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Spontaneous topological Hall effect induced by non-coplanar antiferromagnetic order in intercalated van der Waals materials

Nature Physics volume 19, pages 961–968 (2023)Cite this article

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Abstract

In ferromagnets, an electric current generally induces a transverse Hall voltage in proportion to the internal magnetization. This effect is frequently used for the electrical readout of the spin-↑ and spin-↓ states. Although these properties are usually not expected in antiferromagnets, recent theoretical studies predicted that a non-coplanar antiferromagnetic order with finite scalar spin chirality—meaning a solid angle spanned by neighbouring spins—can induce a large spontaneous Hall effect even without a net magnetization or external magnetic field. This phenomenon—the spontaneous topological Hall effect—can potentially be used for the efficient electrical readout of antiferromagnetic states, but it has not been experimentally verified due to a lack of appropriate materials hosting such magnetism. Here we report the discovery of an all-in–all-out-type non-coplanar antiferromagnetic order in triangular lattice compounds CoTa3S6 and CoNb3S6. These compounds are reported to host unconventionally large spontaneous Hall effects despite their vanishingly small net magnetization, and our analysis reveals that it can be explained in terms of the topological Hall effect that originates from the fictitious magnetic field associated with scalar spin chirality. These results indicate that the scalar spin chirality mechanism offers a promising route to the realization of a giant spontaneous Hall response even in compensated antiferromagnets, and highlight intercalated van der Waals magnets as a promising quasi-two-dimensional material platform to enable various non-trivial ways of electrical reading and the possible writing of non-coplanar antiferromagnetic domains.

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Fig. 1: Magnetic and electron transport properties of CoTa3S6.
Fig. 2: Neutron scattering profiles in Phase I at B = 0 for CoTa3S6.
Fig. 3: List of triple-q magnetic structure bases for CoTa3S6.
Fig. 4: All-in–all-out-type non-coplanar antiferromagnetic order in CoTa3S6 and its verification by neutron Laue diffraction experiments.

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The data presented in this paper are available from the corresponding authors on reasonable request.

References

  1. Nagaosa, N. et al. Anomalous Hall effect. Rev. Mod. Phys. 82, 1539 (2010).

    ADS  Google Scholar 

  2. Chen, H. et al. Anomalous Hall effect arising from noncollinear antiferromagnetism. Phys. Rev. Lett. 112, 017205 (2014).

    ADS  Google Scholar 

  3. Nakatsuji, S. et al. Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature. Nature 527, 212–215 (2015).

    Google Scholar 

  4. Nayak, A. et al. Large anomalous Hall effect driven by a nonvanishing Berry curvature in the noncolinear antiferromagnet Mn3Ge. Sci. Adv. 2, 1501870 (2016).

    Google Scholar 

  5. Kuroda, K. et al. Evidence for magnetic Weyl fermions in a correlated metal. Nat. Mater. 16, 1090–1095 (2017).

    Google Scholar 

  6. Higo, T. et al. Large magneto-optical Kerr effect and imaging of magnetic octupole domains in an antiferromagnetic metal. Nat. Photon. 12, 73–78 (2018).

    Google Scholar 

  7. Tsai, H. et al. Electrical manipulation of a topological antiferromagnetic state. Nature 580, 608–613 (2020).

    Google Scholar 

  8. Baltz, V. et al. Antiferromagnetic spintronics. Rev. Mod. Phys. 90, 015005 (2018).

    MathSciNet  ADS  Google Scholar 

  9. Parkin, S. S. S. & Friend, R. H. 3d transition-metal intercalates of the niobium and tantalum dichalcogenides. I. Magnetic properties. Philos. Mag. B 41, 65–93 (1980).

    Google Scholar 

  10. Parkin, S. S. S. & Friend, R. H. 3d transition-metal intercalates of the niobium and tantalum dichalcogenides. II. Transport properties. Philos. Mag. B 41, 95–112 (1980).

    Google Scholar 

  11. Parkin, S. S. P., Marseglia, E. A. & Brown, P. J. Magnetic structure of Co1/3NbS2 and Co1/3TaS2. J. Phys. C: Solid State Phys. 16, 2765 (1983).

    ADS  Google Scholar 

  12. Ghimire, N. J. et al. Large anomalous Hall effect in the chiral-lattice antiferromagnet CoNb3S6. Nat. Commun. 9, 3280 (2018).

    ADS  Google Scholar 

  13. Park, P. et al. Field-tunable toroidal moment and anomalous Hall effect in noncollinear antiferromagnetic Weyl semimetal Co1/3TaS2. npg Quantum Mater. 7, 42 (2022).

    ADS  Google Scholar 

  14. Šmejkal, L. et al. Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets. Sci. Adv. 6, 8809 (2020).

