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Nanosculpted 3D helices of a magnetic Weyl semimetal with switchable non-reciprocal electron transport

Nature Nanotechnology (2026)Cite this article

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Abstract

The emergent properties of materials are governed by the symmetries of their underlying atomic, spin and charge order. Therefore, intrinsic material properties usually constrain the exploration of symmetry-breaking effects. Focused ion beam (FIB) fabrication now enables the structuring of bulk crystals into ultraprecise transport devices, allowing the study of geometrical symmetry breaking on mesoscopic length scales. Here we extend FIB nanostructuring into three-dimensional, curvilinear geometries. Using single crystals of the high-mobility, centrosymmetric magnetic Weyl semimetal Co3Sn2S2, we sculpt helices with lengths of 3–14 μm, diameters of 1–4 μm and pitches ranging from 500 nm to 2 μm. Lock-in measurements on the helical devices at temperatures between 10 K and 190 K show that the combination of imposed inversion symmetry-breaking geometry and ferromagnetism yields non-reciprocal electron transport—or diode effect—at zero applied magnetic field, exceeding classical self-field expectations by orders of magnitude at low temperatures. We attribute this behaviour to the quasi-ballistic motion of carriers as the mean free path approaches the length scale of the chiral device geometry. Finally, we show that current pulses can switch the magnetization of the device. These results highlight the potential of FIB nanosculpting to engineer symmetry and functionality beyond conventional device geometries.

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Fig. 1: Ion beam sculpting 3D nanohelix devices of crystalline Co3Sn2S2.
Fig. 2: Anomalous non-reciprocity in nanosculpted helix devices of Co3Sn2S2.
Fig. 3: Signature of quasi-ballistic transport in Co3Sn2S2 devices.
Fig. 4: Temperature and size dependence of the electrical non-reciprocity and current-induced, field-free magnetization switching.

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Data availability

All experimental data are available via Zenodo at https://doi.org/10.5281/zenodo.17163308 (ref. 58).

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Acknowledgements

We are grateful for the assistance and guidance of the CEMS Semiconductor Science Research Support Team for the use of cleanroom facilities. We are grateful to members of CEMS as well as H. Isobe, L. Turnbull, C. Donnelly, A. Fernández-Pacheco and M. Hirschberger for the fruitful discussions. This work was supported in part by JSPS KAKENHI (grant nos 23H05431, Y.T.; and 24H00197, 24H02231 and 24K00583, N.N.), the Japan Science and Technology Agency (JST) CREST programme (grant no. JPMJCR20T1, X.Y.) and the RIKEN TRIP initiative. M.T.B. acknowledges the support of the RIKEN Special Postdoctoral Researcher Program and the RIKEN Incentive Research Project scheme.

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Authors and Affiliations

  1. RIKEN Center for Emergent Matter Science, Wako, Japan

    Max T. Birch, Yukako Fujishiro, Ilya Belopolski, Yi-Ling Chiew, Zhuolin Li, Xiuzhen Yu, Naoto Nagaosa, Minoru Kawamura & Yoshinori Tokura

  2. RIKEN Pioneering Research Institute, Wako, Japan

    Yukako Fujishiro

  3. Department of Applied Physics, The University of Tokyo, Tokyo, Japan

    Masataka Mogi & Yoshinori Tokura

  4. Fundamental Quantum Science Program (FQSP), TRIP Headquarters, RIKEN, Wako, Japan

    Naoto Nagaosa

  5. Tokyo College, The University of Tokyo, Tokyo, Japan

    Yoshinori Tokura

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Contributions

M.T.B., N.N., M.K. and Y.T. conceived the project. Y.F. grew the bulk Co3Sn2S2 single crystal. M.T.B. fabricated the FIB devices with support from Y.-L.C. and X.Y. M.T.B. performed the transport measurements and data analysis with support from Y.F., I.B., M.M. and M.K. Y.-L.C. and X.Y. performed the TEM measurements and analysis. Z.L. carried out the COMSOL simulations. M.T.B., N.N. and Y.T. interpreted the data and wrote the paper, along with input and contributions from all coauthors.

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Correspondence to Max T. Birch or Yoshinori Tokura.

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Extended data

Extended Data Fig. 1 Focused ion beam sculpted devices of Co3Sn2S2.

a-f Resistance measured as a function of temperature, and scanning electron micrographs of the six investigated focused ion beam-fabricated devices, with helical pitch L, rod radius R, conducting cross sectional area A, and contact separation D: a, left-handed (LH) helix with L = 1.0 μm, R = 1.0 μm, A = ~ 0.18 μm2, D = 16.4 μm. b, right-handed (RH) helix with L = 1.0 μm, R = 1.0 μm, A = ~ 0.18 μm2, D = 16.8 μm. c, achiral (AC) rod with A = ~ 0.23 μm2, rod length = 9.8 μm and D = 15.9 μm. d, LH helix with L = 0.5 μm, R = 0.5 μm, A = ~ 0.06 μm2, D = 10 μm. e, RH helix with L = 2.0 μm, R = 2.1 μm, A = ~2 μm2, D = 25.7 μm. f, Hall bar with thickness 1.6 μm, width 4.1 μm, and contact separation (widest separation) 15.7 μm. In all cases, the Co3Sn2S2 structures were fabricated by Ga ion milling, and fixed to patterned Au electrodes on Al2O3 substrates with in-situ Pt deposition. All scale bars are 10 μm.

Extended Data Fig. 2 Co3Sn2S2 helix device fabrication.

a A schematic illustration of the helix device FIB fabrication process. b Scanning electron micrograph of comb-like Co3Sn2S2 structure, fabricated from a slab extracted from the bulk single crystal, and attached to the copper grid. The scale bar is 10 μm. c A single Co3Sn2S2 rod is picked up by the micromanipulator and transferred to another copper grid, where the scale bar is 5 μm. d The rod is milled with a thread-like pattern from several angles to create the helical shape. The scale bar is 1 μm. e The finished helix-shaped sample is picked up by the micromanipulator and transferred to the Al2O3 substrate and fixed via Pt deposition to the prepatterned Au contacts, creating the final device structure.

Extended Data Fig. 3 Transmission electron microscopy analysis.

a Scanning electron micrograph of an additional helical Co3Sn2S2 sample, prepared using the identical fabrication process, but made thinner to facilitate the transmission imaging. The scale bar is 1 μm. b Thickness map obtained from electron energy-loss spectroscopy (EELS). The inset shows a line profile taken from the top to bottom of the helix, as indicated by the dashed white rectangle, showing a central thickness of ~ 300 nm, tapering to below 150 nm at the edges, making these areas suitable for high-resolution TEM imaging. The scale bar is 500 nm. c TEM image at the outer edge of the example spiral. A ~ 4 nm thick layer consisting of a mixture of amorphous and polycrystalline phases is observed, caused by the ion beam damage during FIB fabrication. The scale bar is 10 nm. d High-resolution TEM image of the region marked by the blue square in c. Clear ordered lattice fringes are observed within the bulk of the helix, confirming the preservation of the single crystalline structure, and indicating that the core Co3Sn2S2 material remains largely unaffected by the FIB fabrication. The scale bar is 5 nm.

Extended Data Fig. 4 Crossover in dominant scattering and nonreciprocal scattering mechanisms.

a-e The upper panels show the first harmonic resistance \({R}_{{xx}}^{1\omega }\) measured as a function of magnetic field, for the left-handed (LH) helix with pitch length L = 1.0 μm, at a range of temperatures and an AC current of 40 μA. The lower panels show the second harmonic resistance \({R}_{{xx}}^{2\omega }\) measured under the same conditions. The result of the self-field estimation is plotted in grey, and has been multiplied by a factor of 30 for comparison. In both cases, there is a crossover behavior as a function of temperature: the scattering and nonreciprocity at low temperature is dominated by the positive, ordinary magnetoresistance, typical of high mobility systems; while at high temperature the temperature-fluctuation spin/magnon scattering, negative magnetoresistance is the main contribution.

