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Realization of ground state in artificial kagome spin ice via topological defect-driven magnetic writing

Nature Nanotechnologyvolume 13pages5358 (2018) | Download Citation


Arrays of non-interacting nanomagnets are widespread in data storage and processing. As current technologies approach fundamental limits on size and thermal stability, enhancing functionality through embracing the strong interactions present at high array densities becomes attractive. In this respect, artificial spin ices are geometrically frustrated magnetic metamaterials that offer vast untapped potential due to their unique microstate landscapes, with intriguing prospects in applications from reconfigurable logic to magnonic devices or hardware neural networks. However, progress in such systems is impeded by the inability to access more than a fraction of the total microstate space. Here, we demonstrate that topological defect-driven magnetic writing—a scanning probe technique—provides access to all of the possible microstates in artificial spin ices and related arrays of nanomagnets. We create previously elusive configurations such as the spin-crystal ground state of artificial kagome dipolar spin ices and high-energy, low-entropy ‘monopole-chain’ states that exhibit negative effective temperatures.

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  1. 1.

    Pauling, L. The structure and entropy of ice and of other crystals with some randomness of atomic arrangement. J. Am. Chem. Soc. 57, 2680–2684 (1935).

  2. 2.

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

  3. 3.

    Ladak, S., Read, D., Perkins, G. K., Cohen, L. F. & Branford, W. Direct observation of magnetic monopole defects in an artificial spin-ice system. Nat. Phys. 6, 359–363 (2010).

  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).

  5. 5.

    Nisoli, C. et al. Ground state lost but degeneracy found: the effective thermodynamics of artificial spin ice. Phys. Rev. Lett. 98, 217203 (2007).

  6. 6.

    Qi, Y., Brintlinger, T. & Cumings, J. Direct observation of the ice rule in an artificial kagome spin ice. Phys. Rev. B 77, 094418 (2008).

  7. 7.

    Morgan, J. P., Stein, A., Langridge, S. & Marrows, C. H. Thermal ground-state ordering and elementary excitations in artificial magnetic square ice. Nat. Phys. 7, 75–79 (2010).

  8. 8.

    Lammert, P. E. et al. Direct entropy determination and application to artificial spin ice. Nat. Phys. 6, 786–789 (2010).

  9. 9.

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

  10. 10.

    Farhan, a et al. Direct observation of thermal relaxation in artificial spin ice. Phys. Rev. Lett. 111, 057204 (2013).

  11. 11.

    Budrikis, Z., Politi, P. & Stamps, R. L. A network model for field and quenched disorder effects in artificial spin ice. New. J. Phys. 14, 045008 (2012).

  12. 12.

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

  13. 13.

    Ladak, S., Read, D., Tyliszczak, T., Branford, W. & Cohen, L. F. Monopole defects and magnetic Coulomb blockade. New. J. Phys. 13, 023023 (2011).

  14. 14.

    Grundler, D. Reconfigurable magnonics heats up. Nat. Phys. 11, 438–441 (2015).

  15. 15.

    Krawczyk, M. & Grundler, D. Review and prospects of magnonic crystals and devices with reprogrammable band structure. J. Phys. Condens. Mat. 26, 123202 (2014).

  16. 16.

    Zhang, S. et al. Crystallites of magnetic charges in artificial spin ice. Nature 500, 553–557 (2013).

  17. 17.

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

  18. 18.

    Farhan, A. et al. Thermally induced magnetic relaxation in building blocks of artificial kagome spin ice. Phys. Rev. B 89, 214405 (2014).

  19. 19.

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

  20. 20.

    Garcia, R., Knoll, A. W. & Riedo, E. Advanced scanning probe lithography. Nat. Nanotech. 9, 577–587 (2014).

  21. 21.

    Eigler, D. M. & Schweizer, E. K. Positioning single atoms with a scanning tunnelling microscope. Nature 344, 524–526 (1990).

  22. 22.

    Van Loenen, E., Dijkkamp, D., Hoeven, A., Lenssinck, J. & Dieleman, J. Direct writing in Si with a scanning tunneling microscope. Appl. Phys. Lett. 55, 1312–1314 (1989).

  23. 23.

    Pavliček, N. et al. Synthesis and characterization of triangulene. Nat. Nanotech. 12, 308–311 (2017).

  24. 24.

    Albisetti, E. et al. Nanopatterning reconfigurable magnetic landscapes via thermally assisted scanning probe lithography. Nat. Nanotech. 11, 545–551 (2016).

  25. 25.

    Krause, S., Berbil-Bautista, L., Herzog, G., Bode, M. & Wiesendanger, R. Current-induced magnetization switching with a spin-polarized scanning tunneling microscope. Science 317, 1537–1540 (2007).

  26. 26.

    Gartside, J., Burn, D., Cohen, L. & Branford, W. A novel method for the injection and manipulation of magnetic charge states in nanostructures. Sci. Rep. 6, 32864 (2016).

  27. 27.

    Wang, Y.-L. et al. Rewritable artificial magnetic charge ice. Science 352, 962–966 (2016).

  28. 28.

    Mermin, N. D. The topological theory of defects in ordered media. Rev. Mod. Phys. 51, 591–648 (1979).

  29. 29.

    Nisoli, C. et al. Effective temperature in an interacting vertex system: theory and experiment on artificial spin ice. Phys. Rev. Lett. 105, 047205 (2010).

