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Influence of dipolar interactions on the critical dynamics in nickel

L. Beddrich1,2,3,*, J. K. Jochum2, S. Säubert1,2, C. Franz2,3, and P. Böni1

  • *Contact author: lukas.beddrich@fz-juelich.de
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Phys. Rev. B 113, 184411 – Published 4 May, 2026

DOI: https://doi.org/10.1103/wscm-w7rx

Abstract

The study of critical phenomena has always been deeply connected with magnetism in solid state materials. Nickel, one of the three archetypical room temperature ferromagnets, is understood to be an itinerant system with a high degree of localization regarding its magnetically active electron states. We report a high-resolution neutron spectroscopy investigation of nickel (Ni) near its Curie temperature TC, extending measurements to unprecedentedly small wave vectors qmin=6.6×10−3Å−1 and achieving an energy resolution of ΔE=4.9µeV. Our analysis of the spin-wave dispersion reveals that the dipolar wave vector qD=6.4×10−3Å−1 is approximately half of the previously reported value, but strictly nonzero to rationalize the observed excitations. The spin-wave stiffness D(T) is in good agreement with the literature, but most importantly, we uncover evidence that the linewidth of the spin waves follows the dynamical scaling characteristic of a dipolar ferromagnet rather than an isotropic one. In contrast, the linewidth of the fluctuations above TC exhibit scaling consistent with the Résibois-Piette function and renormalization-group predictions, despite the itinerant ferromagnetic nature of Ni. This observation suggests a pronounced localization of the 3d electrons responsible for magnetic scattering.

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References (65)

