{"id":135913,"date":"2025-05-27T12:31:10","date_gmt":"2025-05-27T12:31:10","guid":{"rendered":"https:\/\/www.europesays.com\/uk\/135913\/"},"modified":"2025-05-27T12:31:10","modified_gmt":"2025-05-27T12:31:10","slug":"magnetic-geometry-induced-quantum-geometry-and-nonlinear-transports","status":"publish","type":"post","link":"https:\/\/www.europesays.com\/uk\/135913\/","title":{"rendered":"Magnetic geometry induced quantum geometry and nonlinear transports"},"content":{"rendered":"
  • \n

    Bloembergen, N. Nonlinear optics and spectroscopy. Rev. Mod. Phys. 54<\/b>, 685\u2013695 (1982).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Lakshmanan, M. & Rajaseekar, S. Nonlinear Dynamics: Integrability, Chaos and Patterns (Springer Science & Business Media, 2012).<\/p>\n<\/li>\n

  • \n

    Isobe, H., Xu, S.-Y. & Fu, L. High-frequency rectification via chiral Bloch electrons. Sci. Adv. 6<\/b>, eaay2497 (2020).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n     PubMed Central<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Ideue, T. et al. Bulk rectification effect in a polar semiconductor. Nat. Phys. 13<\/b>, 578\u2013583 (2017).<\/p>\n

    Article<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Sodemann, I. & Fu, L. Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials. Phys. Rev. Lett. 115<\/b>, 216806 (2015).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Ma, Q. et al. Observation of the nonlinear Hall effect under time-reversal-symmetric conditions. Nature 565<\/b>, 337\u2013342 (2019).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Kang, K., Li, T., Sohn, E., Shan, J. & Mak, K. F. Nonlinear anomalous Hall effect in few-layer WTe2. Nat. Mater. 18<\/b>, 324\u2013328 (2019).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Du, Z. Z., Lu, H.-Z. & Xie, X. C. Nonlinear Hall effects. Nat. Rev. Phys. 3<\/b>, 744\u2013752 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Wang, C., Gao, Y. & Xiao, D. Intrinsic nonlinear Hall effect in antiferromagnetic tetragonal CuMnAs. Phys. Rev. Lett. 127<\/b>, 277201 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Liu, H. et al. Intrinsic second-order anomalous Hall effect and its application in compensated antiferromagnets. Phys. Rev. Lett. 127<\/b>, 277202 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Gao, A. et al. Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure. Science 381<\/b>, 181\u2013186 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Wang, N. et al. Quantum-metric-induced nonlinear transport in a topological antiferromagnet. Nature 621<\/b>, 487\u2013492 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Resta, R. The insulating state of matter: a geometrical theory. Eur. Phys. J. B 79<\/b>, 121\u2013137 (2011).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Jungwirth, T., Marti, X., Wadley, P. & Wunderlich, J. Antiferromagnetic spintronics. Nat. Nanotechnol. 11<\/b>, 231\u2013241 (2016).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Baltz, V. et al. Antiferromagnetic spintronics. Rev. Mod. Phys. 90<\/b>, 015005 (2018).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Godinho, J. et al. Electrically induced and detected N\u00e9el vector reversal in a collinear antiferromagnet. Nat. Commun. 9<\/b>, 4686 (2018).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n     PubMed Central<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Shao, D.-F., Zhang, S.-H., Gurung, G., Yang, W. & Tsymbal, E. Y. Nonlinear anomalous Hall effect for N\u00e9el vector detection. Phys. Rev. Lett. 124<\/b>, 067203 (2020).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Chen, W., Gu, M., Li, J., Wang, P. & Liu, Q. Role of hidden spin polarization in nonreciprocal transport of antiferromagnets. Phys. Rev. Lett. 129<\/b>, 276601 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Wang, J., Zeng, H., Duan, W. & Huang, H. Intrinsic nonlinear Hall detection of the N\u00e9el vector for two-dimensional antiferromagnetic spintronics. Phys. Rev. Lett. 131<\/b>, 056401 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Watanabe, H. & Yanase, Y. Nonlinear electric transport in odd-parity magnetic multipole systems: Application to Mn-based compounds. Phys. Rev. Res. 2<\/b>, 043081 (2020).<\/p>\n

