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Emergent dynamic chirality in a thermally driven artificial spin ratchet


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.

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Figure 1: Schematic representation of the chiral ice and evolution of the net magnetization at individual vertices within the array.
Figure 2: Measured clockwise evolution of the magnetization following saturation along the +y direction.
Figure 3: Simulated stray field structure and energy barriers for clockwise and counterclockwise rotations of the average magnetization.
Figure 4: Counterclockwise evolution of the system following saturation in the −y direction.


  1. 1

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

    CAS  Article  Google Scholar 

  2. 2

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

    CAS  Article  Google Scholar 

  3. 3

    Morrison, M. J., Nelson, T. R. & Nisoli, C. Unhappy vertices in artificial spin ice: new degeneracies from vertex frustration. New J. Phys. 15, 045009 (2013).

    Article  Google Scholar 

  4. 4

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

    Article  Google Scholar 

  5. 5

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

    CAS  Article  Google Scholar 

  6. 6

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

    CAS  Article  Google Scholar 

  7. 7

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

    CAS  Article  Google Scholar 

  8. 8

    Branford, W. R., Ladak, S., Read, D. E., Zeissler, K. & Cohen, L. F. Emerging chirality in artificial spin ice. Science 335, 1597–1600 (2012).

    CAS  Article  Google Scholar 

  9. 9

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

    Article  Google Scholar 

  10. 10

    Gliga, S., Kákay, A., Hertel, R. & Heinonen, O. G. Spectral analysis of topological defects in an artificial spin-ice lattice. Phys. Rev. Lett. 110, 117205 (2013).

    Article  Google Scholar 

  11. 11

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

    Article  Google Scholar 

  12. 12

    Bhat, V. S., Heimbach, F., Stasinopoulos, I. & Grundler, D. Magnetization dynamics of topological defects and the spin solid in a kagome artificial spin ice. Phys. Rev. B 93, 140401(R) (2016).

    Article  Google Scholar 

  13. 13

    Kelly, T. R., De Silva, H. & Silva, R. A. Unidirectional rotary motion in a molecular system. Nature 401, 150–152 (1999).

    CAS  Article  Google Scholar 

  14. 14

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

    CAS  Article  Google Scholar 

  15. 15

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

    CAS  Article  Google Scholar 

  16. 16

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

    CAS  Article  Google Scholar 

  17. 17

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

    Article  Google Scholar 

  18. 18

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

    CAS  Article  Google Scholar 

  19. 19

    Hel-Or, Y., Peleg, S. & Avnir, D. Two-dimensional rotational dynamic chirality and a chirality scale. Langmuir 6, 1691–1695 (1990).

    CAS  Article  Google Scholar 

  20. 20

    Browne, W. R. & Feringa, B. L. Making molecular machines work. Nat. Nanotech. 1, 25–35 (2006).

    CAS  Article  Google Scholar 

  21. 21

    Romanczuk, P., Chaté, H., Chen, L., Ngo, S. & Toner, J. Emergent smectic order in simple active particle models. New J. Phys. 18, 063015 (2016).

    Article  Google Scholar 

  22. 22

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

    Article  Google Scholar 

  23. 23

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

    CAS  Article  Google Scholar 

  24. 24

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

    CAS  Article  Google Scholar 

  25. 25

    Gliga, S., Hertel, R. & Schneider, C. M. Switching a magnetic antivortex core with ultrashort field pulses. J. Appl. Phys. 103, 07B115 (2008).

    Article  Google Scholar 

  26. 26

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

    Article  Google Scholar 

  27. 27

    Kumar, D., Barman, S. & Barman, A. Magnetic vortex based transistor operations. Sci. Rep. 4, 4180 (2014).

    Google Scholar 

  28. 28

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

    CAS  Article  Google Scholar 

  29. 29

    Otálora, J. A., Yan, M., Schultheiss, H., Hertel, R. & Kákay, A. Curvature-induced asymmetric spin-wave dispersion. Phys. Rev. Lett. 117, 227203 (2016).

    Article  Google Scholar 

  30. 30

    Yan, M., Andreas, C., Kákay, A., Garcia-Sanchez, F. & Hertel, R. Chiral symmetry breaking and pair-creation mediated Walker breakdown in magnetic nanotubes. Appl. Phys. Lett. 100, 252401 (2012).

    Article  Google Scholar 

  31. 31

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

    Article  Google Scholar 

  32. 32

    Fletcher, S. P., Dumur, F., Pollard, M. M. & Feringa, B. L. A reversible, unidirectional molecular rotary motor driven by chemical energy. Science 310, 80–82 (2005).

    CAS  Article  Google Scholar 

  33. 33

    Wong, H.-S. P. & Salahuddin, S. Memory leads the way to better computing. Nat. Nanotech. 10, 191–194 (2015).

    CAS  Article  Google Scholar 

  34. 34

    Le Guyader, L. 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).

    CAS  Article  Google Scholar 

  35. 35

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

    Article  Google Scholar 

  36. 36

    Chantrell, R. W., Fidler, J., Schrefl, T. & Wongsam, M. Encyclopedia of Materials: Science and Technology Micromagnetics: finite element approach. 5651–5660 (Elsevier, 2001).

    Chapter  Google Scholar 

  37. 37

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

    CAS  Article  Google Scholar 

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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.

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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.

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Correspondence to Sebastian Gliga.

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The authors declare no competing financial interests.

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Gliga, S., Hrkac, G., Donnelly, C. et al. Emergent dynamic chirality in a thermally driven artificial spin ratchet. Nature Mater 16, 1106–1111 (2017).

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