Emergent dynamic chirality in a thermally driven artificial spin ratchet

Published online:


Modern nanofabrication techniques have opened the possibility to create novel functional materials, whose properties transcend those of their constituent elements. In particular, tuning the magnetostatic interactions in geometrically frustrated arrangements of nanoelements called artificial spin ice1,2 can lead to specific collective behaviour3, including emergent magnetic monopoles4,5, charge screening6,7 and transport8,9, as well as magnonic response10,11,12. Here, we demonstrate a spin-ice-based active material in which energy is converted into unidirectional dynamics. Using X-ray photoemission electron microscopy we show that the collective rotation of the average magnetization proceeds in a unique sense during thermal relaxation. Our simulations demonstrate that this emergent chiral behaviour is driven by the topology of the magnetostatic field at the edges of the nanomagnet array, resulting in an asymmetric energy landscape. In addition, a bias field can be used to modify the sense of rotation of the average magnetization. This opens the possibility of implementing a magnetic Brownian ratchet13,14, which may find applications in novel nanoscale devices, such as magnetic nanomotors, actuators, sensors or memory cells.

  • Subscribe to Nature Materials for full access:



Additional access options:

Already a subscriber?  Log in  now or  Register  for online access.


  1. 1.

    et al. Artificial ‘spin ice’ in a geometrically frustrated lattice of nanoscale ferromagnetic islands. Nature 439, 303–306 (2006).

  2. 2.

    & Artificial ferroic systems: novel functionality from structure, interactions and dynamics. J. Phys. Condens. Matter 25, 363201 (2013).

  3. 3.

    , & Unhappy vertices in artificial spin ice: new degeneracies from vertex frustration. New J. Phys. 15, 045009 (2013).

  4. 4.

    et al. Real-space observation of emergent magnetic monopoles and associated Dirac strings in artificial kagome spin ice. Nat. Phys. 7, 68–74 (2010).

  5. 5.

    Dynamics of bound monopoles in artificial spin ice: How to store energy in Dirac strings. Phys. Rev. Lett. 116, 077202 (2016).

  6. 6.

    et al. Emergent ice rule and magnetic charge screening from vertex frustration in artificial spin ice. Nat. Phys. 10, 670–675 (2014).

  7. 7.

    et al. Thermodynamics of emergent magnetic charge screening in artificial spin ice. Nat. Commun. 7, 12635 (2016).

  8. 8.

    , , , & Emerging chirality in artificial spin ice. Science 335, 1597–1600 (2012).

  9. 9.

    et al. Understanding magnetotransport signatures in networks of connected permalloy nanowires. Phys. Rev. B 95, 060405(R) (2017).

  10. 10.

    , , & Spectral analysis of topological defects in an artificial spin-ice lattice. Phys. Rev. Lett. 110, 117205 (2013).

  11. 11.

    et al. Dynamic response of an artificial square spin ice. Phys. Rev. B 93, 100401(R) (2016).

  12. 12.

    , , & Magnetization dynamics of topological defects and the spin solid in a kagome artificial spin ice. Phys. Rev. B 93, 140401(R) (2016).

  13. 13.

    , & Unidirectional rotary motion in a molecular system. Nature 401, 150–152 (1999).

  14. 14.

    et al. Thermally driven ratchet motion of a skyrmion microcrystal and topological magnon Hall effect. Nat. Mater. 13, 241–246 (2014).

  15. 15.

    et al. Gold helix photonic metamaterial as broadband circular polarizer. Science 325, 1513–1515 (2009).

  16. 16.

    et al. Chiral magnetic order at surfaces driven by inversion asymmetry. Nature 447, 190–193 (2007).

  17. 17.

    et al. Asymmetric spin-wave dispersion on Fe(110): direct evidence of the Dzyaloshinskii–Moriya interaction. Phys. Rev. Lett. 104, 137203 (2010).

  18. 18.

    True and false chirality and parity violation. Chem. Phys. Lett. 123, 423–427 (1986).

  19. 19.

    , & Two-dimensional rotational dynamic chirality and a chirality scale. Langmuir 6, 1691–1695 (1990).

  20. 20.

    & Making molecular machines work. Nat. Nanotech. 1, 25–35 (2006).

  21. 21.

    , , , & Emergent smectic order in simple active particle models. New J. Phys. 18, 063015 (2016).

  22. 22.

    & Artificial Brownian motors: controlling transport on the nanoscale. Rev. Mod. Phys. 81, 387–442 (2009).

  23. 23.

    et al. Thermal fluctuations in artificial spin ice. Nat. Nanotech. 9, 514–519 (2014).

  24. 24.

    et al. Exploring hyper-cubic energy landscapes in thermally active finite artificial spin-ice systems. Nat. Phys. 9, 375–382 (2013).

  25. 25.

    , & Switching a magnetic antivortex core with ultrashort field pulses. J. Appl. Phys. 103, 07B115 (2008).

  26. 26.

    & Micromagnetic studies of vortices leaving and entering square nanoboxes. J. Appl. Phys. 97, 10E307 (2005).

  27. 27.

    , & Magnetic vortex based transistor operations. Sci. Rep. 4, 4180 (2014).

  28. 28.

    Nonreciprocal surface waves. Surf. Sci. Rep. 7, 103–187 (1987).