    ADS  Google Scholar 

  15. Park, H. et al. First-principles study of magnetic states and the anomalous Hall conductivity of MNb3S6 (M = Co, Fe, Mn, and Ni). Phys. Rev. Materials 6, 024201 (2022).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  17. 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).

    ADS  Google Scholar 

  18. Akagi, Y. & Motome, Y. Spin chirality ordering and anomalous Hall effect in the ferromagnetic Kondo lattice model on a triangular lattice. J. Phys. Soc. Jpn 79, 083711 (2010).

    ADS  Google Scholar 

  19. Feng, W. et al. Topological magneto-optical effects and their quantization in noncoplanar antiferromagnets. Nat. Commun. 11, 118 (2020).

    ADS  Google Scholar 

  20. Taguchi, Y. et al. Spin chirality, Berry phase, and anomalous Hall effect in a frustrated ferromagnet. Science 291, 2573–2576 (2001).

    Google Scholar 

  21. Neubauer, A. et al. Topological Hall effect in the A phase of MnSi. Phys. Rev. Lett. 102, 186602 (2009).

    ADS  Google Scholar 

  22. Kurumaji, T. et al. Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet. Science 365, 914–918 (2019).

    Google Scholar 

  23. Moon, R. M. et al. Polarization analysis of thermal-neutron scattering. Phys. Rev. 181, 920 (1969).

    ADS  Google Scholar 

  24. Yanagi, Y. et al. Generation of modulated magnetic structures based on cluster multipole expansion: application to α-Mn and CoM3S6. Phys. Rev. B 107, 014407 (2023).

    ADS  Google Scholar 

  25. Seemann, M. et al. Symmetry-imposed shape of linear response tensors. Phys. Rev. B 92, 155138 (2015).

    ADS  Google Scholar 

  26. Ueda, K. et al. Magnetic-field induced multiple topological phases in pyrochlore iridates with Mott criticality. Nat. Commun. 8, 15515 (2017).

    ADS  Google Scholar 

  27. Ueda, K. et al. Spontaneous Hall effect in the Weyl semimetal candidate of all-in all-out pyrochlore iridate. Nat. Commun. 9, 3032 (2018).

    ADS  Google Scholar 

  28. Akagi, Y., Udagawa, M. & Motome, Y. Hidden multiple-spin interactions as an origin of spin scalar chiral order in frustrated Kondo lattice models. Phys. Rev. Lett. 108, 096401 (2012).

    ADS  Google Scholar 

  29. Moriya, T. Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120, 91 (1960).

    ADS  Google Scholar 

  30. Bazhan, A. N. & Bazan, C. H. Weak ferromagnetism in CoF2 and NiF2. JETP 42, 898 (1975).

    ADS  Google Scholar 

  31. Suzuki, M.-T. et al. Multipole expansion for magnetic structures: a generation scheme for a symmetry-adapted orthonormal basis set in the crystallographic point group. Phys. Rev. B 99, 174407 (2019).

    ADS  Google Scholar 

  32. Hirschberger, M. Topological Nernst effect of the two-dimensional skyrmion lattice. Phys. Rev. Lett. 125, 076602 (2020).

    ADS  Google Scholar 

  33. Nomoto, T. & Arita, R. Cluster multipole dynamics in noncollinear antiferromagnets. Phys. Rev. Research 2, 012045(R) (2020).

    ADS  Google Scholar 

  34. Tenasini, G. et al. Giant anomalous Hall effect in quasi-two-dimensional layered antiferromagnet Co1/3NbS2. Phys. Rev. Research 2, 023051 (2020).

    ADS  Google Scholar 

  35. Gong, C. & Zhang, X. Two-dimensional magnetic crystals and emergent heterostructure devices. Science 363, eaav4450 (2019).

    Google Scholar 

  36. Tokura, Y. & Nagaosa, N. Transverse spin forces and non-equilibrium particle dynamics in a circularly polarized vacuum optical trap. Nat. Commun. 9, 3704 (2018).

    Google Scholar 

  37. Takata, S. et al. The design and q resolution of the small and wide angle neutron scattering instrument (TAIKAN) in J-PARC. JPS Conf. Proc. 8, 036020 (2015).

    Google Scholar 

  38. Inamura, Y. et al. Development status of software ‘Utsusemi’ for chopper spectrometers at MLF, J-PARC. J. Phys. Soc. Jpn 82, SA031 (2013).

    Google Scholar 

  39. Ohhara, T. et al. SENJU: a new time-of-flight single-crystal neutron diffractometer at J-PARC. J. Appl. Cryst. 49, 120–127 (2016).

    Google Scholar 

  40. Ohhara, T. et al. Development of data processing software for a new TOF single crystal neutron diffractometer at J-PARC. Nucl. Instrum. Methods Phys. Res. A: Accel. Spectrom. Detect. Assoc. Equip. 600, 195–197 (2009).

