Fiebig, M., Lottermoser, T., Meier, D. & Trassin, M. The evolution of multiferroics. Nat. Rev. Mater. 1, 1–14 (2016).
Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90, 015001 (2018).
Nagaosa, N. & Tokura, Y. Topological properties and dynamics of magnetic skyrmions. Nat. Nanotechnol. 8, 899–911 (2013).
Fert, A., Reyren, N. & Cros, V. Magnetic skyrmions: advances in physics and potential functions. Nat. Rev. Mater. 2, 1–15 (2017).
Manchon, A. et al. Present-induced spin–orbit torques in ferromagnetic and antiferromagnetic methods. Rev. Mod. Phys. 91, 035004 (2019).
Yang, S.-H., Naaman, R., Paltiel, Y. & Parkin, S. S. P. Chiral spintronics. Nat. Rev. Phys. 3, 328–343 (2021).
Fernández-Pacheco, A. et al. Three-dimensional nanomagnetism. Nat. Commun. 8, 15756 (2017).
Sheka, D. D. A perspective on curvilinear magnetism. Appl. Phys. Lett. 118, 230502 (2021).
Gubbiotti, G. et al. 2025 roadmap on 3D nanomagnetism. J. Phys. Condens. Matter 37, 143502 (2025).
Fernández-Pacheco, A. et al. Three dimensional magnetic nanowires grown by centered electron-beam induced deposition. Sci. Rep. 3, 1492 (2013).
Zhakina, E. et al. Reconfigurable three-dimensional superconducting nanoarchitectures. Adv. Funct. Mater. 2506057 (2025).
Donnelly, C. et al. Ingredient-specific X-ray section tomography of 3D buildings on the nanoscale. Phys. Rev. Lett. 114, 115501 (2015).
Meng, F. et al. Non-planar geometrical results on the magnetoelectrical sign in a three-dimensional nanomagnetic circuit. ACS Nano 15, 6765–6773 (2021).
Donnelly, C. et al. Advanced free-space magnetic area textures induced by three-dimensional magnetic nanostructures. Nat. Nanotechnol. 17, 136–142 (2022).
Farinha, A. M. A., Yang, S.-H., Yoon, J., Pal, B. & Parkin, S. S. P. Interaction of geometrical and spin chiralities in 3D twisted magnetic ribbons. Nature 639, 67–72 (2025).
Moll, P. J. W. et al. Subject-induced density wave within the heavy-fermion compound CeRhIn5. Nat. Commun. 6, 6663 (2015).
Moll, P. J. W. Targeted ion beam microstructuring of quantum matter. Annu. Rev. Condens. Matter Phys. 9, 147–162 (2018).
Guo, C. et al. Switchable chiral transport in charge-ordered kagome steel CsV3Sb5. Nature 611, 461–466 (2022).
Höflich, Okay. et al. Roadmap for centered ion beam applied sciences. Appl. Phys. Rev. 10, 041311 (2023).
Turnbull, L. A. et al. Interlinking helical spin textures in nanopatterned chiral magnets. Preprint at https://arxiv.org/abs/2511.11372 (2025).
Liu, E. et al. Large anomalous Corridor impact in a ferromagnetic kagome-lattice semimetal. Nat. Phys. 14, 1125–1131 (2018).
Morali, N. et al. Fermi-arc variety on floor terminations of the magnetic Weyl semimetal Co3Sn2S2. Science 365, 1286–1291 (2019).
Rikken, G. L. J. A., Fölling, J. & Wyder, P. Electrical magnetochiral anisotropy. Phys. Rev. Lett. 87, 236602 (2001).
Wakatsuki, R. et al. Nonreciprocal cost transport in noncentrosymmetric superconductors. Sci. Adv. 3, e1602390 (2017).
Tokura, Y. & Nagaosa, N. Nonreciprocal responses from non-centrosymmetric quantum supplies. Nat. Commun. 9, 3740 (2018).
Atzori, M., Prepare, C., Hillard, E. A., Avarvari, N. & Rikken, G. L. J. A. Magneto-chiral anisotropy: from fundamentals to views. Chirality 33, 844–857 (2021).
Yokouchi, T. et al. Electrical magnetochiral impact induced by chiral spin fluctuations. Nat. Commun. 8, 866 (2017).
Ideue, T. et al. Bulk rectification impact in a polar semiconductor. Nat. Phys. 13, 578–583 (2017).
Tanaka, M. et al. Topological kagome magnet Co3Sn2S2 skinny flakes with excessive electron mobility and enormous anomalous Corridor impact. Nano Lett. 20, 7476–7481 (2020).
He, Y. et al. Giant linear non-saturating magnetoresistance and excessive mobility in ferromagnetic MnBi. Nat. Commun. 12, 4576 (2021).
Morimoto, T. & Nagaosa, N. Chiral anomaly and big magnetochiral anisotropy in noncentrosymmetric Weyl semimetals. Phys. Rev. Lett. 117, 146603 (2016).
