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Measurement of the charge and current of magnetic monopoles in spin ice

Abstract

The transport of electrically charged quasiparticles (based on electrons or ions) plays a pivotal role in modern technology as well as in determining the essential functions of biological organisms. In contrast, the transport of magnetic charges has barely been explored experimentally, mainly because magnetic charges, in contrast to electric ones, are generally considered at best to be convenient macroscopic parameters1,2, rather than well-defined quasiparticles. However, it was recently proposed that magnetic charges can exist in certain materials in the form of emergent excitations that manifest like point charges, or magnetic monopoles3. Here we address the question of whether such magnetic charges and their associated currents—‘magnetricity’—can be measured directly in experiment, without recourse to any material-specific theory. By mapping the problem onto Onsager's theory of electrolytes4, we show that this is indeed possible, and devise an appropriate method for the measurement of magnetic charges and their dynamics. Using muon spin rotation as a suitable local probe, we apply the method to a real material, the ‘spin ice’ Dy2Ti2O7 (refs 5–8). Our experimental measurements prove that magnetic charges exist in this material, interact via a Coulomb potential, and have measurable currents. We further characterize deviations from Ohm's law, and determine the elementary unit of magnetic charge to be 5 μB Å-1, which is equal to that recently predicted using the microscopic theory of spin ice3. Our measurement of magnetic charge and magnetic current establishes an instance of a perfect symmetry between electricity and magnetism.

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Figure 1: Magnetic Wien effect, and the detection of magnetic charge by implanted muons.
Figure 2: Exponential decay of muon spin precession in Dy2Ti2O7.
Figure 3: A quantity that is proportional to magnetic charge conductivity in Dy 2 Ti 2 O 7 , illustrating a non-Ohmic increase in conductivity with field.
Figure 4: Temperature dependence of the muon relaxation rate λ in Dy2Ti2O7.
Figure 5: Experimentally measured ‘elementary’ magnetic charge in Dy2Ti2O7.

References

  1. Morrish, A. H. The Physical Principles of Magnetism (Wiley and Sons, 1965)

    Google Scholar 

  2. Jackson, J. D. Classical Electrodynamics (Wiley and Sons, 1998)

    MATH  Google Scholar 

  3. Castelnovo, C., Moessner, R. & Sondhi, S. L. Magnetic monopoles in spin ice. Nature 451, 42–45 (2007)

    ADS  Article  Google Scholar 

  4. Onsager, L. Deviations from Ohm's law in weak electrolytes. J. Chem. Phys. 2, 599–615 (1934)

    ADS  CAS  Article  Google Scholar 

  5. Harris, M. J., Bramwell, S. T., McMorrow, D. F., Zeiske, T. & Godfrey, K. W. Geometrical frustration in the ferromagnetic pyrochlore Ho2Ti2O7 . Phys. Rev. Lett. 79, 2554–2557 (1997)

    ADS  CAS  Article  Google Scholar 

  6. Ramirez, A. P., Hayashi, A., Cava, R. J., Siddharthan, R. B. & Shastry, S. Zero-point entropy in spin ice. Nature 399, 333–336 (1999)

    ADS  CAS  Article  Google Scholar 

  7. Bramwell, S. T. & Gingras, M. J. P. Spin ice state in frustrated magnetic pyrochlore materials. Science 294, 1495–1501 (2001)

    ADS  CAS  Article  Google Scholar 

  8. Snyder, J. et al. Low-temperature spin freezing in the Dy2Ti2O7 spin ice. Phys. Rev. B 69, 064414 (2004)

    ADS  Article  Google Scholar 

  9. Lee, S.-H. et al. Emergent excitations in a geometrically frustrated magnet. Nature 418, 856–858 (2002)

    ADS  CAS  Article  Google Scholar 

  10. Keren, A. et al. Dynamic properties of a diluted pyrochlore cooperative paramagnet (Tb p Y1-p )2Ti2O7 . Phys. Rev. Lett. 92, 107204 (2004)

    ADS  CAS  Article  Google Scholar 

  11. Moessner, R. & Chalker, J. T. Properties of a classical spin liquid: the Heisenberg pyrochlore antiferromagnet. Phys. Rev. Lett. 80, 2929–2932 (1998)

    ADS  CAS  Article  Google Scholar 

  12. Hermele, M., Fisher, M. P. A. & Balents, L. Pyrochlore photons: the U(1) spin liquid in a S = 1/2 three-dimensional frustrated magnet. Phys. Rev. B 69, 064404 (2004)

