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An inverse transition of magnetic domain patterns in ultrathin films


Inverse freezing and inverse melting are processes where a more symmetric phase is found at lower temperatures than at higher temperatures. Such inverse transitions are very rare1. Here we report the existence of an inverse transition effect in ultrathin Fe films that are magnetized perpendicular to the film plane. The magnetization of these films is not uniform, but instead manifests itself as stripe domains with opposite perpendicular magnetization2,3,4. Predictions relating to the disordering of this striped ground state in the limit of monolayer film thicknesses are controversial. Mean-field arguments5,6,7 predict a continuous reduction of the stripe width when the temperature is increased; other studies8,9,10,11 suggest that topological defects, such as dislocations and disclinations, might penetrate the system and induce geometrical phase transitions. We find, from scanning electron microscopy imaging, that when the temperature is increased, the low-temperature stripe domain structure transforms into a more symmetric, labyrinthine structure. However, at even higher temperatures and before the loss of magnetic order, a re-occurrence of the less symmetric stripe phase is found. Despite the widespread theoretical and experimental work on striped systems, this phase sequence and the microscopic instabilities driving it have not been observed before.

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Figure 1: The four phases in ultrathin f.c.c.
Figure 2: Mean-field aspects of the phase transition.
Figure 3: The role of dislocations.
Figure 4: Microscopic mechanisms of transformations.


  1. Greer, A. L. Too hot to melt. Nature 404, 134–135 (2000)

    CAS  Article  Google Scholar 

  2. Garel, T. & Doniach, S. Phase transitions with spontaneous modulation—the dipolar Ising ferromagnet. Phys. Rev. B 26, 325–329 (1982)

    ADS  Article  Google Scholar 

  3. Seul, M. & Andelman, D. Domain shapes and patterns: the phenomenology of modulated phases. Science 267, 476–483 (1995)

    ADS  CAS  Article  Google Scholar 

  4. Sornette, D. Undulation instability in stripe domain structures of bubble materials. J. Phys. 48, 151–163 (1987)

    Article  Google Scholar 

  5. Czech, R. & Villain, J. Instability of two-dimensional Ising ferromagnets with dipole interaction. J. Phys. Condens. Matter 1, 619–627 (1989)

    ADS  Article  Google Scholar 

  6. Kashuba, A. & Pokrovsky, V. L. Stripe domain structures in a thin ferromagnetic film. Phys. Rev. B 48, 10335–10344 (1993)

    ADS  CAS  Article  Google Scholar 

  7. Gehring, G. A. & Keskin, M. The temperature dependence of the domain spacing in ultrathin magnetic films. J. Phys. Condens. Matter 5, L581–L585 (1993)

    ADS  CAS  Article  Google Scholar 

  8. Nelson, D. R. in Fundamental Problems in Statistical Mechanics V (ed. Cohen, E. G. D.) 53–108 (North-Holland, Amsterdam, 1980)

    Google Scholar 

  9. Abanov, Ar., Kalatsky, V., Pokrovsky, V. L. & Saslow, W. M. Phase diagram of ultrathin ferromagnetic films with perpendicular anisotropy. Phys. Rev. B 51, 1023–1038 (1995)

    ADS  CAS  Article  Google Scholar 

  10. De'Bell, K., MacIsaac, A. B. & Whitehead, J. P. Dipolar effects in magnetic thin films and quasi-two-dimensional systems. Rev. Mod. Phys. 72, 225–257 (2000)

    ADS  CAS  Article  Google Scholar 

  11. Stoycheva, A. D. & Singer, S. J. Stripe melting in a two-dimensional system with competing interactions. Phys. Rev. Lett. 84, 4657–4660 (2000)

    ADS  CAS  Article  Google Scholar 

  12. Vaterlaus, A. et al. Two-step disordering of perpendicularly magnetized ultrathin films. Phys. Rev. Lett. 84, 2247–2250 (2000)

    ADS  CAS  Article  Google Scholar 

  13. Stampanoni, M., Vaterlaus, A., Aeschlimann, M., Meier, F. & Pescia, D. Magnetic properties of thin fcc iron films on Cu(001). J. Appl. Phys. 64, 5321–5324 (1988)

    ADS  CAS  Article  Google Scholar 

  14. Thomassen, J. et al. Magnetic live surface layers in Fe/Cu(100). Phys. Rev. Lett. 69, 3831–3834 (1992)

    ADS  CAS  Article  Google Scholar 

  15. Kirilyuk, A., Giergiel, J., Shen, J., Straub, M. & Kirschner, J. Growth of stabilized γ-Fe films and their magnetic properties. Phys. Rev. B 54, 1050–1063 (1996)

    ADS  CAS  Article  Google Scholar 

  16. Man, K. L., Altman, M. S. & Poppa, H. Spin polarized low energy electron microscopy investigations of magnetic transitions in Fe/Cu(100). Surf. Sci. 480, 163–172 (2001)

    ADS  CAS  Article  Google Scholar 

  17. Pierce, J. P., Torija, M. A., Shen, J. & Plummer, E. W. Mapping the magnetic phase diagram of metastable fct Fe/Cu(100) using Co atoms. Phys. Rev. B 64, 224409 (2001)

    ADS  Article  Google Scholar 

  18. Kivelson, S. A., Fradkin, E. & Emery, V. J. Electronic liquid-crystal phases of a doped Mott insulator. Nature 393, 550–553 (1998)

    ADS  CAS  Article  Google Scholar 

  19. Seul, M. & Wolfe, R. Evolution of disorder in two-dimensional stripe patterns: Smectic instabilities and dislocation unbinding. Phys. Rev. Lett. 68, 2460–2463 (1992)

    ADS  CAS  Article  Google Scholar 

  20. Yochelis, A., Hagberg, A., Meron, E., Lin, A. L. & Swinney, H. L. Development of standing-wave labyrinthine patterns. SIAM J. Appl. Dyn. Syst. 1, 236–247 (2002)

    ADS  MathSciNet  Article  Google Scholar 

  21. Newell, A. C., Passot, T., Bowman, C., Ercolani, N. & Indik, R. Defects are weak and self-dual solutions of the Cross-Newell phase diffusion equation for natural patterns. Physica D 97, 185–205 (1996)

    ADS  Article  Google Scholar 

  22. Harrison, C. et al. Mechanism of ordering in striped patterns. Science 290, 1558–1560 (2000)

    ADS  CAS  Article  Google Scholar 

  23. Pearson, J. E. Complex patterns in a simple system. Science 261, 189–192 (1993)

    ADS  CAS  Article  Google Scholar 

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We thank the Swiss National Foundation and ETH Zurich for financial support.

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Correspondence to O. Portmann.

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Portmann, O., Vaterlaus, A. & Pescia, D. An inverse transition of magnetic domain patterns in ultrathin films. Nature 422, 701–704 (2003).

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