Emergent electromagnetic induction in a helical-spin magnet

This article has been updated


An inductor, one of the most fundamental circuit elements in modern electronic devices, generates a voltage proportional to the time derivative of the input current1. Conventional inductors typically consist of a helical coil and induce a voltage as a counteraction to time-varying magnetic flux penetrating the coil, following Faraday’s law of electromagnetic induction. The magnitude of this conventional inductance is proportional to the volume of the inductor’s coil, which hinders the miniaturization of inductors2. Here, we demonstrate an inductance of quantum-mechanical origin3, generated by the emergent electric field induced by current-driven dynamics of spin helices in a magnet. In microscale rectangular magnetic devices with nanoscale spin helices, we observe a typical inductance as large as −400 nanohenry, comparable in magnitude to that of a commercial inductor, but in a volume about a million times smaller. The observed inductance is enhanced by nonlinearity in current and shows non-monotonous frequency dependence, both of which result from the current-driven dynamics of the spin-helix structures. The magnitude of the inductance rapidly increases with decreasing device cross-section, in contrast to conventional inductors. Our findings may pave the way to microscale, simple-shaped inductors based on emergent electromagnetism related to the quantum-mechanical Berry phase.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Concept of emergent inductance.
Fig. 2: Emergent inductance in Gd3Ru4Al12.
Fig. 3: Nonlinearity of emergent inductance.
Fig. 4: Frequency dependence of emergent inductance.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Change history

  • 02 November 2020

    This Article was amended to correct the Peer review information, which was originally incorrect.


  1. 1.

    Landau, L. D. & Lifshitz, E. M. Electrodynamics of Continuous Media Ch. 32 (Pergamon, 1960).

  2. 2.

    Kang, J. et al. On-chip intercalated-graphene inductors for next-generation radio frequency electronics. Nat. Electron. 1, 46–51 (2018).

    Article  Google Scholar 

  3. 3.

    Nagaosa, N. Emergent inductor by spiral magnets. Jpn J. Appl. Phys. 58, 120909 (2019).

    ADS  CAS  Article  Google Scholar 

  4. 4.

    Meservey, R. & Tedrow, P. M. Measurements of the kinetic inductance of superconducting linear structures. J. Appl. Phys. 40, 2028 (1969).

    ADS  Article  Google Scholar 

  5. 5.

    Berry, M. V. Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. Lond. A 392, 45–57 (1984).

    ADS  MathSciNet  Article  Google Scholar 

  6. 6.

    Xiao, D., Chang, M.-C. & Niu, Q. Berry phase effects on electronic properties. Rev. Mod. Phys. 82, 1959–2007 (2010).

    ADS  MathSciNet  CAS  Article  Google Scholar 

  7. 7.

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

    ADS  CAS  Article  PubMed  Google Scholar 

  8. 8.

    Mühlbauer, S. et al. Skyrmion lattice in a chiral magnet. Science 323, 915–919 (2009).

    ADS  Article  PubMed  Google Scholar 

  9. 9.

    Yu, X. Z. et al. Real-space observation of a two-dimensional skyrmion crystal. Nature 465, 901–904 (2010).

    ADS  CAS  Article  PubMed  Google Scholar 

  10. 10.

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

    ADS  CAS  Article  PubMed  PubMed Central  Google Scholar 

  11. 11.

    Volovik, G. E. Linear momentum in ferromagnets. J. Phys. C 20, L83 (1987).

    ADS  Article  Google Scholar 

  12. 12.

    Froelich, J. & Studer, U. M. Gauge invariance and current algebra in nonrelativistic many-body theory. Rev. Mod. Phys. 65, 733–802 (1993).

    ADS  MathSciNet  Article  Google Scholar 

  13. 13.

    Barnes, S. E. & Maekawa, S. Generalization of Faraday’s law to include nonconservative spin forces. Phys. Rev. Lett. 98, 246601 (2007).

    ADS  CAS  Article  PubMed  PubMed Central  Google Scholar 

  14. 14.

    Yang, S. A. et al. Universal electromotive force induced by domain wall motion. Phys. Rev. Lett. 102, 067201 (2009).

    ADS  Article  PubMed  PubMed Central  Google Scholar 

  15. 15.

    Hayashi, M. et al. Time-domain observation of the spinmotive force in permalloy nanowires. Phys. Rev. Lett. 108, 147202 (2012).

    ADS  Article  PubMed  PubMed Central  Google Scholar 

  16. 16.