  1. R. D. Lowde and C. G. Windsor, Generalized susceptibility of nickel, Phys. Rev. Lett. 18, 1136 (1967).
  2. V. J. Minkiewicz, M. F. Collins, R. Nathans, and G. Shirane, Critical and spin-wave fluctuations in nickel by neutron scattering, Phys. Rev. 182, 624 (1969).
  3. H. A. Mook, J. W. Lynn, and R. M. Nicklow, Temperature dependence of the magnetic excitations in nickel, Phys. Rev. Lett. 30, 556 (1973).
  4. J. W. Lynn and H. A. Mook, Temperature dependence of the dynamic susceptibility of nickel, Phys. Rev. B 23, 198 (1981).
  5. Y. J. Uemura, G. Shirane, O. Steinsvoll, and J. Wicksted, New explanation of the spin-wave-like excitations in Ni above Tc, Phys. Rev. Lett. 51, 2322 (1983).
  6. O. Steinsvoll, C. F. Majkrzak, G. Shirane, and J. Wicksted, Paramagnetic scattering from metallic Ni, Phys. Rev. B 30, 2377 (1984).
  7. H. A. Mook, D. M. Paul, and S. Hayden, Temperature dependence of the high-energy magnetic excitations for Ni, Phys. Rev. B 38, 12058(R) (1988).
  8. G. Shirane, Magnetic correlations in 3d ferromagnets above Tc, J. Magn. Magn. Mater. 45, 33 (1984).
  9. Y. Endoh and P. Böni, Magnetic excitations in metallic ferro- and antiferromagnets, J. Phys. Soc. Jpn. 75, 111002 (2006).
  10. O. W. Dietrich, J. Als-Nielsen, and L. Passell, Neutron scattering from the Heisenberg ferromagnets EuO and EuS. III. Spin dynamics of EuO, Phys. Rev. B 14, 4923 (1976).
  11. J. Als-Nielsen, O. W. Dietrich, and L. Passell, Neutron scattering from the Heisenberg ferromagnets EuO and EuS. II. Static critical properties, Phys. Rev. B 14, 4908 (1976).
  12. P. Böni and G. Shirane, Paramagnetic neutron scattering from the Heisenberg ferromagnet EuO, Phys. Rev. B 33, 3012 (1986).
  13. S. Schorr, P. Vorderwisch, and F. Mezei, Critical dynamics in EuO below the Curie point, Physica B 234-236, 749 (1997).
  14. P. Böni, M. Hennion, and J. L. Martínez, Magnon dispersion of the dipolar ferromagnet EuS near the zone center, Phys. Rev. B 52, 10142 (1995).
  15. G. Shirane, Y. J. Uemura, J. P. Wicksted, Y. Endoh, and Y. Ishikawa, Paramagnetic scattering from a cubic ferromagnet Pd2MnSn, Phys. Rev. B 31, 1227 (1985).
  16. H. A. Graf, P. Böni, G. Shirane, M. Kohgi, and Y. Endoh, Paramagnetic neutron scattering from Pd2MnSn, Phys. Rev. B 40, 4243 (1989).
  17. F. Mezei, Role of spin-nonconserving forces in the critical dynamics of Fe at the Curie point, Phys. Rev. Lett. 49, 1096 (1982).
  18. J. Kindervater, S. Säubert, and P. Böni, Dipolar effects on the critical fluctuations in Fe: Investigation by the neutron spin-echo technique MIEZE, Phys. Rev. B 95, 014429 (2017).
  19. S. Säubert, J. Kindervater, F. Haslbeck, C. Franz, M. Skoulatos, and P. Böni, Dipolar interactions in Fe: A study with the neutron Larmor precession technique MIEZE in a longitudinal field configuration, Phys. Rev. B 99, 184423 (2019).
  20. P. Böni, J. L. Martínez, and J. M. Tranquada, Longitudinal spin fluctuations in nickel, Phys. Rev. B 43, 575 (1991).
  21. P. Böni, H. A. Mook, J. L. Martínez, and G. Shirane, Comparison of the paramagnetic spin fluctuations in nickel with asymptotic renormalization-group theory, Phys. Rev. B 47, 3171 (1993).
  22. Y. Ishikawa, Y. Noda, C. Fincher, and G. Shirane, Low-energy paramagnetic spin fluctuations in the weak itinerant ferromagnet mnsi, Phys. Rev. B 25, 254 (1982).
  23. B. I. Halperin and P. C. Hohenberg, Generalization of scaling laws to dynamical properties of a system near its critical point, Phys. Rev. Lett. 19, 700 (1967).
  24. T. Holstein and H. Primakoff, Field dependence of the intrinsic domain magnetization of a ferromagnet, Phys. Rev. 58, 1098 (1940).
  25. H. A. Mook, Magnetic moment distribution of nickel metal, Phys. Rev. 148, 495 (1966).
  26. B. I. Halperin and P. C. Hohenberg, Scaling laws for dynamic critical phenomena, Phys. Rev. 177, 952 (1969).
  27. R. Folk and H. Iro, Paramagnetic neutron scattering and renormalization-group theory for isotropic ferromagnets at Tc, Phys. Rev. B 32, 1880 (1985).
  28. P. Résibois and C. Piette, Temperature dependence of the linewidth in critical spin fluctuation, Phys. Rev. Lett. 24, 514 (1970).
  29. H. Iro, The dynamical correlation function for isotropic ferromagnets for T ≥ Tc, Z. Phys. B 68, 485 (1987).
  30. C. J. Glinka, V. J. Minkiewicz, and L. Passell, Small-angle critical neutron scattering from cobalt, Phys. Rev. B 16, 4084 (1977).
  31. P. Böni, D. Görlitz, J. Kötzler, and J. L. Martínez, Dynamics of longitudinal and transverse fluctuations above Tc in EuS, Phys. Rev. B 43, 8755 (1991).
  32. F. Mezei, Critical dynamics in EuO at the ferromagnetic Curie point, Physica B+C 136, 417 (1986).
  33. E. Frey and F. Schwabl, Critical dynamics of dipolar ferromagnets, Phys. Lett. A 123, 49 (1987).
  34. E. Frey and F. Schwabl, On the critical dynamics of ferromagnets, Z. Phys. B 71, 355 (1988).
  35. E. Frey and F. Schwabl, Critical dynamics of magnets, Adv. Phys. 43, 577 (1994).
  36. F. Mezei, Neutron spin echo: A new concept in polarized thermal neutron techniques, Z. Phys. 255, 146 (1972).
  37. R. Gähler, R. Golub, and T. Keller, Neutron resonance spin echo—a new tool for high resolution spectroscopy, Physica B 180-181, 899 (1992).
  38. C. Franz, O. Soltwedel, C. Fuchs, S. Säubert, F. Haslbeck, A. Wendl, J.K. Jochum, P. Böni, and C. Pfleiderer, The longitudinal neutron resonant spin echo spectrometer RESEDA, Nucl. Instrum. Methods Phys. Res., Sect. A 939, 22 (2019).
  39. R. Gähler, R. Golub, K. Habicht, T. Keller, and J. Felber, Space-time description of neutron spin echo spectrometry, Physica B 229, 1 (1996).
  40. F. Mezei, C. Pappas, and T. Gutberlet, Neutron Spin Echo Spectroscopy: Basics, Trends and Applications (Springer Science & Business Media, Berlin, 2002), Vol. 601.
  41. L. Van Hove, Correlations in space and time and born approximation scattering in systems of interacting particles, Phys. Rev. 95, 249 (1954).
  42. C. Franz, O. Soltwedel, S. Säubert, A. Wendl, W. Gottwald, F. Haslbeck, L. Spitz, and C. Pfleiderer, Longitudinal neutron resonance spin echo spectroscopy under large energy transfers, J. Phys.: Conf. Ser. 1316, 012005 (2019).
  43. L. Beddrich, Consequences of lattice dimensionality in solid state magnetism, Ph.D. thesis, Technische Universität München, 2023.
  44. L. Beddrich, J. K. Jochum, P. Bender, L. Spitz, A. Wendl, C. Franz, S. Busch, F. Juranyi, C. Pfleiderer, and O. Soltwedel, Comparison of time-of-flight and MIEZE neutron spectroscopy of H2O, J. Appl. Crystallogr. 58, 1122 (2025).
  45. M. Köhli, M. Klein, F. Allmendinger, A.-K. Perrevoort, T. Schröder, N. Martin, C. J. Schmidt, and U. Schmidt, Cascade—a multi-layer boron-10 neutron detection system, J. Phys.: Conf. Ser. 746, 012003 (2016).
  46. Heinz Maier-Leibnitz Zentrum (MLZ), Experimental facilities Heinz Maier-Leibnitz Zentrum (MLZ) (2022), https://www.frm2.tum.de/fileadmin/w00bnv/www/content_uploads/experimental-facilities_online.pdf.
  47. A. Schober, A. Wendl, F. X. Haslbeck, J. K. Jochum, L. Spitz, and C. Franz, The software package MIEZEPY for the reduction of MIEZE data, J. Phys. Commun. 3, 103001 (2019).
  48. H. Iro, The dynamical correlation function of an isotropic heisenberg ferromagnet in the critical region, J. Magn. Magn. Mater. 73, 175 (1988).
  49. B. Hammouda and D. F. R. Mildner, Small-angle neutron scattering resolution with refractive optics, J. Appl. Crystallogr. 40, 250 (2007).
  50. J. C. Le Guillou and J. Zinn-Justin, Critical exponents for the n-vector model in three dimensions from field theory, Phys. Rev. Lett. 39, 95 (1977).
  51. C. A. Neugebauer, Temperature dependence of the saturation magnetization of nickel films of thickness less than 100A, J. Appl. Phys. 31, S152 (1960).
  52. J. Kötzler, Critical phenomena in dipolar magnets, J. Magn. Magn. Mater. 54-57, 649 (1986).
  53. H. Schinz and F. Schwabl, Dynamics of dipolar ferromagnets below Tc, Phys. Rev. B 57, 8438 (1998).
  54. P. Böni, B. Roessli, D. Görlitz, and J. Kötzler, Damping of spin waves and singularity of the longitudinal modes in the dipolar critical regime of the heisenberg ferromagnet EuS, Phys. Rev. B 65, 144434 (2002).
  55. F. Mezei, Critical dynamics in isotropic ferromagnets, J. Magn. Magn. Mater. 45, 67 (1984).
  56. G. Parette and R. Kahn, Étude de la diffusion critique des neutrons par le fer dans les régions ≪ hydrodynamique ≫ et ≪ quasi hydrodynamique ≫, J. Phys. France 32, 447 (1971).
  57. E. Frey, F. Schwabl, and S. Thoma, Shape functions of dipolar ferromagnets at and above the curie point, Phys. Rev. B 40, 7199 (1989).
  58. P. Böni and G. Shirane, Paramagnetic neutron scattering from ni (invited), J. Appl. Phys. 57, 3012 (1985).
  59. G. G. Lonzarich and L. Taillefer, Effect of spin fluctuations on the magnetic equation of state of ferromagnetic or nearly ferromagnetic metals, J. Phys. C: Solid State Phys. 18, 4339 (1985).
  60. L. Dobrzynski, R. J. Papoular, and M. Sakata, Internal magnetization density distribution of iron and nickel by the maximum entropy method, J. Phys. Soc. Jpn. 65, 255 (1996).
  61. L. Hodges, N. D. Lang, H. Ehrenreich, and A. J. Freeman, Magnetic form factor of nickel, J. Appl. Phys. 37, 1449 (1966).
  62. P.-W. Ma and S. L. Dudarev, Nonuniversal structure of point defects in face-centered cubic metals, Phys. Rev. Mater. 5, 013601 (2021).
  63. L. Beddrich, J. K. Jochum, C. Franz, S. Säubert, and P. Böni, Supplementary material - The influence of dipolar interactions on the critical dynamics in nickel, Zenodo (2026), https://doi.org/10.5281/zenodo.17347394.
  64. J. K. Bhattacharjee and R. A. Ferrell, Dynamic scaling for the isotropic ferromagnet: ε expansion to two-loop order, Phys. Rev. B 24, 6480 (1981).
  65. J. Crangle, The magnetization of pure iron and nickel, Proc. R. Soc. London, Ser. A 321, 15 (1971).

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Phys. Rev. B 113, 184411– Published 4 May, 2026
  • Received 17 October 2025
  • Revised 8 February 2026
  • Accepted 12 March 2026
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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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