- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Polymerization in magnetic metamaterials

Samuel D. Slöetjes, Matías P. Grassi, and Vassilios Kapaklis

  • Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden

PDF

Phys. Rev. Research 5, L032029 – Published 30 August, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L032029

Abstract

We numerically study a mesoscopic system consisting of magnetic nanorings in the presence of thermal magnetization fluctuations. We find the formation of dipolar-field-mediated “bonds” promoting the formation of annuli clusters, where the amount of bonds between two rings varies between zero and two. This system resembles the formation of polymers from artificial atoms, which in our case are the annuli and where the valency of the atom is set by the ring multipolarity. We investigate the thermodynamic properties of the resulting structures, and find a transition associated with the formation of the bonds. In addition, we find that the system has a tendency to form topological structures, with a distinct critical temperature in relation to the one for bond formation.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (32)

  1. L. J. Heyderman and R. L. Stamps, Artificial ferroic systems: Novel functionality from structure, interactions and dynamics, J. Phys.: Condens. Matter 25, 363201 (2013).
  2. K. Kaya, E. Iseri, and W. van der Wijngaart, Soft metamaterial with programmable ferromagnetism, Microsys. Nanoeng. 8, 127 (2022).
  3. E. Digernes, S. D. Slöetjes, A. Strømberg, A. D. Bang, F. K. Olsen, E. Arenholz, R. V. Chopdekar, J. K. Grepstad, and E. Folven, Direct imaging of long-range ferromagnetic and antiferromagnetic order in a dipolar metamaterial, Phys. Rev. Res. 2, 013222 (2020).
  4. S. D. Slöetjes, H. H. Urdahl, J. K. Grepstad, and E. Folven, Tailoring the magnetic order in a supermagnetic metamaterial, AIP Adv. 7, 056325 (2017).
  5. E. Mengotti, L. J. Heyderman, A. F. Rodríguez, F. Nolting, R. V. Hügli, and H.-B. Braun, Real-space observation of emergent magnetic monopoles and associated Dirac strings in artificial kagome spin ice, Nat. Phys. 7, 68 (2011).
  6. J. Drisko, T. Marsh, and J. Cumings, Topological frustration of artificial spin ice, Nat. Commun. 8, 14009 (2017).
  7. O. Tchernyshyov and G.-W. Chern, Fractional Vortices and Composite Domain Walls in Flat Nanomagnets, Phys. Rev. Lett. 95, 197204 (2005).
  8. M. J. Morrison, T. R. Nelson, and C. Nisoli, Unhappy vertices in artificial spin ice: New degeneracies from vertex frustration, New J. Phys. 15, 045009 (2013).
  9. I. Gilbert, G.-W. Chern, S. Zhang, L. O'Brien, B. Fore, C. Nisoli, and P. Schiffer, Emergent ice rule and magnetic charge screening from vertex frustration in artificial spin ice, Nat. Phys. 10, 670 (2014).
  10. H. Stopfel, E. Östman, I.-A. Chioar, D. Greving, U. B. Arnalds, T. P. A. Hase, A. Stein, B. Hjörvarsson, and V. Kapaklis, Magnetic order and energy-scale hierarchy in artificial spin-ice structures, Phys. Rev. B 98, 014435 (2018).
  11. H. Stopfel, U. B. Arnalds, A. Stein, T. P. A. Hase, B. Hjörvarsson, and V. Kapaklis, Multiple energy scales in mesospin systems: The vertex-frustrated Saint George lattice, Phys. Rev. Mater. 5, 114410 (2021).
  12. I. Gilbert, Y. Lao, I. Carrasquillo, L. O'Brien, J. D. Watts, M. Manno, C. Leighton, A. Scholl, C. Nisoli, and P. Schiffer, Emergent reduced dimensionality by vertex frustration in artificial spin ice, Nat. Phys. 12, 162 (2016).
  13. B. E. Skovdal, N. Strandqvist, H. Stopfel, M. Pohlit, T. Warnatz, S. D. Slöetjes, V. Kapaklis, and B. Hjörvarsson, Temperature-induced collapse of spin dimensionality in magnetic metamaterials, Phys. Rev. B 104, 014434 (2021).
  14. J. Rothman, M. Kläui, L. Lopez-Diaz, C. A. F. Vaz, A. Bleloch, J. A. C. Bland, Z. Cui, and R. Speaks, Observation of a Bi-Domain State and Nucleation Free Switching in Mesoscopic Ring Magnets, Phys. Rev. Lett. 86, 1098 (2001).