    Yamane, Y. et al. Continuous generation of spinmotive force in a patterned ferromagnetic film. Phys. Rev. Lett. 107, 236602 (2011).

    ADS  CAS  Article  PubMed  PubMed Central  Google Scholar 

  17. 17.

    Yamane, Y., Ieda, J. & Sinova, J. Electric voltage generation by antiferromagnetic dynamics. Phys. Rev. B 93, 180408 (2016).

    ADS  Article  Google Scholar 

  18. 18.

    Tatara, G. & Kohno, H. Theory of current-driven domain wall motion: spin transfer versus momentum transfer. Phys. Rev. Lett. 92, 086601 (2004).

    ADS  Article  PubMed  PubMed Central  Google Scholar 

  19. 19.

    Gladyshevskii, R. E., Strusievicz, O. R., Cenzual, K. & Parthé, E. Structure of Gd3Ru4Al12, a new member of the EuMg5.2 structure family with minority atom clusters. Acta Crystallogr. B 49, 474–478 (1993).

    Article  Google Scholar 

  20. 20.

    Niermann, J. & Jeitschko, W. Ternary rare earth (R) transition metal aluminides R 3T 4Al12 (T = Ru and Os) with Gd3Ru4Al12 type structure. Z. Inorg. Gen. Chem. 628, 2549 (2002).

    CAS  Google Scholar 

  21. 21.

    Nakamura, S. et al. Spin trimer formation in the metallic compound Gd3Ru4Al12 with a distorted kagome lattice structure. Phys. Rev. B 98, 054410 (2018).

    ADS  CAS  Article  Google Scholar 

  22. 22.

    Chandragiri, V., Iyer, K. K. & Sampathkumaran, E. V. Magnetic behavior of Gd3Ru4Al12, a layered compound with distorted kagomé net. J. Phys. Condens. Matter 28, 286002 (2016).

    Article  PubMed  Google Scholar 

  23. 23.

    Hirschberger, M. et al. Skyrmion phase and competing magnetic orders on a breathing kagomé lattice. Nat. Commun. 10, 5831 (2019).

    ADS  CAS  Article  PubMed  PubMed Central  Google Scholar 

  24. 24.

    Iwasaki, J., Mochizuki, M. & Nagaosa, N. Universal current–velocity relation of skyrmion motion in chiral magnets. Nat. Commun. 4, 1463 (2013).

    ADS  Article  PubMed  Google Scholar 

  25. 25.

    Kleemann, W. Universal domain wall dynamics in disordered ferroic materials. Annu. Rev. Mater. Res. 37, 415 (2007).

    ADS  CAS  Article  Google Scholar 

  26. 26.

    Schulz, T. et al. Emergent electrodynamics of skyrmions in a chiral magnet. Nat. Phys. 8, 301–304 (2012).

    CAS  Article  Google Scholar 

  27. 27.

    Yokouchi, T. et al. Current-induced dynamics of skyrmion strings. Sci. Adv. 4, eaat1115 (2018).

    ADS  CAS  Article  PubMed  PubMed Central  Google Scholar 

  28. 28.

    Funato, H., Kawamura, A. & Kamiyama, K. Realization of negative inductance using variable active–passive reactance (VAPAR). IEEE Trans. Power Electron. 12, 589 (1997).

    ADS  Article  Google Scholar 

  29. 29.

    Zhang, S. L. et al. Room-temperature helimagnetism in FeGe thin films. Sci. Rep. 7, 123 (2017).

    ADS  CAS  Article  PubMed  PubMed Central  Google Scholar 

  30. 30.

    Emori, S., Bauer, U., Ahn, S.-M., Martinez, E. & Beach, G. S. D. Current-driven dynamics of chiral ferromagnetic domain walls. Nat. Mater. 12, 611–616 (2013).

    ADS  CAS  Article  Google Scholar 

  31. 31.

    Yokouchi, T. et al. Formation of in-plane skyrmions in epitaxial MnSi thin films as revealed by planar Hall effect. J. Phys. Soc. Jpn 84, 104708 (2015).

    ADS  Article  Google Scholar 

  32. 32.

    World’s highest inductance values! Expanded lineup of ultra-compact 0201-inch (0603mm)-size high-frequency chip inductors for smartphones — the LQP03TN_02 series-. muRata https://article.murata.com/en-eu/article/expanded-lineup-of-ultra-compact-0201-inch-0603mm-size?intcid5 (2014).