  30. 30.

    Anghinolfi, L. et al. Thermodynamic phase transitions in a frustrated magnetic metamaterial. Nat. Commun. 6, 8278 (2015).

  31. 31.

    Hartmann, U. The point dipole approximation in magnetic force microscopy. Phys. Lett. A. 137, 475–478 (1989).

  32. 32.

    Lohau, J., Kirsch, S., Carl, A., Dumpich, G. & Wassermann, E. F. Quantitative determination of effective dipole and monopole moments of magnetic force microscopy tips. J. Appl. Phys. 86, 3410 (1999).

  33. 33.

    Magiera, M. P., Hucht, A., Hinrichsen, H., Dahmen, S. R. & Wolf, D. E. Magnetic vortices induced by a moving tip. Europhys. Lett. 100, 27004 (2012).

  34. 34.

    Magiera, M. P. & Schulz, S. Magnetic vortices induced by a monopole tip. IEEE Trans. Magn. 50, 1–4 (2014).

  35. 35.

    Liao, H. et al. Gapless spin-liquid ground state in the = 1/2 kagome antiferromagnet. Phys. Rev. Lett. 118, 137202 (2017).

  36. 36.

    Möller, G. & Moessner, R. Magnetic multipole analysis of kagome and artificial spin-ice dipolar arrays. Phys. Rev. B 80, 140409 (2009).

  37. 37.

    Chern, G.-W., Mellado, P. & Tchernyshyov, O. Two-stage ordering of spins in dipolar spin ice on the kagome lattice. Phys. Rev. Lett. 106, 207202 (2011).

  38. 38.

    Rougemaille, N. et al. Artificial kagome arrays of nanomagnets: a frozen dipolar spin ice. Phys. Rev. Lett. 106, 057209 (2011).

  39. 39.

    Arnalds, U. B. et al. Thermalized ground state of artificial kagome spin ice building blocks. Appl. Phys. Lett. 101, 112404 (2012).

  40. 40.

    Chern, G.-W. & Tchernyshyov, O. Magnetic charge and ordering in kagome spin ice. Phil. Trans. R. Soc. Lond. A 370, 5718–5737 (2012).

  41. 41.

    Purcell, E. M. & Pound, R. V. A nuclear spin system at negative temperature. Phys. Rev. 81, 279 (1951).

  42. 42.

    Abraham, E. & Penrose, O. Physics of negative absolute temperatures. Phys. Rev. E 95, 012125 (2017).

  43. 43.

    Cugliandolo, L. F. The effective temperature. J. Phys. A 44, 483001 (2011).

  44. 44.

    Fierro, A., Nicodemi, M. & Coniglio, A. Thermodynamics and statistical mechanics of frozen systems in inherent states. Phys. Rev. E 66, 061301 (2002).

  45. 45.

    Martiniani, S., Schrenk, K. J., Ramola, K., Chakraborty, B. & Frenkel, D. Numerical test of the edwards conjecture shows that all packings are equally probable at jamming. Nat. Phys. 13, 848–851 (2017).

  46. 46.

    Hubert, A., Rave, W. & Tomlinson, S. L. Imaging magnetic charges with magnetic force microscopy. Phys. Stat. Solidi B 204, 817–828 (1997).

  47. 47.

    Jaafar, M., Asenjo, A. & Vazquez, M. Calibration of coercive and stray fields of commercial magnetic force microscope probes. IEEE Trans. Nanotech. 7, 245–250 (2008).

  48. 48.

    McVitie, S., Ferrier, R., Scott, J., White, G. & Gallagher, A. Quantitative field measurements from magnetic force microscope tips and comparison with point and extended charge models. J. Appl. Phys. 89, 3656–3661 (2001).

  49. 49.

    Donahue, M. & Porter, D. OOMMF Programming Manual v.1.0 (National Institute of Standards and Technology, 1999).

  50. 50.

    McMichael, R. & Donahue, M. Head to head domain wall structures in thin magnetic strips. IEEE Trans. Magn. 33, 4167 (1997).

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This work was supported by the Engineering and Physical Sciences Research Council (grant number EP/G004765/1) and the Leverhulme Trust (grant number RPG 2012-692) to W.R.B. and supported by the Engineering and Physical Sciences Research Council (grant number EP/J014699/1) to L.F.C.

Author information


  1. Blackett Laboratory, Imperial College London, London, SW7 2AZ, UK

    • Jack C. Gartside
    • , Daan M. Arroo
    • , Andy Moskalenko
    • , Lesley F. Cohen
    •  & Will R. Branford
  2. Diamond Light Source, Didcot, OX11 0DE, UK

    • David M. Burn
  3. Department of Materials, Imperial College London, London, SW7 2AZ, UK

    • Victoria L. Bemmer


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J.C.G. conceived the experiment with the assistance of D.M.A., D.M.B. and W.R.B. J.C.G. fabricated the samples and performed the experimental measurements, J.C.G., V.L.B. and A.M. developed the practical selective writing capabilities on SPM systems. J.C.G., D.M.A. and D.M.B. performed micromagnetic simulations. J.C.G. performed the experimental measurements and D.M.A. performed the effective temperature analysis. J.C.G., D.M.A., W.R.B. and L.F.C. contributed to the manuscript. All authors contributed to discussions informing the research.

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The authors declare no competing financial interests.

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Correspondence to Jack C. Gartside.

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