  29. 29.

    , , , & Curvature-induced asymmetric spin-wave dispersion. Phys. Rev. Lett. 117, 227203 (2016).

  30. 30.

    , , , & Chiral symmetry breaking and pair-creation mediated Walker breakdown in magnetic nanotubes. Appl. Phys. Lett. 100, 252401 (2012).

  31. 31.

    Curvature-induced magnetochirality. SPIN 03, 1340009 (2013).

  32. 32.

    , , & A reversible, unidirectional molecular rotary motor driven by chemical energy. Science 310, 80–82 (2005).

  33. 33.

    & Memory leads the way to better computing. Nat. Nanotech. 10, 191–194 (2015).

  34. 34.

    et al. Studying nanomagnets and magnetic heterostructures with X-ray PEEM at the Swiss Light Source. J. Electron Spectrosc. Related Phenom. 185, 371–380 (2012).

  35. 35.

    et al. Element-specific magnetic microscopy with circularly polarized X-rays. Science 259, 658–661 (1993).

  36. 36.

    , , & Encyclopedia of Materials: Science and Technology Micromagnetics: finite element approach. 5651–5660 (Elsevier, 1993).

  37. 37.

    et al. A path method for finding energy barriers and minimum energy paths in complex micromagnetic systems. J. Magn. Magn. Mater. 250, L12 (2002).

Download references


The authors thank O. Sendetskyi, H. Arava, V. Guzenko, E. Deckardt and J. Bosgra for technical assistance. S.G. wishes to thank N. Leo and A. S. Arrott for helpful discussions as well as S. Arnold for advice on the graphics in the manuscript. R.L.S. thanks F. Nascimento for discussions. S.G. was funded by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement no. 708674. The work of G.H. was supported by the EPSRC (grants EP/M015173/1 and EP/L019876/1), the Vienna Science and Technology Fund under WWTF Project MA14-44 and the Royal Society under Grant No. UF080837. The work of R.L.S. was supported by the EPSRC (grants EP/ L002922/1 and EP/M024423/1). This work was supported by JSPS Core-to-Core Program, A. Advanced Research Networks. A.F. was supported by the Swiss National Science Foundation. Part of this work was performed at the Surface/Interface: Microscopy (SIM) beamline of the Swiss Light Source, Paul Scherrer Institut, Villigen, Switzerland. This research used resources of the Advanced Light Source, which is a DOE Office of Science User Facility under contract no. DE-AC02-05CH11231. Use of the Center for Nanoscale Materials, an Office of Science user facility, was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357.

Author information


  1. SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, UK

    • Sebastian Gliga
    •  & Robert L. Stamps
  2. Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland

    • Sebastian Gliga
    • , Claire Donnelly
    • , Jonathan Büchi
    • , Jizhai Cui
    • , Alan Farhan
    • , Eugenie Kirk
    • , Nicholas S. Bingham
    •  & Laura J. Heyderman
  3. Paul Scherrer Institut, 5232 Villigen PSI, Switzerland

    • Sebastian Gliga
    • , Claire Donnelly
    • , Armin Kleibert
    • , Jizhai Cui
    • , Alan Farhan
    • , Eugenie Kirk
    • , Nicholas S. Bingham
    •  & Laura J. Heyderman
  4. College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, UK

    • Gino Hrkac
  5. Advanced Light Source, Lawrence Berkeley National Laboratory (LBNL), 1 Cyclotron Road, Berkeley, California 94720, USA

    • Alan Farhan
    •  & Andreas Scholl
  6. Department of Materials Science and Engineering, University of California, Davis, Davis, California 95616, USA

    • Rajesh V. Chopdekar
  7. Department of Physics, University of Tokyo, Tokyo 113-0033, Japan

    • Yusuke Masaki
  8. National Research Council Research Associate at the US Naval Research Laboratory, 4555 Overlook Avenue, SW Washington DC 20375, USA

    • Nicholas S. Bingham


  1. Search for Sebastian Gliga in:

  2. Search for Gino Hrkac in:

  3. Search for Claire Donnelly in:

  4. Search for Jonathan Büchi in:

  5. Search for Armin Kleibert in:

  6. Search for Jizhai Cui in:

  7. Search for Alan Farhan in:

  8. Search for Eugenie Kirk in:

  9. Search for Rajesh V. Chopdekar in:

  10. Search for Yusuke Masaki in:

  11. Search for Nicholas S. Bingham in:

  12. Search for Andreas Scholl in:

  13. Search for Robert L. Stamps in:

  14. Search for Laura J. Heyderman in:


R.L.S. and S.G. conceived the spin ice geometry and the experiment. S.G., A.F., C.D. and J.C. prepared the samples. S.G., C.D., J.C., J.B., A.K., A.F., R.V.C., E.K., A.S. and N.S.B. performed the experiments and analysed the experimental data. G.H., S.G. and J.B. performed and evaluated the micromagnetic simulations. S.G., G.H., R.L.S., J.B., C.D., A.K., Y.M. and L.J.H. interpreted the results. S.G. wrote the manuscript with input from all coauthors. All authors discussed the results and commented on the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Sebastian Gliga.

Supplementary information

PDF files

  1. 1.

    Supplementary Information

    Supplementary Information