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Switching chiral solitons for algebraic operation of topological quaternary digits

Nature Physics volume 13, pages 444–447 (2017)Cite this article

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Abstract

Chiral objects can be found throughout nature1,2,3,4; in condensed matter chiral objects are often excited states protected by a system’s topology. The use of chiral topological excitations to carry information has been demonstrated, where the information is robust against external perturbations5,6. For instance, reading, writing, and transfer of binary information have been demonstrated with chiral topological excitations in magnetic systems, skyrmions7,8,9,10,11,12,13,14, for spintronic devices13,14,15,16,17,18,19. The next step is logic or algebraic operations of such topological bits20,21,22. Here, we show experimentally the switching between chiral topological excitations or chiral solitons of different chirality in a one-dimensional electronic system with Z4 topological symmetry23,24. We found that a fast-moving achiral soliton merges with chiral solitons to switch their handedness. This can lead to the realization of algebraic operation of Z4 topological charges25. Chiral solitons could be a platform for storage and operation of robust topological multi-digit information.

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Figure 1: Characterizing chiral switching between topological solitons.
Figure 2: Trace section of the time-dependent chiral switching.
Figure 3: Algebraic operation using solitons.

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References

  1. Simon, J. Magnetic fields without magnetic fields. Nature 515, 202–203 (2014).

    Article  ADS  Google Scholar 

  2. Shelke, S. A. & Piccirilli, J. A. RNA made in its own mirror image. Nature 515, 347–348 (2014).

    Article  ADS  Google Scholar 

  3. Romanov-Michailidis, F. & Rovis, T. Natural polarity inverted. Nature 523, 417–418 (2015).

    Article  ADS  Google Scholar 

  4. Boyd, R. W. Neutrons with a twist. Nature 525, 462–464 (2015).

    Article  ADS  Google Scholar 

  5. Parkin, S. S. P., Hayashi, M. & Thomas, L. Magnetic domain-wall racetrack memory. Science 320, 190–194 (2008).

    Article  ADS  Google Scholar 

  6. Braun, H.-B. Topological effects in nanomagnetism: from superparamagnetism to chiral quantum solitons. Adv. Phys. 61, 1–116 (2012).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. Heinze, S. et al. Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions. Nat. Phys. 7, 713–718 (2011).

    Article  Google Scholar 

  10. Yu, X. Z. et al. Near room-temperature formation of a skyrmion crystal in thin-films of the helimagnet FeGe. Nat. Mater. 10, 106–109 (2011).

    Article  ADS  Google Scholar 

  11. Milde, P. et al. Unwinding of a skyrmion lattice by magnetic monopoles. Science 340, 1076–1080 (2013).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. Romming, N. et al. Writing and deleting single magnetic skyrmions. Science 341, 636–639 (2013).

    Article  ADS  Google Scholar 

  14. Hagemeister, J., Romming, N., von Bergmann, K., Vedmedenko, E. Y. & Wiesendanger, R. Stability of single skyrmionic bits. Nat. Commun. 6, 8455 (2015).

    Article  ADS  Google Scholar 

  15. Fert, A., Cros, V. & Sampaio, J. Skyrmions on the track. Nat. Nanotech. 8, 152–156 (2013).

    Article  ADS  Google Scholar 

  16. Sampaio, J., Cros, V., Rohart, S., Thiaville, A. & Fert, A. Nucleation, stability and current-induced motion of isolated magnetic skyrmions in nanostructures. Nat. Nanotech. 8, 839–844 (2013).

    Article  ADS  Google Scholar 

  17. Hanneken, C. et al. Electrical detection of magnetic skyrmions by tunnelling non-collinear magnetoresistance. Nat. Nanotech. 10, 1039–1042 (2015).

    Article  ADS  Google Scholar 

  18. Jiang, W. et al. Blowing magnetic skyrmion bubbles. Science 349, 283–286 (2015).

    Article  ADS  Google Scholar 

  19. Zhang, X., Zhou, Y., Ezawa, M., Zhao, G. P. & Zhao, W. Magnetic skyrmion transistor: skyrmion motion in a voltage-gated nanotrack. Sci. Rep. 5, 11369 (2015).

    Article  ADS  Google Scholar 

  20. Zhang, S., Baker, A. A., Komineas, S. & Hesjedal, T. Topological computation based on direct magnetic logic communication. Sci. Rep. 5, 15773 (2015).

    Article  ADS  Google Scholar 

  21. Zhang, X. et al. All-magnetic control of skyrmions in nanowires by a spin wave. Nanotechnology 26, 225701 (2015).

    Article  ADS  Google Scholar 

  22. Zhang, X., Ezawa, M. & Zhou, Y. Magnetic skyrmion logic gates: conversion, duplication and merging of skyrmions. Sci. Rep. 5, 9400 (2015).

