Nature 458, 740-742 (9 April 2009) | doi:10.1038/nature07874; Received 30 October 2008; Accepted 2 February 2009

Interdimensional universality of dynamic interfaces

Kab-Jin Kim1, Jae-Chul Lee1,2, Sung-Min Ahn1, Kang-Soo Lee1, Chang-Won Lee3, Young Jin Cho3, Sunae Seo3, Kyung-Ho Shin2, Sug-Bong Choe1 & Hyun-Woo Lee4

  1. Center for Subwavelength Optics and School of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea
  2. Center for Spintronics Research, Korea Institute of Science and Technology, Seoul 136-791, Korea
  3. Samsung Advanced Institute of Technology, Yongin 449-712, Korea
  4. PCTP and Department of Physics, Pohang University of Science and Technology, Pohang, Kyungbuk 790-784, Korea

Correspondence to: Sug-Bong Choe1Hyun-Woo Lee4 Correspondence and requests for materials should be addressed to S.-B.C. (Email: sugbong@snu.ac.kr) or H.-W.L. (Email: hwl@postech.ac.kr).

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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