Magnetic monopole noise

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.

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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.

Data availability

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

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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.

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Authors

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.

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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(ωT) – Sfit(ωT)) 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(ωT) from two different rod-shaped Dy2Ti2O7 samples. We observe that the SΦ(ωT) 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(ωT) 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.

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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

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