Wang, Y. et al. Gigantic magnetochiral anisotropy within the topological semimetal ZrTe5. Phys. Rev. Lett. 128, 176602 (2022).
Yang, S.-Y. et al. Subject-modulated anomalous Corridor conductivity and planar Corridor impact in Co3Sn2S2 nanoflakes. Nano Lett. 20, 7860–7867 (2020).
Maurenbrecher, H. et al. Chiral anisotropic magnetoresistance of ferromagnetic helices. Appl. Phys. Lett. 112, 242401 (2018).
Parrott, J. E. A brand new idea of the scale impact in electrical conduction. Proc. Phys. Soc. 85, 1143 (1965).
Baringhaus, J. et al. Distinctive ballistic transport in epitaxial graphene nanoribbons. Nature 506, 349–354 (2014).
Moll, P. J. W., Kushwaha, P., Nandi, N., Schmidt, B. & Mackenzie, A. P. Proof for hydrodynamic electron circulation in PdCoO2. Science 351, 1061–1064 (2016).
Bachmann, M. D. et al. Directional ballistic transport within the two-dimensional steel PdCoO2. Nat. Phys. 18, 819–824 (2022).
Yasuda, Okay. et al. Giant non-reciprocal cost transport mediated by quantum anomalous Corridor edge states. Nat. Nanotechnol. 15, 831–835 (2020).
Evers, F. et al. Principle of chirality induced spin selectivity: progress and challenges. Adv. Mater. 34, 2106629 (2022).
Shitade, A. & Minamitani, E. Geometric spin–orbit coupling and chirality-induced spin selectivity. New J. Phys. 22, 113023 (2020).
Track, A. M. et al. Nonlinear electron transport in an uneven microjunction: a ballistic rectifier. Phys. Rev. Lett. 80, 3831–3834 (1998).
Kida, N. et al. Optical magnetoelectric impact in a submicron patterned magnet. Phys. Rev. Lett. 94, 077205 (2005).
Isobe, H. & Nagaosa, N. Toroidal scattering and nonreciprocal transport by magnetic impurities. J. Phys. Soc. Jpn 91, 115001 (2022).
Gaididei, Y., Kravchuk, V. P. & Sheka, D. D. Curvature results in skinny magnetic shells. Phys. Rev. Lett. 112, 257203 (2014).
Ishizuka, H. & Nagaosa, N. Anomalous electrical magnetochiral impact by chiral spin-cluster scattering. Nat. Commun. 11, 2986 (2020).
Yamaguchi, D., Kitaori, A., Nagaosa, N. & Tokura, Y. Magnetoelectric management of spin helicity and nonreciprocal cost transport in a multiferroic steel. Adv. Mater. 37, 2420614 (2025).
Nakamura, D. et al. Nonreciprocal transport in a room-temperature chiral magnet. Sci. Adv. 11, eadw8023 (2025).
Jiang, N., Nii, Y., Arisawa, H., Saitoh, E. & Onose, Y. Electrical present management of spin helicity in an itinerant helimagnet. Nat. Commun. 11, 1601 (2020).
Masuda, H. et al. Room temperature chirality switching and detection in a helimagnetic MnAu2 skinny movie. Nat. Commun. 15, 1999 (2024).
González-Hernández, R., Ritzinger, P., Výborný, Okay., Železný, J. & Manchon, A. Non-relativistic torque and Edelstein impact in non-collinear magnets. Nat. Commun. 15, 7663 (2024).
Ando, F. et al. Remark of superconducting diode impact. Nature 584, 373–376 (2020).
Nadeem, M., Fuhrer, M. S. & Wang, X. The superconducting diode impact. Nat. Rev. Phys. 5, 558–577 (2023).
Pop, F., Auban-Senzier, P., Canadell, E., Rikken, G. L. J. A. & Avarvari, N. Electrical magnetochiral anisotropy in a bulk chiral molecular conductor. Nat. Commun. 5, 3757 (2014).
Krstić, V., Roth, S., Burghard, M., Kern, Okay. & Rikken, G. L. J. A. Magneto-chiral anisotropy in cost transport by way of single-walled carbon nanotubes. J. Chem. Phys. 117, 11315–11319 (2002).
Varnavides, G., Yacoby, A., Felser, C. & Narang, P. Cost transport and hydrodynamics in supplies. Nat. Rev. Mater. 8, 726–741 (2023).
Ding, L. et al. Quantum oscillations, magnetic breakdown and thermal Corridor impact in Co3Sn2S2. J. Phys. Appl. Phys. 54, 454003 (2021).
Birch, M. T. et al. Dataset for: Nanosculpted 3D helices of a magnetic Weyl semimetal with switchable nonreciprocal electron transport. Zenodo https://doi.org/10.5281/zenodo.17163308 (2025).