Magnetic-vortex Dynamic Quasi-crystal Formation in Soft Magnetic Nano-disks

  • Kim, Junhoe (National Creative Initiative Center for Spin Dynamics and Spin-Wave Devices, Nanospinics Laboratory, Research Institute of Advanced Materials, Department of Materials Science and Engineering, Seoul National University) ;
  • Kim, Sang-Koog (National Creative Initiative Center for Spin Dynamics and Spin-Wave Devices, Nanospinics Laboratory, Research Institute of Advanced Materials, Department of Materials Science and Engineering, Seoul National University)
  • Received : 2017.02.22
  • Accepted : 2017.03.14
  • Published : 2017.03.31


We report a micromagnetic numerical study on different quasi-crystal formations of magnetic vortices in a rich variety of dynamic transient states in soft magnetic nano-disks. Only the application of spin-polarized dc currents to a single magnetic vortex leads to the formation of topological-soliton quasi-crystals composed of different configurations of skyrmions with positive and negative half-integer numbers (magnetic vortices and antivortices). Such topological object formations in soft magnets, not only in the absence of Dzyaloshinskii-Moriya interaction but also without magnetocrystalline anisotropy, are discussed in terms of two different topological charges, the winding number and the skyrmion number. This work offers an insight into the dynamic topological-spin-texture quasi-crystal formations in soft magnets.


Supported by : National Research Foundation of Korea (NRF)


