., Gingras, M. J. & Greedan, J. E. Magnetic pyrochlore oxides. Rev. Mod. Phys.82, 53 (2010).10.1103/RevModPhys.82.53 DOI

Manchon, A., Koo, H. C., Nitta, J., Frolov, S. M. & Duine, R. A. New perspectives for Rashba spin-orbit coupling. Nat. Mater.14, 871 (2015). 10.1038/nmat4360 PubMed DOI

Tomiyoshi, S. Polarized neutron diffraction study of the spin structure of Mn3Sn. J. Phys. Soc. Jpn.51, 803–810 (1982).10.1143/JPSJ.51.803 DOI

Nakatsuji, S., Kiyohara, N. & Higo, T. Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature. Nature527, 212 (2015). 10.1038/nature15723 PubMed DOI

Tsai, H. et al. Electrical manipulation of a topological antiferromagnetic state. Nature580, 608 (2020). 10.1038/s41586-020-2211-2 PubMed DOI

Krishnaswamy, G. K. et al. Time-dependent multistate switching of topological antiferromagnetic order in Mn3Sn. Phys. Rev. Appl.18, 024064 (2022).10.1103/PhysRevApplied.18.024064 DOI

Pal, B. et al. Setting of the magnetic structure of chiral kagome antiferromagnets by a seeded spin-orbit torque. Sci. Adv.8, eabo5930 (2022). 10.1126/sciadv.abo5930 PubMed DOI PMC

Xie, H. et al. Magnetization switching in polycrystalline Mn3Sn thin film induced by self-generated spin-polarized current. Nat. Commun.13, 5744 (2022). 10.1038/s41467-022-33345-2 PubMed DOI PMC

Disseler, S. M. et al. Magnetic structure and ordering of multiferroic hexagonal LuFeO3. Phys. Rev. Lett.114, 217602 (2015). 10.1103/PhysRevLett.114.217602 PubMed DOI

Suresh, P. et al. Magnetic ground state of the multiferroic hexagonal LuFeO3. Phys. Rev. B97, 184419 (2018).10.1103/PhysRevB.97.184419 DOI

Das, H., Wysocki, A. L., Geng, Y., Wu, W. & Fennie, C. J. Bulk magnetoelectricity in the hexagonal manganites and ferrites. Nat. Commun.5, 2998 (2014). 10.1038/ncomms3998 PubMed DOI

Garate, I. & Franz, M. Magnetoelectric response of the time-reversal invariant helical metal. Phys. Rev. B81, 172408 (2010).10.1103/PhysRevB.81.172408 DOI

Tang, J. & Cheng, R. Lossless Spin-Orbit Torque in Antiferromagnetic Topological Insulator MnBi2Te4. Phys. Rev. Lett. 132, 136701 (2024). PubMed

Qi, X.-L., Hughes, T. L. & Zhang, S.-C. Topological field theory of time-reversal invariant insulators. Phys. Rev. B78, 195424 (2008).10.1103/PhysRevB.78.195424 DOI

Chen, H., Niu, Q. & Macdonald, A. H. Anomalous Hall effect arising from noncollinear antiferromagnetism. Phys. Rev. Lett.112, 017205 (2014). 10.1103/PhysRevLett.112.017205 PubMed DOI

Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B54, 11169–11186 (1996).10.1103/PhysRevB.54.11169 PubMed DOI

Pizzi, G. et al. Wannier90 as a community code: new features and applications. J. Phys. Condens. Matter32, 165902 (2020). 10.1088/1361-648X/ab51ff PubMed DOI

Železný, J. Wannier linear response. Bitbucket https://bitbucket.org/zeleznyj/wannier-linear-response (2024).