Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Magnetic monopole noise

Nature volume 571, pages 234–239 (2019)Cite this article

Subjects

Abstract

Magnetic monopoles1,2,3 are hypothetical elementary particles with quantized magnetic charge. In principle, a magnetic monopole can be detected by the quantized jump in magnetic flux that it generates upon passage through a superconducting quantum interference device (SQUID)4. Following the theoretical prediction that emergent magnetic monopoles should exist in several lanthanide pyrochlore magnetic insulators5,6, including Dy2Ti2O7, the SQUID technique has been proposed for their direct detection6. However, this approach has been hindered by the high number density and the generation–recombination fluctuations expected of such thermally generated monopoles. Recently, theoretical advances have enabled the prediction of the spectral density of magnetic-flux noise from monopole generation–recombination fluctuations in these materials7,8. Here we report the development of a SQUID-based flux noise spectrometer and measurements of the frequency and temperature dependence of magnetic-flux noise generated by Dy2Ti2O7 crystals. We detect almost all of the features of magnetic-flux noise predicted for magnetic monopole plasmas7,8, including the existence of intense magnetization noise and its characteristic frequency and temperature dependence. Moreover, comparisons of simulated and measured correlation functions of the magnetic-flux noise indicate that the motions of magnetic charges are strongly correlated. Intriguingly, because the generation–recombination time constant for Dy2Ti2O7 is in the millisecond range, magnetic monopole flux noise amplified by SQUID is audible to humans.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: SQUID detection of quantized flux jump of magnetic monopoles.
Fig. 2: Spectral density of fluctuations in monopole number and magnetization.
Fig. 3: Spectral density of magnetic-flux noise in Dy2Ti2O7.
Fig. 4: Spectral density of magnetic-flux noise for a correlated monopole fluid.

Similar content being viewed by others

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

  1. Dirac, P. Quantised singularities in the electromagnetic field. Proc. R. Soc. Lond. A 133, 60–72 (1931).

    Article  ADS  Google Scholar 

  2. Hooft, G. Magnetic monopoles in unified gauge theories. Nucl. Phys. B 79, 276–284 (1974).

    Article  ADS  MathSciNet  Google Scholar 

  3. Polyakov, A. M. Particle spectrum in the quantum field theory. J. Exp. Theor. Phys. Lett. 20, 194–195 (1974).

    Google Scholar 

  4. Cabrera, B. First results from a superconductive detector for moving magnetic monopoles. Phys. Rev. Lett. 48, 1378–1381 (1982).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  6. Castelnovo, C., Moessner, R. & Sondhi, S. L. Magnetic monopoles in spin ice. Nature 451, 42–45 (2008).

    Article  ADS  CAS  Google Scholar 

  7. Klyuev, A., Ryzhkin, M. & Yakimov, A. Statistics of fluctuations of magnetic monopole concentration in spin ice. Fluct. Noise Lett. 16, 1750035 (2017).

    Article  ADS  Google Scholar 

  8. Kirschner, F. K. K., Flicker, F., Yacoby, A., Yao, N. & Blundell, S. J. Proposal for the detection of magnetic monopoles in spin ice via nanoscale magnetometry. Phys. Rev. B 97, 140402 (2018).

    Article  ADS  CAS  Google Scholar 

  9. Castelnovo, C., Moessner, R. & Sondhi, S. Spin ice, fractionalization, and topological order. Annu. Rev. Condens. Matter Phys. 3, 35–55 (2012).

    Article  CAS  Google Scholar 

  10. Jaubert, L. & Holdsworth, P. Magnetic monopole dynamics in spin ice. J. Phys. Condens. Matter 23, 164222 (2011).

    Article  ADS  CAS  Google Scholar 

  11. Rosenkranz, S. et al. Crystal-field interaction in the pyrochlore magnet Ho2Ti2O7. J. Appl. Phys. 87, 5914–5916 (2000).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. Ramirez, A., Hayashi, A., Cava, R., Siddharthan, R. & Shastry, B. Zero-point entropy in ‘spin ice’. Nature 399, 333–335 (1999).

    Article  ADS  CAS  Google Scholar 

  14. Kaiser, V. et al. Emergent electrochemistry in spin ice: Debye–Hückel theory and beyond. Phys. Rev. B 98, 144413 (2018).

    Article  ADS  CAS  Google Scholar 

  15. Burgess, R. E. The statistics of charge carrier fluctuations in semiconductors. Proc. Phys. Soc. B 69, 1020–1027 (1956).

    Article  ADS  Google Scholar 

  16. van Vliet, K. M. & Fassett, J. R. Fluctuation Phenomena in Solids (ed. Burgess, R. E.) (Academic Press, 1965).

  17. Mitin, V., Reggiani, L. & Varani, L. in Noise and Fluctuations Control in Electronic Devices Ch. 2 (American Scientific Publishers, 2002).

  18. Konczakowska, A. & Wilamowski, B. M. in Fundamentals of Industrial Electronics Ch. 11 (Taylor and Francis, 2011).

  19. Melko, R. G. & Gingras, M. J. P. Monte Carlo studies of the dipolar spin ice model. J. Phys. Condens. Matter 16, 1277–1319 (2004).