Extended Data Fig. 5 Current-induced magnetisation switching efficacy.

a The second harmonic voltage \({V}_{x}^{2\omega }\) measured as a function of magnetic field at 150 K, for the left-handed (LH) helix with pitch length L = 0.5 μm, with an AC current of 40 μA. b The response of the device in the current-induced switching experiment, showing the measured change in the second harmonic longitudinal voltage \(\Delta {V}_{x}^{2\omega }\) at 150 K and zero applied magnetic field, plotted as a function of t, and measured with an AC current of 40 μA. In both plots, the horizontal coloured lines are a guide to the eye. Comparison of the change in \({V}_{x}^{2\omega }\) indicates that close to 100% of the magnetisation is reversed within the helical device.

Extended Data Fig. 6 Characterisation of the Co3Sn2S2 Hall bar device.

a Hall angle, calculated as the ratio of Hall and longitudinal conductivities, σxy/σxx measured as a function of temperature under an applied magnetic field of 3 T. b From the same temperature dependent data, the Hall conductivity is plotted as a function of the longitudinal conductivity. The constant value of σxy over a range of temperatures is commonly taken as an indication of the intrinsic nature of the anomalous Hall conductivity, which here is clearly preserved in the device after focused ion beam patterning. c, d The longitudinal and Hall resistivities, ρxx and ρyx measured as a function of applied magnetic field B at 10 K. e, f The corresponding calculated longitudinal and Hall conductivities at 10 K.

Extended Data Fig. 7 Current dependent measurements of nonreciprocal helical Co3Sn2S2 devices.

a-c First harmonic resistance \({R}_{{xx}}^{1\omega }\) measured as a function of magnetic field B at 10 K with an AC current of 10 μA, for the helical devices with pitch length L = 0.5, 1.0 and 2.0 μm. d-f The antisymmetrised second harmonic voltage \({V}_{x}^{2\omega }\) measured at 10 K with various AC currents, demonstrating the expected I2 scaling for all three devices.

Extended Data Fig. 8 Fitting the current dependent measurements.

The ratio of the second to first harmonic resistances, \({R}_{{xx}}^{2\omega }/{R}_{{xx}}^{1\omega },\) at 10 K and zero applied magnetic field, plotted as a function of the applied current I for the three helical devices with pitch lengths L = 0.5, 1.0 and 2.0 μm, as labelled. Error bars indicate the standard error across 10 data points around B = 0, dominated by the noise in the \({R}_{{xx}}^{2\omega }\) measurement. The linear fits give a value for Γ of each device via the gradient, which is plotted as a function of L in the inset.

Extended Data Fig. 9 Field angle dependent measurements.

a The resistance \({R}_{{xx}}^{1\omega }\) of the right handed (RH) L = 2.0 μm device measured as a function of applied magnetic field B (at angle θ = 90°, indicated in the inset diagram) at 10 K and with an AC current of 140 μA. b The corresponding second harmonic resistance \({R}_{{xx}}^{2\omega }\). c-f The same as a and b, but at θ = 45° and 0°.

Extended Data Fig. 10 Field angle rotation measurements.

a The resistance \({R}_{{xx}}^{1\omega }\) of the right handed (RH) L = 2.0 μm device measured as a function of the applied magnetic field angle θ (indicated in the inset diagram) at 10 K, with an applied magnetic field of 14 T and an AC current of 140 μA. Red and blue indicate up and down measurement directions. b The corresponding second harmonic resistance \({R}_{{xx}}^{2\omega }\). c, d The same as a and b, but at an applied magnetic field of 5 T.

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Birch, M.T., Fujishiro, Y., Belopolski, I. et al. Nanosculpted 3D helices of a magnetic Weyl semimetal with switchable non-reciprocal electron transport. Nat. Nanotechnol. (2026). https://doi.org/10.1038/s41565-025-02104-x

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