    ADS  Article  Google Scholar 

  13. Burnell, F. J., Chakravarty, S. & Sondhi, S. L. Monopole flux state on the pyrochlore lattice. Phys. Rev. B 79, 144432 (2009)

    ADS  Article  Google Scholar 

  14. Jaubert, L. D. C. & Holdsworth, P. C. W. Signature of magnetic monopole and Dirac string dynamics in spin ice. Nature Phys. 5, 258–261 (2009)

    ADS  CAS  Article  Google Scholar 

  15. Fennell, T. et al. Magnetic coulomb phase in the spin ice Ho2Ti2O7 . Science 10.1126/science.1177582 (26 August 2009)

  16. Morris, D. J. P. et al. Dirac strings and magnetic monopoles in spin ice Dy2Ti2O7 . Science 10.1126/science.1178868 (26 August 2009)

  17. Kadowaki, H. et al. Observation of magnetic monopoles in spin ice. Preprint at 〈http://arXiv.org/abs/0908.3568v2〉 (2009)

  18. Moore, W. J. Physical Chemistry (Longman, 1978)

    Google Scholar 

  19. Bass, L. Wien dissociation as a rate process. Trans. Faraday Soc. 64, 2153–2159 (1968)

    CAS  Article  Google Scholar 

  20. Mason, D. P. & McIlroy, D. K. A perturbation solution to the problem of Wien dissociation in weak electrolytes. Proc. R. Soc. Lond. A 359, 303–317 (1978)

    ADS  CAS  Article  Google Scholar 

  21. Uemura, Y. J. in Muon Science: Muons in Physics, Chemistry and Materials (eds Lee, S., Kilcoyne, S. & Cywinski, R.) 85–113 (SUSSP and Institute of Physics, 1998)

    Google Scholar 

  22. Orendácˇ, M., Hanko, Cˇ. E. & Orendácˇová, A. Magnetocaloric study of spin relaxation in dipolar spin ice Dy2Ti2O7 . Phys. Rev. B 75, 104425 (2007)

    ADS  Article  Google Scholar 

  23. den Hertog, B. C. & Gingras, M. J. P. Dipolar interactions and origin of spin ice in Ising pyrochlore magnets. Phys. Rev. Lett. 84, 3430–3433 (2000)

    ADS  CAS  Article  Google Scholar 

  24. Bramwell, S. T. & Harris, M. J. Frustration in Ising-type spin models on the pyrochlore lattice. J. Phys. Condens. Matter 10, L215–L220 (1998)

    ADS  CAS  Article  Google Scholar 

  25. Ryzhkin, I. A. Magnetic relaxation in rare-earth oxide pyrochlores. J. Exp. Theor. Phys. 101, 481–486 (2005)

    ADS  CAS  Article  Google Scholar 

  26. Eigen, M. & de Maeyer, L. Self-dissociation and protonic charge transport in water and ice. Proc. R. Soc. Lond. A 247, 505–533 (1958)

    ADS  CAS  Article  Google Scholar 

  27. Lago, J., Blundell, S. J. & Baines, C. µSR investigation of spin dynamics in the spin-ice material Dy2Ti2O7 . J. Phys. Condens. Matter 19, 326210 (2007)

    Article  Google Scholar 

  28. Bertin, E. et al. Effective hyperfine temperature in frustrated Gd2Sn2O7: two level model and 155Gd Mössbauer measurements. Eur. Phys. J. B 27, 347–354 (2002)

    ADS  CAS  Article  Google Scholar 

  29. Preskill, J. Magnetic monopoles. Annu. Rev. Nucl. Part. Sci. 34, 461–530 (1984)

    ADS  CAS  Article  Google Scholar 

  30. Wang, R. F. et al. Artificial ‘spin ice’ in a geometrically frustrated lattice of nanoscale ferromagnetic islands. Nature 439, 303–306 (2006)

    ADS  CAS  Article  Google Scholar 

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Acknowledgements

We thank C. Castelnovo, M. J. P. Gingras, P. C. W. Holdsworth, L. Jaubert, D. F. McMorrow, R. Moessner and I. Terry for discussions.

Author Contributions S.T.B., S.R.G. and T.F. conceived the method; S.T.B. derived the theory; all authors planned the experiment; D.P. prepared the samples; S.R.G., S.T.B., R.A. and S.C. performed the experiment and analysed the data; S.T.B. and S.R.G. wrote the paper; and all authors contributed to the manuscript.

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Bramwell, S., Giblin, S., Calder, S. et al. Measurement of the charge and current of magnetic monopoles in spin ice. Nature 461, 956–959 (2009). https://doi.org/10.1038/nature08500

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