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Microscopic theory of a precessing ferromagnet for ultrasensitive magnetometry

Xueqi Ni1,*, Zhixing Zou1, Ruvi Lecamwasam2, Andrea Vinante3,4, Dmitry Budker5,6,7,8, Ping Koy Lam2,9,10, Tao Wang2,†, and Jiangbin Gong1,10,‡

  • *Contact author: xueqi.ni@u.nus.edu
  • †Contact author: tao_wang@imre.a-star.edu.sg
  • ‡Contact author: phygj@nus.edu.sg
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Phys. Rev. Research 7, 043120 – Published 31 October, 2025

DOI: https://doi.org/10.1103/1v1p-kpb2

Abstract

Levitated systems have great potential in quantum sensing and exploring fundamental physics at the macroscopic scale. Of particular interest are recent works suggesting that a levitated ferromagnet can beat the standard quantum limit of magnetometry, a benchmark for quantum sensors. In this work, we show how a microscopic theory capturing atomic-scale spin-lattice interactions can be used to fully explain the emergence of collective precession dynamics of a levitated ferromagnet and the origin of its enhanced magnetometric sensitivity beyond that of independent spins. Our theory further takes us to two innovative experimental designs of immediate interest: measurement of the celebrated Berry phase with a precessing ferromagnetic needle and the use of its nutation motion to sense a low-frequency oscillating magnetic field. With a microscopic theory established for levitated ferromagnetic needles, future studies of macroscopic quantum effects and the associated quantum-classical transition also become possible.

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References (69)

