Fractal Dimension of Magnetic Domain Walls in CoFe/Pt Multilayers

  • Received : 2010.05.03
  • Accepted : 2010.07.05
  • Published : 2010.09.30


We present the fractal properties of the magnetic domain walls in $(5-{\AA}\;Co_{90}Fe_{10}/10-{\AA}\;Pt)_n$ multilayer films with perpendicular magnetic anisotropy for the number of repeats n (1 to 5). In these films, the magnetization reversed due to the domain wall propagation throughout the films with rare nucleations. As n increased, it was observed that the jaggedness of the domain walls increased noticeably, which is possibly due to the accumulation of irregularities at the layer interfaces. The jaggedness of the domain walls was analyzed in terms of the fractal dimension by use of the ruler method, and it was revealed that the fractal dimension significantly changed from $1.0{\pm}0.002$ to $1.3{\pm}0.05$ as n increased from 1 to 5.


Supported by : NRF


  1. S. S. P. Parkin, M. Hayashi, and L. Thomas, Science 320, 190 (2008).
  2. D. A. Allwood, G. Xiong, C. C. Faulkner, D. Atkinson, D. Petit, and R. P. Cowburn, Science 309, 1688 (2005).
  3. G. A. Prinz, Science 282, 1660 (1998).
  4. J. Pommier, P. Meyer, G. Pénissard, and J. Ferre, Phys. Rev. Lett. 65, 2054 (1990).
  5. S.-B. Choe and S.-C. Shin, Appl. Phys. Lett. 80, 1791 (2002).
  6. S.-B. Choe and S.-C. Shin, J. Appl. Phys. 87, 5076 (2000).
  7. J. Y. Ahn, N. J. Lee, and T. H. Kim, J. Magnetics 14, 144 (2009).
  8. H. Ji and M. O. Robbins, Phys. Rev. A. 44, 2538 (1991).
  9. G. V. Sayko, A. K. Zvezdin, T. G. Pokhil, B. S. Vvedensky, and E. N. Nikolaev, IEEE Trans. Magn. 28, 2931 (1992).
  10. D.-H. Kim, Y.-C. Cho, S.-B. Choe, and S.-C. Shin, Phys. Stat. Sol. 241, 1669 (2004).
  11. A. Kirilyuk, J. Ferré, and D. Renard, Europhys. Lett. 24, 403 (1993).
  12. B.-S. Han, D. Li, D.-J. Zheng, and Y. Zhou, Phys. Rev. B 66, 014433 (2002).
  13. B. E. Bernacki and M. Mansuripur, J. Appl. Phys. 69, 4960 (1991).
  14. D.-H. Kim, Y.-C. Cho, S.-B. Choe, and S.-C. Shin, Appl. Phys. Lett. 82, 3698 (2003).
  15. A. Kirilyuk, J. Ferre, V. Grolier, J. P. Jamet, and D. Renard, J. Magn. Magn. Mater. 171, 45 (1996).
  16. J. Feder, Fractals, Plenum, New York (1988).