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

Abstract

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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Fig. 1: The TMW process.
Fig. 2: Realization of TMW read/write functionality in ASI.
Fig. 3: Realization of the kagome ASI ground state via TMW.
Fig. 4: Negative effective temperature in ASI.

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References

  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).

    Article  Google Scholar 

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

    Article  Google Scholar 

  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).

    Article  Google Scholar 

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

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  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).

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  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).

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  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).

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  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).

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  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).

    Article  Google Scholar 

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

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

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

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

    Article  Google Scholar 

Download references

Acknowledgements

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.

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Contributions

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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Correspondence to Jack C. Gartside.

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Gartside, J.C., Arroo, D.M., Burn, D.M. et al. Realization of ground state in artificial kagome spin ice via topological defect-driven magnetic writing. Nature Nanotech 13, 53–58 (2018). https://doi.org/10.1038/s41565-017-0002-1

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