  1. A. Malozemoff and J. Slonzewski, Magnetic Domain Walls in Bubble Materials, Academic, New York (1979).
  2. A. Hubert and R. Schafer, Magnetic Domains: The Analysis of Magnetic Microstructure, Springer, Berlin (1998).
  3. T. Shinjo, T. Okuno, R. Hassdorf, K. Shigeto, and T. Ono, Science 289, 930 (2000).
  4. A. Wachowiak, J. Wiebe, M. Bode, O. Pietzsch, M. Morgenstern, and R. Wiesendanger, Science 298, 577 (2002).
  5. K. Shigeto, T. Okuno, K. Mibu, T. Shinjo, and T. Ono, Appl. Phys. Lett. 80, 4190 (2002).
  6. K.-S. Lee, B.-W. Kang, Y.-S. Yu, and S.-K. Kim, Appl. Phys. Lett. 85, 1568 (2004).
  7. K.-S. Lee, S. Choi, and S.-K. Kim, Appl. Phys. Lett. 87, 192502 (2005).
  8. B. Van Waeyenberge, A. Puzic, H. Stoll, K. W. Chou, T. Tyliszczak, R. Hertel, M. Fahnle, H. Bruckl, K. Rott, G. Reiss, I. Neudecker, D. Weiss, C. H. Back, and G. Schutz, Nature 444, 461 (2006).
  9. R. Hertel and C. Schneider, Phys. Rev. Lett. 97, 177202 (2006).
  10. K. Y. Guslienko, B. A. Ivanov, V. Novosad, Y. Otani, H. Shima, and K. Fukamichi, J. Appl. Phys. 91, 8037 (2002).
  11. M. Buess, R. Hollinger, T. Haug, K. Perzlmaier, U. Krey, D. Pescia, M. R. Scheinfein, D. Weiss, and C. H. Back, Phys. Rev. Lett. 93, 077207 (2004).
  12. H. Wang and C. E. Campbell, Phys. Rev. B 76, 220407(R) (2007).
  13. R. P. Cowburn, Nature Mater. 6, 255 (2007).
  14. J. Thomas, Nature Nanotechnol. 2, 206 (2007).
  15. K.-S. Lee, M.-W. Yoo, Y.-S. Choi, and S.-K. Kim, Phys. Rev. Lett. 106, 147201 (2011).
  16. M. Kammerer, M. Weigand, M. Curcic, M. Noske, M. Sproll, A. Vansteenkiste, B. Van Waeyenberge, H. Stoll, G. Woltersdorf, C. H. Back, and G. Schuetz, Nature Commun. 2, 279 (2011).
  17. R. Wang and X. Dong, Appl. Phys. Lett. 100, 082402 (2012).
  18. M.-W. Yoo, J. Lee, and S.-K. Kim, Appl. Phys. Lett. 100, 172413 (2012).
  19. S.-K. Kim, K.-S. Lee, Y.-S. Yu, and Y.-S. Choi, Appl. Phys. Lett. 92, 022509 (2008).
  20. S. Bohlens, B. Kruger, A. Drews, M. Bolte, G. Meier, and D. Pfannkuche, Appl. Phys. Lett. 93, 142508 (2008).
  21. S. Barman, A. Barman, and Y. Otani, IEEE Trans. Magn. 46, 1342 (2010).
  22. H. Jung, Y.-S. Choi, K.-S. Lee, D.-S. Han, Y.-S. Yu, M.Y. Im, P. Fischer, and S.-K. Kim, ACS Nano 6, 3712 (2012).
  23. D.-S. Han, A. Vogel, H. Jung, K.-S. Lee, M. Weigand, H. Stoll, G. Schutz, P. Fischer, G. Meier, and S.-K. Kim, Sci. Rep. 3, 2262 (2013).
  24. T. H. R. Skyrme, Nucl. Phys. 31, 556 (1962).
  25. A. A. Belavin and A. M. Polyakov, JETP Lett. 22, 245 (1975).
  26. S. Muhlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, and P. Boni, Science 323, 915 (2009).
  27. X. Z. Yu, Y. Onose, N. Kanazawa, J. H. Park, J. H. Han, Y. Matsui, N. Nagaosa, and Y. Tokura, Nature 465, 901 (2010).
  28. S. Heinze, K. V. Bergmann, M. Menzel, J. Brede, A. Kubetzka, R. Wiesendager, G. Bihlmayer, and S. Blugel, Nature Physics 7, 713 (2011).
  29. A. Fert, V. Cros, and J. Sampaio, Nature Nanotech. 8, 152 (2013).
  30. I. E. Dzyaloshinskii, J. Phys. Chem. Sol. 4, 241 (1958).
  31. T. Moriya, Phys. Rev. 120, 91 (1960).
  32. X. Z. Yu, N. Kanazawa, W. Z. Zhang, T. Nagai, K. Kimoto, Y. Matsui, Y. Onose, and Y. Tokura, Nature Commun. 3, 988 (2012).
  33. J. Iwasaki, M. Mochizuki, and N. Nagaosa, Nature Nanotech. 8, 742 (2013).
  34. O. Tretiakov and O. Tchernyshyov, Phys. Rev. B 75, 012408 (2007).
  35. E. E. Huber Jr., D. O. Smith, and J. B. Goodenough, J. Appl. Phys. 29, 294 (1958).
  36. The version of the OOMMF code used is 1.2a4. See
  37. L. D. Landau and E. M. Lifshitz, Phys. Z. Sowjetunion 8, 153 (1935).
  38. T. L. Gilbert, Phys. Rev. 100, 1243 (1955).
  39. J. C. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996).
  40. Y.-S. Choi, M.-W. Yoo, K.-S. Lee, Y.-S. Yu, H. Jung, and S.-K. Kim, Appl. Phys. Lett. 96, 072507 (2010).
  41. J.-G. Caputo, Y. Gaididei, F. G. Mertens, and D. D. Sheka, Phys. Rev. Lett. 98, 056604 (2007).
  42. D. D. Sheka, Y. Gaididei, and F. G. Mertens, Appl. Phys. Lett. 91, 082509 (2007).
  43. Y. Liu, H. He, and Z. Zhang, Appl. Phys. Lett. 91, 242501 (2007).
  44. O. M. Volkov, V. P. Kravchuk, D. D. Sheka, and Y. Gaididei, Phys. Rev. Lett. 84, 052404 (2011).
  45. Y. Gaididei, O. M. Volkov, V. P. Kravchuk, and D. D. Sheka, Phys. Rev. B 86, 144401 (2012).
  46. B. Binz, A. Vishwanath, Physica B 403, 1336 (2008).