    ADS  Google Scholar 

  41. Petricek, V., Dusek, M. & Palatinus, L. Crystallographic computing system JANA2006: general features. Z. Kristallogr. 229, 345–352 (2014).

    Google Scholar 

  42. Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996).

    Google Scholar 

  43. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996).

    ADS  Google Scholar 

  44. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758 (1999).

    ADS  Google Scholar 

  45. Perdew, J. P., Ernzerhof, M. & Burke, K. Rationale for mixing exact exchange with density functional approximations. J. Chem. Phys. 105, 9982 (1996).

    ADS  Google Scholar 

  46. Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188 (1976).

    MathSciNet  ADS  Google Scholar 

  47. Momma, K. & Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Cryst. 44, 1272–1276 (2011).

    Google Scholar 

Download references

Acknowledgements

We thank Y. Taguchi, T. Arima, S. Hayami, Y. Motome, N. Nagaosa and S. Maekawa for enlightening discussions and experimental help. This work was partly supported by Grants-In-Aid for Scientific Research (grant nos. 18H03685, 19H01856, 19H05825, 20H00349, 20H05262, 20K05299, 20K21067, 21H01789, 21H04437, 21H04440, 21H04990, 21K13873, 21K13876, 21K18595, 22H04965) from JSPS; PRESTO (grant nos. JPMJPR18L5, JPMJPR20B4, JPMJPR20L7) and CREST (grant no. JPMJCR1874) from JST; Katsu Research Encouragement Award; and UTEC-UTokyo FSI Research Grant Program of the University of Tokyo, Asahi Glass Foundation and Murata Science Foundation. The neutron scattering experiments at the Materials and Life Science Experimental Facility of the J-PARC and Japan Research Reactor 3 were performed under user programs (proposal nos. 2017L0701, 2020B0119, 21401, 21511 and 22529). The illustration of the crystal structure was drawn by VESTA47.

Author information

Author notes

  1. S. Minami

    Present address: Department of Mechanical Engineering and Sciences, Kyoto University, Kyoto, Japan

Authors and Affiliations

  1. Department of Applied Physics, University of Tokyo, Tokyo, Japan

    H. Takagi, R. Takagi, M. Hirayama, Y. Tokura & S. Seki

  2. Institute of Engineering Innovation, University of Tokyo, Tokyo, Japan

    R. Takagi & S. Seki

  3. PRESTO, Japan Science and Technology Agency (JST), Kawaguchi, Japan

    R. Takagi & S. Seki

  4. RIKEN Center for Emergent Matter Science (CEMS), Wako, Japan

    R. Takagi, M. Hirayama, N. D. Khanh, K. Karube, D. Hashizume, Y. Tokura, R. Arita, T. Nakajima & S. Seki

  5. Department of Physics, University of Tokyo, Tokyo, Japan

    S. Minami

  6. Research Center for Advanced Science and Technology, University of Tokyo, Tokyo, Japan

    T. Nomoto & R. Arita

  7. Neutron Science and Technology Center, Comprehensive Research Organization for Science and Society (CROSS), Tokai, Japan

    K. Ohishi

  8. Center for Computational Materials Science, Institute for Materials Research, Tohoku University, Sendai, Japan

    M.-T. Suzuki & Y. Yanagi

  9. Center for Spintronics Research Network, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, Japan

    M.-T. Suzuki

  10. Liberal Arts and Sciences, Toyama Prefectural University, Imizu, Toyama, Japan

    Y. Yanagi

  11. The Institute for Solid State Physics, University of Tokyo, Kashiwa, Japan

    H. Saito & T. Nakajima

  12. J-PARC Center, Japan Atomic Energy Agency, Tokai, Japan

    R. Kiyanagi

  13. Tokyo College, University of Tokyo, Tokyo, Japan

    Y. Tokura

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Contributions

S.S., H.T. and R.T. planned the project. H.T., R.T., N.D.K., K.K., Y.T. and S.S. prepared the samples and performed the macroscopic measurements. H.T., T. Nakajima, S.S., R.K., K.O., H.S. and D.H. performed the neutron and X-ray diffraction experiments. S.M., T. Nomoto, M.-T.S., Y.Y., M.H. and R.A. performed the theoretical calculations. S.S. and H.T. wrote the manuscript with support from T. Nakajima, S.M. and R.A. All the authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to S. Seki.

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Nature Physics thanks Zurab Guguchia, Saül Vélez and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Figs. 1–11, Notes I–XI and Table 1.

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Takagi, H., Takagi, R., Minami, S. et al. Spontaneous topological Hall effect induced by non-coplanar antiferromagnetic order in intercalated van der Waals materials. Nat. Phys. 19, 961–968 (2023). https://doi.org/10.1038/s41567-023-02017-3

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