    Article<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Kaplan, D., Holder, T. & Yan, B. Unification of nonlinear anomalous Hall effect and nonreciprocal magnetoresistance in metals by the quantum geometry. Phys. Rev. Lett. 132<\/b>, 026301 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Zhong, J. et al. Interface-induced Berry-curvature dipole and second-order nonlinear Hall effect in two-dimensional Fe5GeTe2. Phys. Rev. Appl. 21<\/b>, 024044 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P. Anomalous Hall effect. Rev. Mod. Phys. 82<\/b>, 1539 (2010).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Du, Z. Z., Wang, C. M., Lu, H.-Z. & Xie, X. C. Band signatures for strong nonlinear Hall effect in bilayer WTe2. Phys. Rev. Lett. 121<\/b>, 266601 (2018).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Zhou, B. T., Zhang, C.-P. & Law, K. T. Highly tunable nonlinear Hall effects induced by spin-orbit couplings in strained polar transition-metal dichalcogenides. Phys. Rev. Appl. 13<\/b>, 024053 (2020).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Zhu, Z. H. et al. Anomalous antiferromagnetism in metallic RuO2 determined by resonant X-ray scattering. Phys. Rev. Lett. 122<\/b>, 017202 (2019).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Smolyanyuk, A., Mazin, I. I., Garcia-Gassull, L. & Valent\u00ed, R. Fragility of the magnetic order in the prototypical altermagnet RuO2. Phys. Rev. B 109<\/b>, 134424 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Hiraishi, M. et al. Nonmagnetic ground state in RuO2 revealed by Muon spin rotation. Phys. Rev. Lett. 132<\/b>, 166702 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Gao, Y., Yang, S. A. & Niu, Q. Field induced positional shift of Bloch electrons and its dynamical implications. Phys. Rev. Lett. 112<\/b>, 166601 (2014).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Das, K., Lahiri, S., Atencia, R. B., Culcer, D. & Agarwal, A. Intrinsic nonlinear conductivities induced by the quantum metric. Phys. Rev. B 108<\/b>, L201405 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Wang, Y., Zhang, Z., Zhu, Z.-G. & Su, G. Intrinsic nonlinear Ohmic current. Phys. Rev. B 109<\/b>, 085419 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Nagaosa, N. & Tokura, Y. Emergent electromagnetism in solids. Phys. Scr. 2012<\/b>, 014020 (2012).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Chen, H., Niu, Q. & MacDonald, A. H. Anomalous Hall effect arising from noncollinear antiferromagnetism. Phys. Rev. Lett. 112<\/b>, 017205 (2014).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Hayami, S., Yanagi, Y. & Kusunose, H. Momentum-dependent spin splitting by collinear antiferromagnetic ordering. J. Phys. Soc. Jpn. 88<\/b>, 123702 (2019).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    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<\/b>, 014409 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    \u0160mejkal, L., Sinova, J. & Jungwirth, T. Emerging research landscape of altermagnetism. Phys. Rev. X 12<\/b>, 040501 (2022).<\/p>\n


    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Zhu, Y.-P. et al. Observation of plaid-like spin splitting in a noncoplanar antiferromagnet. Nature 626<\/b>, 523\u2013528 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Krempask\u00fd, J. et al. Altermagnetic lifting of Kramers spin degeneracy. Nature 626<\/b>, 517\u2013522 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n     PubMed Central<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Yan, H., Zhou, X., Qin, P. & Liu, Z. Review on spin-split antiferromagnetic spintronics. Appl. Phys. Lett. 124<\/b>, 030503 (2024).<\/p>\n<\/li>\n

  • \n

    \u017delezn\u00fd, J., Zhang, Y., Felser, C. & Yan, B. Spin-polarized current in noncollinear antiferromagnets. Phys. Rev. Lett. 119<\/b>, 187204 (2017).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Zhang, Y., \u017delezn\u00fd, J., Sun, Y., van den Brink, J. & Yan, B. Spin Hall effect emerging from a noncollinear magnetic lattice without spin\u2013orbit coupling. N. J. Phys. 20<\/b>, 073028 (2018).<\/p>\n

    Article<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Gonz\u00e1lez-Hern\u00e1ndez, R. et al. Efficient electrical spin splitter based on nonrelativistic collinear antiferromagnetism. Phys. Rev. Lett. 126<\/b>, 127701 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Bai, H. et al. Observation of spin splitting torque in a collinear antiferromagnet RuO2. Phys. Rev. Lett. 128<\/b>, 197202 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Shao, D.-F. et al. N\u00e9el spin currents in antiferromagnets. Phys. Rev. Lett. 130<\/b>, 216702 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Watanabe, H., Shinohara, K., Nomoto, T., Togo, A. & Arita, R. Symmetry analysis with spin crystallographic groups: disentangling effects free of spin-orbit coupling in emergent electromagnetism. Phys. Rev. B 109<\/b>, 094438 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Kirikoshi, A. & Hayami, S. Microscopic mechanism for intrinsic nonlinear anomalous Hall conductivity in noncollinear antiferromagnetic metals. Phys. Rev. B 107<\/b>, 155109 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Zhang, Z.-F., Zhu, Z.-G. & Su, G. Symmetry dictionary on charge and spin nonlinear responses for all magnetic point groups with nontrivial topological nature. Natl Sci. Rev. 10<\/b>, nwad104 (2023).<\/p>\n<\/li>\n