    Article  ADS  Google Scholar 

  23. Kim, T.-H. & Yeom, H. W. Topological Solitons versus nonsolitonic phase defects in a quasi-one-dimensional charge-density wave. Phys. Rev. Lett. 109, 246802 (2012).

    Article  ADS  Google Scholar 

  24. Cheon, S., Kim, T.-H., Lee, S.-H. & Yeom, H. W. Chiral solitons in a coupled double Peierls chain. Science 350, 182–185 (2015).

    Article  ADS  Google Scholar 

  25. Lovett, S. Abstract Algebra: Structures and Applications 87–88 (CRC Press, 2015).

    Book  Google Scholar 

  26. Dzyaloshinsky, I. A thermodynamic theory of ‘weak’ ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 4, 241–255 (1958).

    Article  ADS  Google Scholar 

  27. Jackiw, R. & Rebbi, C. Solitons with fermion number 1/2. Phys. Rev. D 13, 3398–3409 (1976).

    Article  ADS  MathSciNet  Google Scholar 

  28. Su, W. P., Schrieffer, J. R. & Heeger, A. J. Solitons in polyacetylene. Phys. Rev. Lett. 42, 1698–1701 (1979).

    Article  ADS  Google Scholar 

  29. Brazovskii, S. A., Gordynin, S. A. & Kirova, N. N. Exact solution of the Peierls model with an arbitrary number of electrons in the unit cell. Pis’ma v Zh. Eksp. Teor. Fiz. 31, 486–491 (1980).

    Google Scholar 

  30. Su, W. P., Schrieffer, J. R. & Heeger, A. J. Soliton excitations in polyacetylene. Phys. Rev. B 22, 2099–2111 (1980).

    Article  ADS  Google Scholar 

  31. Vanderbilt, D. & Mele, E. J. Effects of disorder on the electronic structure of undoped polyacetylene. Phys. Rev. B 22, 3939–3948 (1980).

    Article  ADS  Google Scholar 

  32. Braun, H.-B. et al. Emergence of soliton chirality in a quantum antiferromagnet. Nat. Phys. 1, 159–163 (2005).

    Article  Google Scholar 

  33. Togawa, Y. et al. Chiral magnetic soliton lattice on a chiral helimagnet. Phys. Rev. Lett. 108, 107202 (2012).

    Article  ADS  Google Scholar 

  34. Togawa, Y. et al. Magnetic soliton confinement and discretization effects arising from macroscopic coherence in a chiral spin soliton lattice. Phys. Rev. B 92, 220412 (2015).

    Article  ADS  Google Scholar 

  35. Zhang, H. et al. Atomic structure, energetics, and dynamics of topological solitons in indium chains on Si(111) surfaces. Phys. Rev. Lett. 106, 026801 (2011).

    Article  ADS  Google Scholar 

  36. Yeom, H. W., Oh, D. M., Wippermann, S. & Schmidt, W. G. Impurity-mediated early condensation of a charge density wave in an atomic wire array. ACS Nano 10, 810–814 (2016).

    Article  Google Scholar 

  37. Senft, D. C. & Ehrlich, G. Long jumps in surface diffusion: one-dimensional migration of isolated adatoms. Phys. Rev. Lett. 74, 294–297 (1995).

    Article  ADS  Google Scholar 

  38. Hla, S. W. Atom-by-atom assembly. Rep. Prog. Phys. 77, 056502 (2014).

    Article  ADS  Google Scholar 

  39. Yeom, H. W. et al. Instability and charge density wave of metallic quantum chains on a silicon surface. Phys. Rev. Lett. 82, 4898–4901 (1999).

    Article  ADS  Google Scholar 

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Acknowledgements

We thank S.-H. Lee for discussions in the early stages and technical help on the calculation method. This work was supported by IBS-R014-D1. T.-H.K. was supported by Basic Science Research Program (Grant No. NRF-2014R1A1A1002205) and the SRC Center for Topological Matter (Grant No. 2011-0030046) through the National Research Foundation (NRF) of Korea funded by the Ministry of Science, ICT & Future Planning.

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Authors and Affiliations

  1. Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea

    Tae-Hwan Kim & Han Woong Yeom

  2. Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science (IBS), Pohang 37673, Korea

    Sangmo Cheon & Han Woong Yeom

Authors
  1. Tae-Hwan Kim
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  2. Sangmo Cheon
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Contributions

T.-H.K. performed STM/STS measurements; S.C. performed tight-binding calculations; T.-H.K. and H.W.Y. analysed data and wrote the paper. All authors discussed the results and commented on the manuscript.

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Correspondence to Tae-Hwan Kim or Han Woong Yeom.

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The authors declare no competing financial interests.

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Kim, TH., Cheon, S. & Yeom, H. Switching chiral solitons for algebraic operation of topological quaternary digits. Nature Phys 13, 444–447 (2017). https://doi.org/10.1038/nphys4026

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