  15. M. Kl ui, C. Vaz, L. Lopez-Diaz, and J. Bland, Vortex formation in narrow ferromagnetic rings, J. Phys.: Condens. Matter 15, R985 (2003).
  16. G. Muscas, M. Menniti, R. Brucas, and P. Jönsson, Mesoscale magnetic rings: Complex magnetization reversal uncovered by force, J. Magn. Magn. Mater. 502, 166559 (2020).
  17. F. Giesen, J. Podbielski, and D. Grundler, Mode localization transition in ferromagnetic microscopic rings, Phys. Rev. B 76, 014431 (2007).
  18. F. Montoncello, L. Giovannini, F. Nizzoli, H. Tanigawa, T. Ono, G. Gubbiotti, M. Madami, S. Tacchi, and G. Carlotti, Magnetization reversal and soft modes in nanorings: Transitions between onion and vortex states studied by brillouin light scattering, Phys. Rev. B 78, 104421 (2008).
  19. K. Martens, D. L. Stein, and A. D. Kent, Magnetic reversal in nanoscopic ferromagnetic rings, Phys. Rev. B 73, 054413 (2006).
  20. M. Laufenberg, D. Bedau, H. Ehrke, M. Kläui, U. Rüdiger, D. Backes, L. J. Heyderman, F. Nolting, C. A. Vaz, J. A. C. Bland et al., Quantitative determination of domain wall coupling energetics, Appl. Phys. Lett. 88, 212510 (2006).
  21. R. W. Dawidek, T. J. Hayward, I. T. Vidamour, T. J. Broomhall, G. Venkat, M. A. Mamoori, A. Mullen, S. J. Kyle, P. W. Fry, N.-J. Steinke et al., Dynamically driven emergence in a nanomagnetic system, Adv. Funct. Mater. 31, 2008389 (2021).
  22. A. Vansteenkiste, J. Leliaert, M. Dvornik, M. Helsen, F. Garcia-Sanchez, and B. V. Waeyenberge, The design and verification of mumax3, AIP Adv. 4, 107133 (2014).
  23. J. Leliaert, J. Mulkers, J. D. Clercq, A. Coene, M. Dvornik, and B. V. Waeyenberge, Adaptively time stepping the stochastic Landau-Lifshitz-Gilbert equation at nonzero temperature: Implementation and validation in mumax3, AIP Adv. 7, 125010 (2017).
  24. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.5.L032029 for justification of the bond threshold field; bond identification method; evolution of the total number of domain walls; movie of the bonds evolution over time interval of 200 ns, at a temperature of T̃=0.171.
  25. This value is calculated by evaluating the demagnetization energy between two rings connected by a bond at 50 nm, and subsequently increasing the distance between the rings in steps of 5 nm until the bond no longer exists.
  26. V. L. Berezinskiǐ, Destruction of Long-range Order in One-dimensional and Two-dimensional Systems having a Continuous Symmetry Group I. Classical Systems, Zh. Eksp. Teor. Fiz. 59, 907 (1970) [Sov. J. Exp. Theor. Phys. 32, 493 (1971)].
  27. J. M. Kosterlitz and D. Thouless, Long range order and metastability in two dimensional solids and superfluids (application of dislocation theory), J. Phys. C 5, L124 (1972).
  28. C. Nisoli, Topological order of the rys f-model and its breakdown in realistic square spin ice: Topological sectors of Faraday loops, Europhys. Lett. 132, 47005 (2020).
  29. V. Schánilec, O. Brunn, M. Horáček, S. Krátký, P. Meluzín, T. Šikola, B. Canals, and N. Rougemaille, Approaching the Topological Low-Energy Physics of the f Model in a Two-Dimensional Magnetic Lattice, Phys. Rev. Lett. 129, 027202 (2022).
  30. M. Ewerlin, D. Demirbas, F. Brüssing, O. Petracic, A. A. Unal, S. Valencia, F. Kronast, and H. Zabel, Magnetic Dipole and Higher Pole Interaction on a Square Lattice, Phys. Rev. Lett. 110, 177209 (2013).
  31. E. Y. Vedmedenko, N. Mikuszeit, H. P. Oepen, and R. Wiesendanger, Multipolar Ordering and Magnetization Reversal in Two-Dimensional Nanomagnet Arrays, Phys. Rev. Lett. 95, 207202 (2005).
  32. M. E. Newman and G. T. Barkema, Monte Carlo Methods in Statistical Physics (Clarendon Press, London, 1999).

Outline

Information

Phys. Rev. Research 5, L032029– Published 30 August, 2023
  • Received 22 February 2023
  • Revised 20 July 2023
  • Accepted 25 July 2023
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation