Fiebig, M., Lottermoser, T., Meier, D. & Trassin, M. The evolution of multiferroics. Nat. Rev. Mater. 1, 1–14 (2016).

Article 

Google Scholar
 

Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90, 015001 (2018).

Article 
CAS 

Google Scholar
 

Nagaosa, N. & Tokura, Y. Topological properties and dynamics of magnetic skyrmions. Nat. Nanotechnol. 8, 899–911 (2013).

Article 
CAS 
PubMed 

Google Scholar
 

Fert, A., Reyren, N. & Cros, V. Magnetic skyrmions: advances in physics and potential applications. Nat. Rev. Mater. 2, 1–15 (2017).

Article 

Google Scholar
 

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

Article 
CAS 

Google Scholar
 

Yang, S.-H., Naaman, R., Paltiel, Y. & Parkin, S. S. P. Chiral spintronics. Nat. Rev. Phys. 3, 328–343 (2021).

Article 

Google Scholar
 

Fernández-Pacheco, A. et al. Three-dimensional nanomagnetism. Nat. Commun. 8, 15756 (2017).

Article 
PubMed 
PubMed Central 

Google Scholar
 

Sheka, D. D. A perspective on curvilinear magnetism. Appl. Phys. Lett. 118, 230502 (2021).

Article 
CAS 

Google Scholar
 

Gubbiotti, G. et al. 2025 roadmap on 3D nanomagnetism. J. Phys. Condens. Matter 37, 143502 (2025).

Article 
CAS 

Google Scholar
 

Fernández-Pacheco, A. et al. Three dimensional magnetic nanowires grown by focused electron-beam induced deposition. Sci. Rep. 3, 1492 (2013).

Article 
PubMed 
PubMed Central 

Google Scholar
 

Zhakina, E. et al. Reconfigurable three-dimensional superconducting nanoarchitectures. Adv. Funct. Mater. 2506057 (2025).

Donnelly, C. et al. Element-specific X-ray phase tomography of 3D structures at the nanoscale. Phys. Rev. Lett. 114, 115501 (2015).

Article 
PubMed 

Google Scholar
 

Meng, F. et al. Non-planar geometrical effects on the magnetoelectrical signal in a three-dimensional nanomagnetic circuit. ACS Nano 15, 6765–6773 (2021).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Donnelly, C. et al. Complex free-space magnetic field textures induced by three-dimensional magnetic nanostructures. Nat. Nanotechnol. 17, 136–142 (2022).

Article 
CAS 
PubMed 

Google Scholar
 

Farinha, A. M. A., Yang, S.-H., Yoon, J., Pal, B. & Parkin, S. S. P. Interplay of geometrical and spin chiralities in 3D twisted magnetic ribbons. Nature 639, 67–72 (2025).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Moll, P. J. W. et al. Field-induced density wave in the heavy-fermion compound CeRhIn5. Nat. Commun. 6, 6663 (2015).

Article 
CAS 
PubMed 

Google Scholar
 

Moll, P. J. W. Focused ion beam microstructuring of quantum matter. Annu. Rev. Condens. Matter Phys. 9, 147–162 (2018).

Article 

Google Scholar
 

Guo, C. et al. Switchable chiral transport in charge-ordered kagome metal CsV3Sb5. Nature 611, 461–466 (2022).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Höflich, K. et al. Roadmap for focused ion beam technologies. Appl. Phys. Rev. 10, 041311 (2023).

Article 

Google Scholar
 

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. Giant anomalous Hall effect in a ferromagnetic kagome-lattice semimetal. Nat. Phys. 14, 1125–1131 (2018).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Morali, N. et al. Fermi-arc diversity on surface terminations of the magnetic Weyl semimetal Co3Sn2S2. Science 365, 1286–1291 (2019).

Article 
CAS 
PubMed 

Google Scholar
 

Rikken, G. L. J. A., Fölling, J. & Wyder, P. Electrical magnetochiral anisotropy. Phys. Rev. Lett. 87, 236602 (2001).

Article 
CAS 
PubMed 

Google Scholar
 

Wakatsuki, R. et al. Nonreciprocal charge transport in noncentrosymmetric superconductors. Sci. Adv. 3, e1602390 (2017).

Article 
PubMed 
PubMed Central 

Google Scholar
 

Tokura, Y. & Nagaosa, N. Nonreciprocal responses from non-centrosymmetric quantum materials. Nat. Commun. 9, 3740 (2018).

Article 
PubMed 
PubMed Central 

Google Scholar
 

Atzori, M., Train, C., Hillard, E. A., Avarvari, N. & Rikken, G. L. J. A. Magneto-chiral anisotropy: from fundamentals to perspectives. Chirality 33, 844–857 (2021).

Article 
CAS 
PubMed 

Google Scholar
 

Yokouchi, T. et al. Electrical magnetochiral effect induced by chiral spin fluctuations. Nat. Commun. 8, 866 (2017).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Ideue, T. et al. Bulk rectification effect in a polar semiconductor. Nat. Phys. 13, 578–583 (2017).

Article 
CAS 

Google Scholar
 

Tanaka, M. et al. Topological kagome magnet Co3Sn2S2 thin flakes with high electron mobility and large anomalous Hall effect. Nano Lett. 20, 7476–7481 (2020).

Article 
CAS 
PubMed 

Google Scholar
 

He, Y. et al. Large linear non-saturating magnetoresistance and high mobility in ferromagnetic MnBi. Nat. Commun. 12, 4576 (2021).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Morimoto, T. & Nagaosa, N. Chiral anomaly and giant magnetochiral anisotropy in noncentrosymmetric Weyl semimetals. Phys. Rev. Lett. 117, 146603 (2016).

Article 
PubMed 

Google Scholar
 

Wang, Y. et al. Gigantic magnetochiral anisotropy in the topological semimetal ZrTe5. Phys. Rev. Lett. 128, 176602 (2022).

Article 
CAS 
PubMed 

Google Scholar
 

Yang, S.-Y. et al. Field-modulated anomalous Hall conductivity and planar Hall effect in Co3Sn2S2 nanoflakes. Nano Lett. 20, 7860–7867 (2020).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Maurenbrecher, H. et al. Chiral anisotropic magnetoresistance of ferromagnetic helices. Appl. Phys. Lett. 112, 242401 (2018).

Article 

Google Scholar
 

Parrott, J. E. A new theory of the size effect in electrical conduction. Proc. Phys. Soc. 85, 1143 (1965).

Article 

Google Scholar
 

Baringhaus, J. et al. Exceptional ballistic transport in epitaxial graphene nanoribbons. Nature 506, 349–354 (2014).

Article 
CAS 
PubMed 

Google Scholar
 

Moll, P. J. W., Kushwaha, P., Nandi, N., Schmidt, B. & Mackenzie, A. P. Evidence for hydrodynamic electron flow in PdCoO2. Science 351, 1061–1064 (2016).

Article 
CAS 
PubMed 

Google Scholar
 

Bachmann, M. D. et al. Directional ballistic transport in the two-dimensional metal PdCoO2. Nat. Phys. 18, 819–824 (2022).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Yasuda, K. et al. Large non-reciprocal charge transport mediated by quantum anomalous Hall edge states. Nat. Nanotechnol. 15, 831–835 (2020).

Article 
CAS 
PubMed 

Google Scholar
 

Evers, F. et al. Theory of chirality induced spin selectivity: progress and challenges. Adv. Mater. 34, 2106629 (2022).

Article 
CAS 

Google Scholar
 

Shitade, A. & Minamitani, E. Geometric spin–orbit coupling and chirality-induced spin selectivity. New J. Phys. 22, 113023 (2020).

Article 
CAS 

Google Scholar
 

Song, A. M. et al. Nonlinear electron transport in an asymmetric microjunction: a ballistic rectifier. Phys. Rev. Lett. 80, 3831–3834 (1998).

Article 
CAS 

Google Scholar
 

Kida, N. et al. Optical magnetoelectric effect in a submicron patterned magnet. Phys. Rev. Lett. 94, 077205 (2005).

Article 
CAS 
PubMed 

Google Scholar
 

Isobe, H. & Nagaosa, N. Toroidal scattering and nonreciprocal transport by magnetic impurities. J. Phys. Soc. Jpn 91, 115001 (2022).

Article 

Google Scholar
 

Gaididei, Y., Kravchuk, V. P. & Sheka, D. D. Curvature effects in thin magnetic shells. Phys. Rev. Lett. 112, 257203 (2014).

Article 
PubMed 

Google Scholar
 

Ishizuka, H. & Nagaosa, N. Anomalous electrical magnetochiral effect by chiral spin-cluster scattering. Nat. Commun. 11, 2986 (2020).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Yamaguchi, D., Kitaori, A., Nagaosa, N. & Tokura, Y. Magnetoelectric control of spin helicity and nonreciprocal charge transport in a multiferroic metal. Adv. Mater. 37, 2420614 (2025).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Nakamura, D. et al. Nonreciprocal transport in a room-temperature chiral magnet. Sci. Adv. 11, eadw8023 (2025).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Jiang, N., Nii, Y., Arisawa, H., Saitoh, E. & Onose, Y. Electric current control of spin helicity in an itinerant helimagnet. Nat. Commun. 11, 1601 (2020).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

Masuda, H. et al. Room temperature chirality switching and detection in a helimagnetic MnAu2 thin film. Nat. Commun. 15, 1999 (2024).

Article 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

González-Hernández, R., Ritzinger, P., Výborný, K., Železný, J. & Manchon, A. Non-relativistic torque and Edelstein effect in non-collinear magnets. Nat. Commun. 15, 7663 (2024).

Article 
PubMed 
PubMed Central 

Google Scholar
 

Ando, F. et al. Observation of superconducting diode effect. Nature 584, 373–376 (2020).

Article 
CAS 
PubMed 

Google Scholar
 

Nadeem, M., Fuhrer, M. S. & Wang, X. The superconducting diode effect. Nat. Rev. Phys. 5, 558–577 (2023).

Article 

Google Scholar
 

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).

Article 
PubMed 

Google Scholar
 

Krstić, V., Roth, S., Burghard, M., Kern, K. & Rikken, G. L. J. A. Magneto-chiral anisotropy in charge transport through single-walled carbon nanotubes. J. Chem. Phys. 117, 11315–11319 (2002).

Article 

Google Scholar
 

Varnavides, G., Yacoby, A., Felser, C. & Narang, P. Charge transport and hydrodynamics in materials. Nat. Rev. Mater. 8, 726–741 (2023).

Article 
CAS 

Google Scholar
 

Ding, L. et al. Quantum oscillations, magnetic breakdown and thermal Hall effect in Co3Sn2S2. J. Phys. Appl. Phys. 54, 454003 (2021).

Article 
CAS 

Google Scholar
 

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).