Download references


We thank M. Kawasaki for discussions. This work was supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI (grant no. 19K14667) and Core Research for Evolutional Science and Technology (CREST), Japan Science and Technology Agency (grant no. JPMJCR1874). M.H. was supported as a Humboldt/JSPS International Research Fellow (18F18804).

Author information




Y.T., N.N. and Y.O. conceived the project. T.Y. fabricated the thin-plate devices and conducted transport measurements with assistance from F.K. M.H. grew and characterized the single crystals. T.Y. and N.N. carried out the theoretical analysis. T.Y., Y.T. and N.N. wrote the draft. All authors discussed the results and commented on the manuscript.

Corresponding authors

Correspondence to Tomoyuki Yokouchi or Yoshinori Tokura.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks Seonghoon Woo and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Temperature dependence of longitudinal resistivity.

a, Temperature dependence of resistivity ρxx for the thin-plate sample of Gd3Ru4Al12. b, Magnified image of ρxxT curve around the transition temperature. The transition temperatures (TN1 and TN2) are denoted by inverse triangles.

Extended Data Fig. 2 Magneto-transport properties with H // c-axis.

a–d, Magnetoresistivity for a thin-plate sample of Gd3Ru4Al12 at various temperatures. We determined the TC phase from the dip structure represented by the blue shading. e–h, Magnetic-field derivative of the magnetoresistivity at various temperatures. We ascribe the kinks to the fan-to-ferromagnetic transition (green triangles) and the phase boundaries of the V phase (light blue triangles). The kinks are also observed at the phase boundaries of the skyrmion phase (red squares). il, Magnetic-field dependence of Hall conductivity (σxy) at various temperatures. The red-shaded regions represent the contribution of the topological Hall effect due to the formation of skyrmions.

Extended Data Fig. 3 Frequency dependence of the complex impedance.

Frequency dependence of the imaginary part of the background-subtracted complex impedance (Im ΔZ1f), measured with the lock-in amplifier.

Extended Data Fig. 4 Emergent inductance for various devices with different size and electrode materials.

a–f, Scanning electron microscope images for devices with different sizes and electrode materials. The electrode material is tungsten, except for device 4 in which it is gold. g–k, Magnetic-field dependence of the imaginary part of the background-subtracted impedance (Im ΔZ1f) in thin-plate devices with W electrodes. The green, pink, blue and light blue shading represents H, Sk, TC and fan phases, respectively. l, Magnetic-field dependence of the imaginary part of the complex impedance Im ΔZ1f in a thin-plate device with gold electrodes. m, The magnitude of Im ΔZ1f as a function of the distance of the voltage electrodes (delectrode). The definition of delectrode is shown in the inset. Here, the cross-sectional area is the same for all devices shown in m.

Extended Data Fig. 5 Magneto-transport properties with H parallel to the a-axis.

a, Magnetoresistivity measured with magnetic field (H) and current (I) parallel to the a-axis at 5.5 K. b, c, Magnetic-field dependence of planar Hall resistivity (\({\rho }_{yx}^{{\rm{PHE}}}\)) at 0.4 T (b) and 1.5 T (c). The experimental set-up is shown in the inset in b. The red line in c is a fit to sin 2θH.

Extended Data Fig. 6 Emergent inductance measured with LCR meter.

a, Frequency dependence of complex impedance Z from which we calculated the complex inductance \(\mathop{L}\limits^{ \sim }(\omega )={L}^{{\prime} }(\omega )+i{L}^{{\prime\prime} }(\omega )\) (Fig. 4b). The inset is the magnified view of Im Z in the low-frequency range on a linear scale. Grey shading corresponds to the grey-shaded region in Fig. 4b. b, Frequency dependence of \(\tilde{L}(\omega )\) for a thin-plate device with gold electrodes. ce, Magnetic field dependence of the imaginary part of the complex impedance (Im Z) measured with an LCR meter at various temperatures, for magnetic field applied in the hexagonal plane. See Methods for the procedure for extracting the bulk contribution of Z.

Supplementary information

Supplementary Information

This Supplementary Information file contains the following sections: Current-induced dynamics of helix; Derivation of emergent inductance; The sign of emergent inductance; and Frequency dependence of the current-induced dynamics of a helix.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Yokouchi, T., Kagawa, F., Hirschberger, M. et al. Emergent electromagnetic induction in a helical-spin magnet. Nature 586, 232–236 (2020). https://doi.org/10.1038/s41586-020-2775-x

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing