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X-Ray Free-Electron Laser Observation of Giant and Anisotropic Magnetostriction in β−O2 at 110 Tesla

Akihiko Ikeda1,*,†, Yuya Kubota2,*,‡, Yuto Ishii3, Xuguang Zhou3, Shiyue Peng3, Hiroaki Hayashi3, Yasuhiro H. Matsuda3, Kosuke Noda1, Tomoya Tanaka1 et al.

Kotomi Shimbori1, Kenta Seki1, Hideaki Kobayashi1, Dilip Bhoi1, Masaki Gen3,4, Kamini Gautam4, Mitsuru Akaki5, Shiro Kawachi6, Shusuke Kasamatsu7, Toshihiro Nomura8, Yuichi Inubushi2,9, and Makina Yabashi2,9

  • *These authors contributed equally to this work.
  • †Contact author: a-ikeda@uec.ac.jp
  • ‡Contact author: kubota@spring8.or.jp
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Phys. Rev. Lett. 135, 186702 – Published 28 October, 2025

DOI: https://doi.org/10.1103/r7br-qnrn

Abstract

In strong magnetic fields beyond 100 T, the significant Zeeman energy competes with the lattice interactions, where a considerable magnetostriction is expected. However, the microscopic observation of the magnetostriction above 100 T has been hindered due to the short pulse duration of microseconds and the coil’s destruction. Here, we report the observation of the giant and anisotropic magnetostriction of ∼1% at 110 T in the spin-controlled crystal β−O2 by combining the single-shot diffraction of an x-ray free-electron laser (XFEL) and the newly developed portable 100 T generator (PINK-02). The soft and anisotropic response of β−O2 should originate in the competing van der Waals force and exchange interaction and also the frustration of spin and lattice on the triangular network. The XFEL experiment above 100 T using PINK-02 enables microscopic investigations on materials’ properties at high magnetic fields, providing insights into how spins contribute to the stability of crystal structures.

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References (53)

  1. S. Gerber et al., Three-dimensional charge density wave order in YBa2Cu3O6.67 at high magnetic fields, Science 350, 949 (2015).
  2. S. Ran, I.-L. Liu, Y. S. Eo, D. J. Campbell, P. M. Neves, W. T. Fuhrman, S. R. Saha, C. Eckberg, H. Kim, D. Graf, F. Balakirev, J. Singleton, J. Paglione, and N. P. Butch, Extreme magnetic field-boosted superconductivity, Nat. Phys. 15, 1250 (2019).

  3. Zeeman energy mounts to over 1.34 K for a free-electron spin at 1 T with the relation EZeeman=gμBSzBz, where g, μB, Sz, and Bz are g factors, Bohr magneton, spin, and external magnetic field, respectively.

  4. Y. A. Freiman and H. J. Jodl, Solid oxygen, Phys. Rep. 401, 1 (2004).
  5. Y. A. Freiman, H. J. Jodl, and Y. Crespo, Solid oxygen revisited, Phys. Rep. 743, 1 (2018).
  6. M. Kirsz, C. G. Pruteanu, P. I. C. Cooke, and G. J. Ackland, Understanding solid nitrogen through molecular dynamics simulations with a machine-learning potential, Phys. Rev. B 110, 184107 (2024).
  7. K. Shimizu, K. Suhara, M. Ikumo, M. I. Eremets, and K. Amaya, Superconductivity in oxygen, Nature (London) 393, 767 (1998).
  8. T. Nomura, Y. H. Matsuda, S. Takeyama, A. Matsuo, K. Kindo, J. L. Her, and T. C. Kobayashi, Novel phase of solid oxygen induced by ultrahigh magnetic fields, Phys. Rev. Lett. 112, 247201 (2014).
  9. T. Nomura, Y. H. Matsuda, S. Takeyama, A. Matsuo, K. Kindo, and T. C. Kobayashi, Phase boundary of θ phase of solid oxygen in ultrahigh magnetic fields, Phys. Rev. B 92, 064109 (2015).
  10. T. Nomura, Y. H. Matsuda, and T. C. Kobayashi, H-T phase diagram of solid oxygen, Phys. Rev. B 96, 054439 (2017).
  11. T. Nomura, Y. Kohama, Y. H. Matsuda, K. Kindo, and T. C. Kobayashi, α−β and β−γ phase boundaries of solid oxygen observed by adiabatic magnetocaloric effect, Phys. Rev. B 95, 104420 (2017).
  12. T. Nomura, Y. H. Matsuda, and T. C. Kobayashi, Solid and liquid oxygen under ultrahigh magnetic fields, Oxygen 2, 152 (2022).
  13. F. Dunstetter, V. P. Plakhti, and J. Schweizer, The magnetic structure of β oxygen: A neutron polarisation analysis study, J. Magn. Magn. Mater. 72, 258 (1988).
  14. R. J. Meier, C. J. Schinkel, and A. d. Visser, Magnetisation of condensed oxygen under high pressures and in strong magnetic fields, J. Phys. C 15, 1015 (1982).
  15. A. S. Baryl’nik and A. I. Prokhvatilov, Spontaneous magnetostriction effects in α- and β-phases of oxygen, Low Temp. Phys. 20, 716 (1994).
  16. A. Ikeda, T. Nomura, Y. H. Matsuda, S. Tani, Y. Kobayashi, H. Watanabe, and K. Sato, High-speed 100 MHz strain monitor using fiber Bragg grating and optical filter for magnetostriction measurements under ultrahigh magnetic fields, Rev. Sci. Instrum. 88, 083906 (2017).
  17. A. Ikeda, Y. H. Matsuda, K. Sato, and J. Nasu, A review on magnetic field induced spin crossover in LaCoO3 up to 600 T, J. Phys. Soc. Jpn. 93, 121005 (2024).
  18. A. Ikeda, Y. H. Matsuda, and K. Sato, Two spin-state crystallizations in LaCoO3, Phys. Rev. Lett. 125, 177202 (2020).
  19. T. Nomura, A. Ikeda, M. Gen, A. Matsuo, K. Kindo, Y. Kohama, Y. H. Matsuda, S. Zherlitsyn, J. Wosnitza, H. Tsuda, and T. C. Kobayashi, Physical properties of liquid oxygen under ultrahigh magnetic fields, Phys. Rev. B 104, 224423 (2021).
  20. A. Ikeda, Y. H. Matsuda, K. Sato, Y. Ishii, H. Sawabe, D. Nakamura, S. Takeyama, and J. Nasu, Signature of spin-triplet exciton condensations in LaCoO3 at ultrahigh magnetic fields up to 600 T, Nat. Commun. 14, 1744 (2023).
  21. T. Nomura, P. Corboz, A. Miyata, S. Zherlitsyn, Y. Ishii, Y. Kohama, Y. H. Matsuda, A. Ikeda, C. Zhong, H. Kageyama, and F. Mila, Unveiling new quantum phases in the Shastry-Sutherland compound SrCu2(BO3)2 up to the saturation magnetic field, Nat. Commun. 14, 3769 (2023).
  22. M. Gen, A. Ikeda, K. Aoyama, H. O. Jeschke, Y. Ishii, H. Ishikawa, T. Yajima, Y. Okamoto, X. Zhou, D. Nakamura, S. Takeyama, K. Kindo, Y. H. Matsuda, and Y. Kohama, Signatures of a magnetic superstructure phase induced by ultrahigh magnetic fields in a breathing pyrochlore antiferromagnet, Proc. Natl. Acad. Sci. U.S.A. 120, e2302756120 (2023).
  23. D. Nakamura, A. Ikeda, H. Sawabe, Y. H. Matsuda, and S. Takeyama, Record indoor magnetic field of 1200 T generated by electromagnetic flux-compression, Rev. Sci. Instrum. 89, 095106 (2018).
  24. F. Herlach, Pulsed magnets, Rep. Prog. Phys. 62, 859 (1999).
  25. A. Ikeda, Y. H. Matsuda, X. Zhou, S. Peng, Y. Ishii, T. Yajima, Y. Kubota, I. Inoue, Y. Inubushi, K. Tono, and M. Yabashi, Generating 77 T using a portable pulse magnet for single-shot quantum beam experiments, Appl. Phys. Lett. 120, 142403 (2022).
  26. A. Ikeda, Y. H. Matsuda, X. Zhou, T. Yajima, Y. Kubota, K. Tono, and M. Yabashi, Single shot x-ray diffractometry in SACLA with pulsed magnetic fields up to 16 T, Phys. Rev. Res. 2, 043175 (2020).
  27. T. Ishikawa et al., A compact x-ray free-electron laser emitting in the sub-ångström region, Nat. Photonics 6, 540 (2012).
  28. I. Inoue, T. Osaka, T. Hara, T. Tanaka, T. Inagaki, T. Fukui, S. Goto, Y. Inubushi, H. Kimura, R. Kinjo, H. Ohashi, K. Togawa, K. Tono, M. Yamaga, H. Tanaka, T. Ishikawa, and M. Yabashi, Generation of narrow-band x-ray free-electron laser via reflection self-seeding, Nat. Photonics 13, 319 (2019).
  29. M. Gen, K. Noda, K. Shimbori, T. Tanaka, D. Bhoi, K. Seki, H. Kobayashi, K. Gautam, M. Akaki, Y. Ishii, Y. H. Matsuda, Y. Kubota, Y. Inubushi, M. Yabashi, Y. Kohama, T. Arima, and A. Ikeda, X-ray diffraction study of the magnetization plateau above 40 T in the frustrated helimagnet CuGaCr4S8, Phys. Rev. B 111, 214441 (2025).

  30. Deduced from the following relation: λ=2dhkl0  Tsin(θhkl0  T)=2dhkl110  Tsin(θhkl110  T).

  31. A. Ikeda, S. Furukawa, O. Janson, Y. H. Matsuda, S. Takeyama, T. Yajima, Z. Hiroi, and H. Ishikawa, Magnetoelastic couplings in the deformed kagome quantum spin lattice of volborthite, Phys. Rev. B 99, 140412(R) (2019).
  32. B. Bussery and P. E. S. Wormer, A van der Waals intermolecular potential for (O2)2, J. Chem. Phys. 99, 1230 (1993).
  33. M. Santoro, F. A. Gorelli, L. Ulivi, R. Bini, and H. J. Jodl, Antiferromagnetism in the high-pressure phases of solid oxygen: Low-energy electronic transitions, Phys. Rev. B 64, 064428 (2001).

  34. M(R)=d(1−{1−exp[−(R−R0)/a]}2) with d, a, and R0 being the depth, the inverted width, and the equilibrium position of the potential, respectively.

  35. B. Bussery, S. Y. Umanskii, M. Aubert-Frécon, and O. Bouty, Exchange interaction between two O2 molecules using the asymptotic method, J. Chem. Phys. 101, 416 (1994).
  36. J. Kieffer and D. Karkoulis, pyfai, a versatile library for azimuthal regrouping, J. Phys. Conf. Ser. 425, 202012 (2013).
  37. K. Momma and F. Izumi, vesta3 for three-dimensional visualization of crystal, volumetric, and morphology data, J. Appl. Crystallogr. 44, 1272 (2011).
  38. A. Ikeda, Data: X-ray free-electron laser observation of giant and anisotropic magnetostriction in β−O2 at 110 Tesla, Zenodo (2025), 10.5281/zenodo.17166637.
  39. T. Kameshima, S. Ono, T. Kudo, K. Ozaki, Y. Kirihara, K. Kobayashi, Y. Inubushi, M. Yabashi, T. Horigome, A. Holland, K. Holland, D. Burt, H. Murao, and T. Hatsui, Development of an x-ray pixel detector with multi-port charge-coupled device for x-ray free-electron laser experiments, Rev. Sci. Instrum. 85, 033110 (2014).
  40. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
  41. G. Pizzi et al., wannier90 as a community code: New features and applications, J. Phys. Condens. Matter 32, 165902 (2020).
  42. X. He, N. Helbig, M. J. Verstraete, and E. Bousquet, tb2j: A python package for computing magnetic interaction parameters, Comput. Phys. Commun. 264, 107938 (2021).
  43. J. Klimeš, D. R. Bowler, and A. Michaelides, van der Waals density functionals applied to solids, Phys. Rev. B 83, 195131 (2011).
  44. S. L. Dudarev, S. Y. Savrasov, C. J. Humphreys, and a. P. Sutton, Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study, Phys. Rev. B 57, 1505 (1998).
  45. S. Kasamatsu, T. Kato, and O. Sugino, First-principles description of van der Waals bonded spin-polarized systems using the vdW-DF+U method: Application to solid oxygen at low pressure, Phys. Rev. B 95, 235120 (2017).
  46. K. Katsumata, S. Kimura, U. Staub, Y. Narumi, Y. Tanaka, S. Shimomura, T. Nakamura, S. W. Lovesey, T. Ishikawa, and H. Kitamura, The giant magneto-volume effect in solid oxygen, J. Phys. Condens. Matter 17, L235 (2005).
  47. Y. H. Matsuda, A. Shimizu, A. Ikeda, T. Nomura, T. Yajima, T. Inami, K. Takahashi, and T. C. Kobayashi, High magnetic field x-ray diffraction study of the α phase of solid oxygen: Absence of giant magnetostriction, Phys. Rev. B 100, 214105 (2019).
  48. See Supplemental Material at http://link.aps.org/supplemental/10.1103/r7br-qnrn for the qualitative analysis of the XRD peak profile and a video for the portable 110 T generation.
  49. Y. Zhao and J. Zhang, Microstrain and grain-size analysis from diffraction peak width and graphical derivation of high-pressure thermomechanics, J. Appl. Crystallogr. 41, 1095 (2008).
  50. A. C. Murrieta and F. F. Contreras-Torres, Microstructure of polycrystalline solids: A brief review from methods in X-ray line profile analysis, Mater. Today Proc. 48, 96 (2022).
  51. T. Kakeshita and K. Ullakko, Giant magnetostriction in ferromagnetic shape-memory alloys, MRS Bull. 27, 105 (2002).
  52. Y. Tokura, Critical features of colossal magnetoresistive manganites, Rep. Prog. Phys. 69, 797 (2006).
  53. https://youtu.be/J4MT__Raz_k?si=ZDAQnPCsVrjaSUBv

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Phys. Rev. Lett. 135, 186702– Published 28 October, 2025
  • Received 20 May 2025
  • Revised 18 July 2025
  • Accepted 19 September 2025
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