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  • Letter
  • Open Access

Power spectrum of magnetic relaxation in spin ice: Anomalous diffusion in a Coulomb fluid

David Billington1, Edward Riordan1, Clara Cafolla-Ward1, Jordan Wilson1, Elsa Lhotel2, Carley Paulsen2, Dharmalingham Prabhakaran3, Steven T. Bramwell4, Felix Flicker5 et al.

Sean R. Giblin1,*

  • 1School of Physics and Astronomy, Cardiff University, Queen's Building, The Parade, Cardiff CF24 3AA, United Kingdom
  • 2Institut Néel, CNRS and Université Grenoble Alpes, 38000 Grenoble, France
  • 3Department of Physics, Oxford University, Oxford OX1 3PU, United Kingdom
  • 4London Centre for Nanotechnology and Department of Physics and Astronomy, University College London, 17-19 Gordon Street, London WC1H 0AJ, United Kingdom
  • 5School of Physics, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom

  • *Contact author: giblinsr@cardiff.ac.uk
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Phys. Rev. B 112, L020503 – Published 11 July, 2025

DOI: https://doi.org/10.1103/9ttp-n3p5

Abstract

Magnetization noise measurements on the spin ice Dy2Ti2O7 have revealed a remarkable “pink noise” power spectrum S(f,T) below 4 K, including evidence of magnetic monopole excitations diffusing in a fractal landscape. However, at higher temperatures, the reported values of the anomalous exponent b(T) describing the high-frequency tail of S(f,T) are not easy to reconcile with other results in the literature, which generally suggest significantly smaller deviations from the Brownian motion value of b=2, that become negligible above T=20 K. We accurately estimate b(T) at temperatures between 2 and 20 K, using ac susceptibility measurements that, crucially, stretch up to the relatively high frequency of f=106 Hz. We show that previous noise measurements underestimate b(T) and we suggest reasons for this. Our results establish deviations in b(T) from b=2 up to about 20 K. However, we confirm that b(T) is sample dependent: The details of this dependence agree in part, though not completely, with previous studies of the effect of crystal defects on monopole population and diffusion. Our results establish the form of b(T) which characterizes the subtle, and evolving, nature of monopole diffusion in the dense Coulomb fluid, a highly correlated state, where several dynamical processes combine.

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Phys. Rev. B 112, L020503– Published 11 July, 2025
  • Received 1 November 2024
  • Revised 26 May 2025
  • Accepted 26 June 2025
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