    Article  ADS  Google Scholar 

  20. Vitale, S., Cavalleri, A., Cerdonio, M., Maraner, A. & Prodi, G. A. Thermal equilibrium noise with 1/f spectrum in a ferromagnetic alloy: anomalous temperature dependence. J. Appl. Phys. 76, 6332–6334 (1994).

    Article  ADS  CAS  Google Scholar 

  21. Reim, W., Koch, R., Malozemoff, A., Ketchen, M. & Maletta, H. Magnetic equilibrium noise in spin-glasses: Eu0.4Sr0.6S. Phys. Rev. Lett. 57, 905–908 (1986).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  Google Scholar 

  23. Matsuhira, K. et al. Spin dynamics at very low temperature in spin ice Dy2Ti2O7. J. Phys. Soc. Jpn 80, 123711 (2011).

    Article  ADS  Google Scholar 

  24. Yaraskavitch, L. R. et al. Spin dynamics in the frozen state of the dipolar spin ice material Dy2Ti2O7. Phys. Rev. B 85, 020410 (2012).

    Article  ADS  Google Scholar 

  25. Kassner, E. R. et al. Supercooled spin liquid state in the frustrated pyrochlore Dy2Ti2O7. Proc. Natl Acad. Sci. USA 112, 8549 (2015).

    Article  ADS  CAS  Google Scholar 

  26. Fennell, T. et al. Neutron scattering investigation of the spin ice state in Dy2Ti2O7. Phys. Rev. B 70, 134408 (2004).

    Article  ADS  Google Scholar 

  27. Quilliam, J. A., Meng, S., Mugford, C. G. A. & Kycia, J. B. Evidence of spin glass dynamics in dilute LiHoxY1−xF4. Phys. Rev. Lett. 101, 187204 (2008).

    Article  ADS  CAS  Google Scholar 

  28. Morris, D. et al. Dirac strings and magnetic monopoles in the spin ice Dy2Ti2O7. Science 326, 411–414 (2009).

    Article  ADS  CAS  Google Scholar 

  29. Bramwell, S. T. et al. Measurement of the charge and current of magnetic monopoles in spin ice. Nature 461, 956–959 (2009).

    Article  ADS  CAS  Google Scholar 

  30. Bovo, L., Bloxsom, J., Prabhakaran, D., Aeppli, G. & Bramwell, S. Brownian motion and quantum dynamics of magnetic monopoles in spin ice. Nat. Commun. 4, 1535–1542 (2013).

    Article  ADS  CAS  Google Scholar 

  31. Giblin, S., Bramwell, S., Holdsworth, P., Prabhakaran, D. & Terry, I. Creation and measurement of long-lived magnetic monopole currents in spin ice. Nat. Phys. 7, 252–258 (2011).

    Article  CAS  Google Scholar 

  32. Kaiser, V., Bramwell, S. T., Holdsworth, P. C. W. & Moessner, R. ac Wien effect in spin ice, manifest in nonlinear, nonequilibrium susceptibility. Phys. Rev. Lett. 115, 037201 (2015).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  33. Paulsen, C. et al. Experimental signature of the attractive Coulomb force between positive and negative magnetic monopoles in spin ice. Nat. Phys. 12, 661–666 (2016).

    Article  CAS  Google Scholar 

  34. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N. & Teller, A. H. Equation of state calculations by fast computing machines. J. Chem. Phys. 21, 1087–1092 (1953).

    Article  ADS  CAS  Google Scholar 

  35. Eyvazov, A. B. et al. Common glass-forming spin liquid state in the pyrochlore magnets Dy2Ti2O7 and Ho2Ti2O7. Phys. Rev. B 98, 214430 (2018).

    Article  ADS  CAS  Google Scholar 

  36. Takatsu, H. et al. AC susceptibility of the dipolar spin ice Dy2Ti2O7: experiments and Monte Carlo simulations. J. Phys. Soc. Jpn 82, 104710 (2013).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We are grateful to C. Castelnovo, J. Goff, Y. B. Kim, M. J. Lawler, A. Ramirez, D. Schlom and N. Y. Yao for discussions and communications. J.C.S.D. thanks O. H. S. Davis for discussions and for proposing to study magnetic noise in pyrochlores. R.D. thanks Y. X. Chong for assistance during experimental operations and acknowledges use of the Cornell Center for Materials Research Shared Facilities, supported through the NSF MRSEC programme (DMR-1719875). A.E. acknowledges support via Israeli Pazy Equipment Grant 299/18. F.K.K.K. acknowledges support from Lincoln College, Oxford. F.F. acknowledges support from the Astor Junior Research Fellowship of New College, Oxford. S.J.B. acknowledges support from EPSRC (EP/N023803/1). The conceptual design of our experimental techniques was supported by the W. M. Keck Foundation. J.C.S.D. acknowledges support from Science Foundation Ireland under Award SFI 17/RP/5445 and from the European Research Council (ERC) under award DLV-788932. R.D. and J.C.S.D. acknowledge support, plus funding for instrument development and experimental studies, from the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant GBMF4544.