  1. C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys. 89, 035002 (2017).
  2. K. Bongs, S. Bennett, and A. Lohmann, Quantum sensors will start a revolution—If we deploy them right, Nature (London) 617, 672 (2023).
  3. M. Jiang, H. Su, Y. Chen, M. Jiao, Y. Huang, Y. Wang, X. Rong, X. Peng, and J. Du, Searches for exotic spin-dependent interactions with spin sensors, Rep. Prog. Phys. 88, 016401 (2025).
  4. S. D. Bass and M. Doser, Quantum sensing for particle physics, Nat. Rev. Phys. 6, 329 (2024).
  5. N. Aslam, H. Zhou, E. K. Urbach, M. J. Turner, R. L. Walsworth, M. D. Lukin, and H. Park, Quantum sensors for biomedical applications, Nat. Rev. Phys. 5, 157 (2023).
  6. H. B. Dang, A. C. Maloof, and M. V. Romalis, Ultrahigh sensitivity magnetic field and magnetization measurements with an atomic magnetometer, Appl. Phys. Lett. 97, 151110 (2010).
  7. D. Budker and D. F. Jackson Kimball, Optical Magnetometry (Cambridge University Press, Cambridge, 2013).
  8. S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, and J. I. Cirac, Improvement of frequency standards with quantum entanglement, Phys. Rev. Lett. 79, 3865 (1997).
  9. J. Huang, M. Zhuang, and C. Lee, Entanglement-enhanced quantum metrology: From standard quantum limit to Heisenberg limit, Appl. Phys. Rev. 11, 031302 (2024).
  10. V. Giovannetti, S. Lloyd, and L. Maccone, Quantum-enhanced measurements: Beating the standard quantum limit, Science 306, 1330 (2004).
  11. Y. A. Yang, W.-T. Luo, J.-L. Zhang, S.-Z. Wang, C.-L. Zou, T. Xia, and Z.-T. Lu, Minute-scale Schrödinger-cat state of spin-5/2 atoms, Nat. Photon. 19, 89 (2025).
  12. M. Xu, M. Jiang, Y. Wang, H. Su, Y. Huang, and X. Peng, Cooperative spin amplifier for enhanced quantum sensing, Phys. Rev. Lett. 133, 133202 (2024).
  13. A. W. Young, W. J. Eckner, W. R. Milner, D. Kedar, M. A. Norcia, E. Oelker, N. Schine, J. Ye, and A. M. Kaufman, Half-minute-scale atomic coherence and high relative stability in a tweezer clock, Nature (London) 588, 408 (2020).
  14. C. D. Panda, M. Tao, J. Egelhoff, M. Ceja, V. Xu, and H. Müller, Coherence limits in lattice atom interferometry at the one-minute scale, Nat. Phys. 20, 1234 (2024).
  15. J. Franke, S. R. Muleady, R. Kaubruegger, F. Kranzl, R. Blatt, A. M. Rey, M. K. Joshi, and C. F. Roos, Quantum-enhanced sensing on optical transitions through finite-range interactions, Nature (London) 621, 740 (2023).
  16. K. A. Gilmore, M. Affolter, R. J. Lewis-Swan, D. Barberena, E. Jordan, A. M. Rey, and J. J. Bollinger, Quantum-enhanced sensing of displacements and electric fields with two-dimensional trapped-ion crystals, Science 373, 673 (2021).
  17. M. Auzinsh, D. Budker, D. F. Kimball, S. M. Rochester, J. E. Stalnaker, A. O. Sushkov, and V. V. Yashchuk, Can a quantum nondemolition measurement improve the sensitivity of an atomic magnetometer? Phys. Rev. Lett. 93, 173002 (2004).
  18. B. A. Stickler, B. Papendell, S. Kuhn, B. Schrinski, J. Millen, M. Arndt, and K. Hornberger, Probing macroscopic quantum superpositions with nanorotors, New J. Phys. 20, 122001 (2018).
  19. S. Nimmrichter and K. Hornberger, Macroscopicity of mechanical quantum superposition states, Phys. Rev. Lett. 110, 160403 (2013).
  20. W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, Towards quantum superpositions of a mirror, Phys. Rev. Lett. 91, 130401 (2003).
  21. M. Roda-Llordes, A. Riera-Campeny, D. Candoli, P. T. Grochowski, and O. Romero-Isart, Macroscopic quantum superpositions via dynamics in a wide double-well potential, Phys. Rev. Lett. 132, 023601 (2024).
  22. B. D. Wood, S. Bose, and G. W. Morley, Spin dynamical decoupling for generating macroscopic superpositions of a free-falling nanodiamond, Phys. Rev. A 105, 012824 (2022).
  23. M. Bild, M. Fadel, Y. Yang, U. Von Lüpke, P. Martin, A. Bruno, and Y. Chu, Schrödinger cat states of a 16-microgram mechanical oscillator, Science 380, 274 (2023).
  24. D. F. Jackson Kimball, A. O. Sushkov, and D. Budker, Precessing ferromagnetic needle magnetometer, Phys. Rev. Lett. 116, 190801 (2016).
  25. Y. B. Band, Y. Avishai, and A. Shnirman, Dynamics of a magnetic needle magnetometer: Sensitivity to Landau-Lifshitz-Gilbert damping, Phys. Rev. Lett. 121, 160801 (2018).
  26. P. Fadeev, C. Timberlake, T. Wang, A. Vinante, Y. B. Band, D. Budker, A. O. Sushkov, H. Ulbricht, and D. F. J. Kimball, Ferromagnetic gyroscopes for tests of fundamental physics, Quantum Sci. Technol. 6, 024006 (2021).
  27. T. Wang, S. Lourette, S. R. O'Kelley, M. Kayci, Y. Band, D. F. J. Kimball, A. O. Sushkov, and D. Budker, Dynamics of a ferromagnetic particle levitated over a superconductor, Phys. Rev. Appl. 11, 044041 (2019).
  28. J. Hofer, R. Gross, G. Higgins, H. Huebl, O. F. Kieler, R. Kleiner, D. Koelle, P. Schmidt, J. A. Slater, M. Trupke, K. Uhl, T. Weimann, W. Wieczorek, and M. Aspelmeyer, High-q magnetic levitation and control of superconducting microspheres at millikelvin temperatures, Phys. Rev. Lett. 131, 043603 (2023).
  29. F. Ahrens, W. Ji, D. Budker, C. Timberlake, H. Ulbricht, and A. Vinante, Levitated ferromagnetic magnetometer with energy resolution well below ℏ, Phys. Rev. Lett. 134, 110801 (2025).
  30. M. W. Mitchell and S. Palacios Alvarez, Colloquium: Quantum limits to the energy resolution of magnetic field sensors, Rev. Mod. Phys. 92, 021001 (2020).
  31. A. Vinante, C. Timberlake, D. Budker, D. F. J. Kimball, A. O. Sushkov, and H. Ulbricht, Surpassing the energy resolution limit with ferromagnetic torque sensors, Phys. Rev. Lett. 127, 070801 (2021).
  32. I. K. Kominis, Quantum thermodynamic derivation of the energy resolution limit in magnetometry, Phys. Rev. Lett. 133, 263201 (2024).
  33. M. Aßmann and U. Nowak, Spin-lattice relaxation beyond Gilbert damping, J. Magn. Magn. Mater. 469, 217 (2019).
  34. M. Strungaru, M. O. Ellis, S. Ruta, O. Chubykalo-Fesenko, R. F. Evans, and R. W. Chantrell, Spin-lattice dynamics model with angular momentum transfer for canonical and microcanonical ensembles, Phys. Rev. B 103, 024429 (2021).
  35. J. H. van Vleck, On the anisotropy of cubic ferromagnetic crystals, Phys. Rev. 52, 1178 (1937).
  36. For further discussion on how classical simulations can inform entanglement generation, see Refs. [68, 69].
  37. O. Giraud, P. Braun, and D. Braun, Classicality of spin states, Phys. Rev. A 78, 042112 (2008).
  38. C. Dornes, Y. Acremann, M. Savoini, M. Kubli, M. J. Neugebauer, E. Abreu, L. Huber, G. Lantz, C. A. Vaz, H. Lemke et al., The ultrafast Einstein–de Haas effect, Nature (London) 565, 209 (2019).
  39. L. Zhang and Q. Niu, Angular momentum of phonons and the Einstein–de Haas effect, Phys. Rev. Lett. 112, 085503 (2014).
  40. A. Kani, F. Quijandría, and J. Twamley, Magnonic Einstein–de Haas effect: Ultrafast rotation of magnonic microspheres, Phys. Rev. Lett. 129, 257201 (2022).
  41. X. Nie and D.-X. Yao, Einstein-de Haas effect: A bridge linking mechanics, magnetism, and topology, Sci. Bull. 70, 301 (2025).
  42. See Supplemental Material at http://link.aps.org/supplemental/10.1103/1v1p-kpb2 for animations of the needle precession dynamics obtained from our microscopic Hamiltonian model.
  43. D. Krapf, E. Marinari, R. Metzler, G. Oshanin, X. Xu, and A. Squarcini, Power spectral density of a single Brownian trajectory: What one can and cannot learn from it, New J. Phys. 20, 023029 (2018).
  44. L. Viola and S. Lloyd, Dynamical suppression of decoherence in two-state quantum systems, Phys. Rev. A 58, 2733 (1998).
  45. L. Viola, E. Knill, and S. Lloyd, Dynamical decoupling of open quantum systems, Phys. Rev. Lett. 82, 2417 (1999).
  46. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice Hall PTR, Upper Saddle River, NJ, 1993).
  47. D. Suter, G. C. Chingas, R. A. Harris, and A. Pines, Berry's phase in magnetic resonance, Mol. Phys. 61, 1327 (1987).
  48. K. Arai, J. Lee, C. Belthangady, D. R. Glenn, H. Zhang, and R. L. Walsworth, Geometric phase magnetometry using a solid-state spin, Nat. Commun. 9, 4996 (2018).
  49. T. Wang, W. Lee, M. Limes, T. Kornack, E. Foley, and M. Romalis, Pulsed vector atomic magnetometer using an alternating fast-rotating field, Nat. Commun. 16, 1374 (2025).
  50. G. Vasilakis, V. Shah, and M. V. Romalis, Stroboscopic backaction evasion in a dense alkali-metal vapor, Phys. Rev. Lett. 106, 143601 (2011).
  51. A. V. Gramolin, D. Aybas, D. Johnson, J. Adam, and A. O. Sushkov, Search for axion-like dark matter with ferromagnets, Nat. Phys. 17, 79 (2021).
  52. M. Jiang, H. Su, A. Garcon, X. Peng, and D. Budker, Search for axion-like dark matter with spin-based amplifiers, Nat. Phys. 17, 1402 (2021).
  53. S. Kalia, D. Budker, D. F. J. Kimball, W. Ji, Z. Liu, A. O. Sushkov, C. Timberlake, H. Ulbricht, A. Vinante, and T. Wang, Ultralight dark matter detection with levitated ferromagnets, Phys. Rev. D 110, 115029 (2024).
  54. Y. Liu, I. P. Miranda, L. Johnson, A. Bergman, A. Delin, D. Thonig, M. Pereiro, O. Eriksson, V. Azimi-Mousolou, and E. Sjöqvist, Quantum analog of Landau-Lifshitz-Gilbert dynamics, Phys. Rev. Lett. 133, 266704 (2024).
  55. R. Wieser, Comparison of quantum and classical relaxation in spin dynamics, Phys. Rev. Lett. 110, 147201 (2013).
  56. J. Anders, C. R. Sait, and S. A. Horsley, Quantum Brownian motion for magnets, New J. Phys. 24, 033020 (2022).
  57. G. S. Uhrig, Landau-Lifshitz damping from Lindbladian dissipation in quantum magnets, New J. Phys. 27, 103502 (2025).
  58. X. Ni, Dataset and code for “Microscopic theory of a precessing ferromagnet for ultrasensitive magnetometry” (2025), https://github.com/Xueqi-ni/Microscopic_Model_for_Precessing_Ferromagnets.
  59. Y. Tserkovnyak, A. Brataas, and G. E. W. Bauer, Enhanced Gilbert damping in thin ferromagnetic films, Phys. Rev. Lett. 88, 117601 (2002).
  60. M. C. Hickey and J. S. Moodera, Origin of intrinsic Gilbert damping, Phys. Rev. Lett. 102, 137601 (2009).
  61. U. Delić, M. Reisenbauer, K. Dare, D. Grass, V. Vuletić, N. Kiesel, and M. Aspelmeyer, Cooling of a levitated nanoparticle to the motional quantum ground state, Science 367, 892 (2020).
  62. S. M. Bhagat and P. Lubitz, Temperature variation of ferromagnetic relaxation in the 3d transition metals, Phys. Rev. B 10, 179 (1974).
  63. B. Khodadadi, A. Rai, A. Sapkota, A. Srivastava, B. Nepal, Y. Lim, D. A. Smith, C. Mewes, S. Budhathoki, A. J. Hauser, M. Gao, J.-F. Li, D. D. Viehland, Z. Jiang, J. J. Heremans, P. V. Balachandran, T. Mewes, and S. Emori, Conductivitylike Gilbert damping due to intraband scattering in epitaxial iron, Phys. Rev. Lett. 124, 157201 (2020).
  64. C. Kittel, Theory of the structure of ferromagnetic domains in films and small particles, Phys. Rev. 70, 965 (1946).
  65. A. J. McRoberts, T. Bilitewski, M. Haque, and R. Moessner, Domain wall dynamics in classical spin chains: Free propagation, subdiffusive spreading, and soliton emission, Phys. Rev. Lett. 132, 057202 (2024).
  66. N. Wiener, Generalized harmonic analysis, Acta Math. 55, 117 (1930).
  67. A. Khintchine, Korrelationstheorie der stationären stochastischen Prozesse, Math. Ann. 109, 604 (1934).
  68. J. Gong and P. Brumer, When is quantum decoherence dynamics classical? Phys. Rev. Lett. 90, 050402 (2003).
  69. J. Gong and P. Brumer, Intrinsic decoherence dynamics in smooth Hamiltonian systems: Quantum-classical correspondence, Phys. Rev. A 68, 022101 (2003).

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Phys. Rev. Research 7, 043120– Published 31 October, 2025
  • Received 13 March 2025
  • Revised 30 June 2025
  • Accepted 26 September 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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