Interdimensional universality of dynamic interfaces

Abstract

Despite the complexity and diversity of nature, there exists universality in the form of critical scaling laws among various dissimilar systems and processes such as stock markets1, earthquakes2, crackling noise3, lung inflation4 and vortices in superconductors5. This universality is mainly independent of the microscopic details, depending only on the symmetry and dimension of the system. Exploring how universality is affected by the system dimensions is an important unresolved problem. Here we demonstrate experimentally that universality persists even at a dimensionality crossover in ferromagnetic nanowires. As the wire width decreases, the magnetic domain wall dynamics changes from elastic creep6,7,8,9 in two dimensions to a particle-like stochastic behaviour10 in one dimension. Applying finite-size scaling, we find that all our experimental data in one and two dimensions (including the crossover regime) collapse onto a single curve, signalling universality at the criticality transition. The crossover to the one-dimensional regime occurs at a few hundred nanometres, corresponding to the integration scale for modern nanodevices.

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Figure 1: Nonequilibrium criticality of DW speed along ferromagnetic nanowires.
Figure 2: Finite-size scaling and universal crossover behaviour of DW criticality.
Figure 3: Variation of activation diameter with respect to wire width.

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Acknowledgements

This study was supported by KOSEF through the NRL programme (R0A-2007-000-20032-0). H.-W.L. was supported by KOSEF (R01-2007-000-20281-0, R11-2000-071). K.-J.K. was supported by the Seoul Science Fellowship and the Seoul R&BD programme. J.-C.L. was supported by KOSEF (R11-2008-095-01000-0). K.-H.S. was supported by the KIST Institutional Program and by the TND Frontier Project funded by MEST.

Author Contributions S.-B.C. planned and supervised the project; K.-J.K. designed and performed the experiments; C.-W.L., Y.J.C., and. S.S. prepared sample films; J.-C.L. and K.-H.S. carried out patterning process; S.-M.A. and K.-S.L. characterized the films and nanostructures; K.-J.K., S.-B.C. and H.-W.L. performed theoretical analysis and wrote the manuscript.

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Correspondence to Sug-Bong Choe or Hyun-Woo Lee.

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This file contains Supplementary Methods, Supplementary Discussions, Supplementary References and Supplementary Figures 1-4 with Legends. (PDF 944 kb)

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Kim, K., Lee, J., Ahn, S. et al. Interdimensional universality of dynamic interfaces. Nature 458, 740–742 (2009). https://doi.org/10.1038/nature07874

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