Author information

Author notes

  1. These authors contributed equally: Ritika Dusad, Franziska K. K. Kirschner

Authors and Affiliations

  1. Department of Physics, Cornell University, Ithaca, NY, USA

    Ritika Dusad, Jesse C. Hoke, Benjamin R. Roberts, Anna Eyal & J. C. Séamus Davis

  2. Clarendon Laboratory, University of Oxford, Oxford, UK

    Franziska K. K. Kirschner, Stephen J. Blundell & J. C. Séamus Davis

  3. Department of Physics, Stanford University, Stanford, CA, USA

    Jesse C. Hoke

  4. Department of Physics, Technion – Israel Institute of Technology, Haifa, Israel

    Anna Eyal

  5. Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Oxford, UK

    Felix Flicker

  6. Brockhouse Institute for Materials Research, McMaster University, Hamilton, Ontario, Canada

    Graeme M. Luke

  7. Department of Physics, McMaster University, Hamilton, Ontario, Canada

    Graeme M. Luke

  8. Canadian Institute for Advanced Research, Toronto, Ontario, Canada

    Graeme M. Luke

  9. Department of Physics, University College Cork, Cork, Ireland

    J. C. Séamus Davis

Authors
  1. Ritika Dusad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Franziska K. K. Kirschner
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jesse C. Hoke
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Benjamin R. Roberts
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Anna Eyal
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Felix Flicker
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Graeme M. Luke
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Stephen J. Blundell
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. J. C. Séamus Davis
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

R.D. and J.C.S.D. conceptualized the project and designed the experimental setup. R.D. developed the flux noise spectrometer. R.D., J.C.H., B.R.R. and A.E. carried out the experiments and data analysis. G.M.L. synthesized the Dy2Ti2O7 samples. F.K.K.K. carried out the Monte Carlo simulations with help from F.F. G.M.L., S.J.B. and J.C.S.D. supervised the investigation and wrote the paper with key contributions from R.D., F.K.K.K. and F.F. The manuscript reflects the contributions of all authors.

Corresponding authors

Correspondence to Stephen J. Blundell or J. C. Séamus Davis.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Sensitivity calibration of magnetic-flux noise spectrometer.

Here we show the linear relationship between a flux applied to the pickup coil via a drive coil (Φapplied) and flux output by the SQUID (Φmeasured). The slope gives the transfer function between the pickup coil and the SQUID.

Extended Data Fig. 2 Comparison of Dy2Ti2O7 magnetic-flux noise with background noise.

Typical spectrum of magnetic-flux noise spectral density from a Dy2Ti2O7 sample (at 1.22 K) compared with that of an empty pickup coil corresponding to ~16.8 × 10−12Φ02 Hz−1. The black data points have been shifted vertically for clarity. Error bars represent the standard deviation of each data point, extracted from an average of five independent Dy2Ti2O7 flux noise datasets.

Extended Data Fig. 3 Quality of fits to measured flux noise spectral density.

Residuals (SΦ(ω, T) – Sfit(ω, T)) for fits of the measured flux noise spectral density (Fig. 3) with equation (5) are shown for four temperatures.

Extended Data Fig. 4 Comparison of magnetic-flux noise from different Dy2Ti2O7 samples.

Plot of magnetic-flux noise SΦ(ω, T) from two different rod-shaped Dy2Ti2O7 samples. We observe that the SΦ(ω, T) distributions are very similar and therefore this experiment is qualitatively repeatable for single crystals of Dy2Ti2O7. The differences in magnitude and time constant are due to the geometrical differences between the two samples.

Extended Data Fig. 5 Magnetization relaxation time constants from flux noise spectra.

Time constant obtained from fits to the measured SΦ(ω, T) data shown in Fig. 3. The time constant τ(T) derived from the flux noise behaves in a super-Arrhenius fashion, τ(T) = τ0exp[DT0/(T – T0)], consistent with previous measurements of a.c. susceptibility time constants τM(T) (ref. 35), which also exhibited super-Arrhenius behaviour with τ0 ≈ 1.4 × 10−4 s, D ≈ 14, T0 ≈ 0.26 K.

Extended Data Fig. 6 Variance of Dy2Ti2O7 magnetic-flux noise versus temperature.

Measured variance of flux \({\sigma }_{{\Phi }}^{2}\), showing that it is approximately constant as a function of temperature in the range displayed.

Supplementary information

Supplementary Video 1

The acoustic noise generated when the magnetization noise from a Dy2Ti2O7 sample, amplified by the SQUID, is recorded as an audio file. In the context of refs 7,8, this can be considered as audible magnetic monopole noise.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dusad, R., Kirschner, F.K.K., Hoke, J.C. et al. Magnetic monopole noise. Nature 571, 234–239 (2019). https://doi.org/10.1038/s41586-019-1358-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41586-019-1358-1

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing