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# Search for axion-like dark matter with ferromagnets

## Abstract

Ultralight axion-like particles are well-motivated dark matter candidates, naturally emerging from theories of physics at ultrahigh energies. Here we report the results of a direct search for electromagnetic interactions of axion-like dark matter in the mass range that spans three decades from 12 peV to 12 neV. The detection scheme is based on a modification of Maxwell’s equations in the presence of axion-like dark matter that mixes with a static magnetic field to produce an oscillating magnetic field. The experiment makes use of toroidal magnets with ferromagnetic powder cores made of an iron–nickel alloy, which enhance the static magnetic field by a factor of 24. Using superconducting quantum interference devices, we achieve magnetic sensitivity of 150 $$\mathrm{aT}\, {\mathrm{Hz}}^{-1/2}$$, which is at the level of the most sensitive magnetic field measurements demonstrated with any broadband sensor. We recorded 41 h of data and improved the best limits on the magnitude of electromagnetic coupling constant for axion-like dark matter over a part of our mass range, at 20 peV reaching 4.0 × 10−11 GeV−1 (95% confidence level). Our measurements begin to explore the coupling strengths and masses of axion-like particles, where their mixing with photons could explain the anomalous transparency of the Universe to TeV γ-rays.

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## Data availability

Source data are provided with this paper. All other data that support the plots in this paper and other findings of this study are available from the corresponding author upon reasonable request.

## Code availability

The code that supports the plots in this paper is available from the corresponding author upon reasonable request.

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## Acknowledgements

We thank B. Brubaker for valuable discussions about the data analysis. Data analysis calculations were performed on the Shared Computing Cluster, which is administered by Boston University’s Research Computing Services. We acknowledge support from the NSF grant no. 1806557, the Heising-Simons Foundation grant no. 2015-039, the Simons Foundation grant no. 641332 and the Alfred P. Sloan Foundation grant no. FG-2016-6728.

## Author information

Authors

### Contributions

A.O.S. conceived and supervised the research. A.V.G., A.O.S. and D.J. designed and built the experimental apparatus. D.A. developed the data acquisition system. D.J. performed the COMSOL simulations. A.V.G. and J.A. carried out the magnetic permeability measurements. A.O.S. and A.V.G. analyzed the data. All the authors contributed to data collection and writing the manuscript.

### Corresponding author

Correspondence to Alexander O. Sushkov.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Physics thanks Claudio Gatti, David Kaplan and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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

## Supplementary information

### Supplementary Information

Supplementary text, Figs. 1–6 and Tables 1–6.

## Source data

### Source Data Fig. 2

Toroid permeability and azimuthal magnetic field versus applied current.

### Source Data Fig. 3

Flux-to-voltage transfer function versus frequency, for channels A and B.

### Source Data Fig. 4

95% confidence limits on the electromagnetic coupling strength of axion-like dark matter.

## Rights and permissions

Reprints and Permissions

Gramolin, A.V., Aybas, D., Johnson, D. et al. Search for axion-like dark matter with ferromagnets. Nat. Phys. 17, 79–84 (2021). https://doi.org/10.1038/s41567-020-1006-6

• Accepted:

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• DOI: https://doi.org/10.1038/s41567-020-1006-6

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