  • \n

    Brinkman, W. F. & Elliott, R. J. Theory of spin-space groups. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 294<\/b>, 343\u2013358 (1966).<\/p>\n

    ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Litvin, D. B. & Opechowski, W. Spin groups. Physica 76<\/b>, 538\u2013554 (1974).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Liu, P., Li, J., Han, J., Wan, X. & Liu, Q. Spin-group symmetry in magnetic materials with negligible spin-orbit coupling. Phys. Rev. X 12<\/b>, 021016 (2022).<\/p>\n

    CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Chen, X. et al. Enumeration and representation theory of spin space groups. Phys. Rev. X 14<\/b>, 031038 (2024).<\/p>\n

    CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Xiao, Z., Zhao, J., Li, Y., Shindou, R. & Song, Z.-D. Spin space groups: full classification and applications. Phys. Rev. X 14<\/b>, 031037 (2024).<\/p>\n

    CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Jiang, Y. et al. Enumeration of spin-space groups: toward a complete description of symmetries of magnetic orders. Phys. Rev. X 14<\/b>, 031039 (2024).<\/p>\n

    CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Yang, J., Liu, Z.-X. & Fang, C. Symmetry invariants and classes of quasiparticles in magnetically ordered systems having weak spin-orbit coupling. Nat. Commun. 15<\/b>, 10203 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n     PubMed Central<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Chen, X. et al. Unconventional magnons in collinear magnets dictated by spin space groups. Nature 640<\/b>, 349\u2013354 (2025).<\/p>\n

    Article<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n     PubMed Central<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Gallego, S. V. et al. MAGNDATA: towards a database of magnetic structures. I. The commensurate case. J. Appl. Crystallogr. 49<\/b>, 1750\u20131776 (2016).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Gallego, S. V. et al. MAGNDATA: towards a database of magnetic structures. II. The incommensurate case. J. Appl. Crystallogr. 49<\/b>, 1941\u20131956 (2016).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Liu, Q., Dai, X. & Bl\u00fcgel, S. Different facets of unconventional magnetism. Nat. Phys. 21<\/b>, 329\u2013331 (2025).<\/p>\n

    Article<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Gos\u00e1lbez-Mart\u00ednez, D., Souza, I. & Vanderbilt, D. Chiral degeneracies and Fermi-surface Chern numbers in bcc Fe. Phys. Rev. B 92<\/b>, 085138 (2015).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Ba, J.-Y., Wang, Y.-M., Duan, H.-J., Deng, M.-X. & Wang, R.-Q. Nonlinear planar Hall effect induced by interband transitions: Application to surface states of topological insulators. Phys. Rev. B 108<\/b>, L241104 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Du, Z. Z., Wang, C. M., Li, S., Lu, H.-Z. & Xie, X. C. Disorder-induced nonlinear Hall effect with time-reversal symmetry. Nat. Commun. 10<\/b>, 3047 (2019).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n     PubMed Central<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Du, Z. Z., Wang, C. M., Sun, H.-P., Lu, H.-Z. & Xie, X. C. Quantum theory of the nonlinear Hall effect. Nat. Commun. 12<\/b>, 5038 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n     PubMed Central<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    de Juan, F., Grushin, A. G., Morimoto, T. & Moore, J. E. Quantized circular photogalvanic effect in Weyl semimetals. Nat. Commun. 8<\/b>, 15995 (2017).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n     PubMed Central<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Lu, K. et al. Canted antiferromagnetic order in the monoaxial chiral magnets V1\/3TaS2 and V1\/3NbS2. Phys. Rev. Mater. 4<\/b>, 054416 (2020).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    \u0160mejkal, L., Sinova, J. & Jungwirth, T. Beyond conventional ferromagnetism and antiferromagnetism: a phase with nonrelativistic spin and crystal rotation symmetry. Phys. Rev. X 12<\/b>, 031042 (2022).<\/p>\n


    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Corliss, L. M., Elliott, N., Hastings, J. M. & Sass, R. L. Magnetic structure of chromium selenide. Phys. Rev. 122<\/b>, 1402\u20131406 (1961).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Tajima, Y. et al. Non-coplanar spin structure in a metallic thin film of triangular lattice antiferromagnet CrSe. APL Mater. 12<\/b>, 041112 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Arevalo-Lopez, A. M. & Attfield, J. P. Crystal and magnetic structures of the brownmillerite Ca2Cr2O5. Dalton Trans. 44<\/b>, 10661\u201310664 (2015).<\/p>\n

    Article<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Boehm, M. et al. Complex magnetic ground state of CuB2O4. Phys. Rev. B 68<\/b>, 024405 (2003).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Eriksson, T., Bergqvist, L., Andersson, Y., Nordblad, P. & Eriksson, O. Magnetic properties of selected Mn-based transition metal compounds with \u03b2-Mn structure: experiments and theory. Phys. Rev. B 72<\/b>, 144427 (2005).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Ahn, J., Guo, G.-Y. & Nagaosa, N. Low-frequency divergence and quantum geometry of the bulk photovoltaic effect in topological semimetals. Phys. Rev. X 10<\/b>, 041041 (2020).<\/p>\n

    CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Xiao, C. et al. Intrinsic nonlinear electric spin generation in centrosymmetric magnets. Phys. Rev. Lett. 129<\/b>, 086602 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Xiao, C. et al. Time-reversal-even nonlinear current induced spin polarization. Phys. Rev. Lett. 130<\/b>, 166302 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Lai, S. et al. Third-order nonlinear Hall effect induced by the Berry-connection polarizability tensor. Nat. Nanotechnol. 16<\/b>, 869\u2013873 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Liu, H. et al. Berry connection polarizability tensor and third-order Hall effect. Phys. Rev. B 105<\/b>, 045118 (2022).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Zhang, C.-P., Gao, X.-J., Xie, Y.-M., Po, H. C. & Law, K. T. Higher-order nonlinear anomalous Hall effects induced by Berry curvature multipoles. Phys. Rev. B 107<\/b>, 115142 (2023).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Mandal, D., Sarkar, S., Das, K. & Agarwal, A. Quantum geometry induced third-order nonlinear transport responses. Phys. Rev. B 110<\/b>, 195131 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Fang, Y., Cano, J. & Ghorashi, S. A. A. Quantum geometry induced nonlinear transport in altermagnets. Phys. Rev. Lett. 133<\/b>, 106701 (2024).<\/p>\n

    Article<\/a>\u00a0
    \n     MathSciNet<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Liu, X., Tsirkin, S. S. & Souza, I. Covariant derivatives of Berry-type quantities: application to nonlinear transport. Preprint at https:\/\/arxiv.org\/abs\/2303.10129<\/a> (2023).<\/p>\n<\/li>\n

  • \n

    Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59<\/b>, 1758 (1999).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Kresse, G. & Furthm\u00fcller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54<\/b>, 11169 (1996).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77<\/b>, 3865 (1996).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n     PubMed<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Mostofi, A. A. et al. An updated version of wannier90: a tool for obtaining maximally-localised Wannier functions. Comput. Phys. Commun. 185<\/b>, 2309\u20132310 (2014).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Tsirkin, S. S. High performance Wannier interpolation of Berry curvature and related quantities with WannierBerri code. npj Comput. Mater. 7<\/b>, 33 (2021).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n

  • \n

    Momma, K. & Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 44<\/b>, 1272\u20131276 (2011).<\/p>\n

    Article<\/a>\u00a0
    \n     ADS<\/a>\u00a0
    \n     CAS<\/a>\u00a0
    \n
    \n Google Scholar<\/a>\u00a0\n <\/p>\n<\/li>\n","protected":false},"excerpt":{"rendered":"Bloembergen, N. Nonlinear optics and spectroscopy. Rev. Mod. Phys. 54, 685\u2013695 (1982). Article\u00a0 ADS\u00a0 CAS\u00a0 Google Scholar\u00a0 Lakshmanan,…\n","protected":false},"author":2,"featured_media":135914,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3845],"tags":[20546,3965,11027,3966,74,70,16,15],"class_list":{"0":"post-135913","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-physics","8":"tag-electronic-properties-and-materials","9":"tag-humanities-and-social-sciences","10":"tag-magnetic-properties-and-materials","11":"tag-multidisciplinary","12":"tag-physics","13":"tag-science","14":"tag-uk","15":"tag-united-kingdom"},"share_on_mastodon":{"url":"https:\/\/pubeurope.com\/@uk\/114579816306441426","error":""},"_links":{"self":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts\/135913","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/comments?post=135913"}],"version-history":[{"count":0,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts\/135913\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/media\/135914"}],"wp:attachment":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/media?parent=135913"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/categories?post=135913"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/tags?post=135913"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}