- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review B

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access
  • Access by Xinjiang University

Hyperfine coupling in singlet ground state magnets

Peter Thalmeier

PDF

Phys. Rev. B 114, 084411 – Published 14 August, 2026

DOI: https://doi.org/10.1103/x875-17hm

Abstract

The influence of hyperfine coupling to nuclear spins and of their quadrupolar splitting on the induced moment order in singlet ground state magnets is investigated. The latter are found among non-Kramers f electron compounds. Without coupling to the nuclear spins, these magnets have a quantum critical point (QCP) separating the paramagnetic and induced moment regimes. The hyperfine interaction suppresses the QCP and leads to a gradual crossover between induced electronic and nuclear hyperfine coupling dominated magnetic order. It is shown how the critical temperature depends on the electronic and nuclear control parameters, including the nuclear spin size and its possible nuclear quadrupole splitting. In particular, the dependence of the specific heat on the control parameters and applied field is investigated for ferro- and antiferromagnetic order. It is shown that the three-peak structure in the electronic-induced moment regime gradually changes to a two-peak structure in the hyperfine coupling dominated nuclear moment order regime or for increasing field strength. Most importantly, the possibility of a reentrance behavior of magnetic order or likewise nonmonotonic critical fields due to hyperfine coupling influence is demonstrated. Finally, the systematic evolution of the phase diagram under the influence of nuclear quadrupole coupling is clarified.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (45)

  1. N. Majlis, The Quantum Theory of Magnetism (World Scientific, Singapore, 2007).
  2. B. Schmidt and P. Thalmeier, Frustrated two dimensional quantum magnets, Phys. Rep. 703, 1 (2017).
  3. P. Thalmeier, Induced order and collective excitations in three-singlet quantum magnets, Phys. Rev. B 103, 144435 (2021).
  4. A. Akbari, B. Schmidt, and P. Thalmeier, Topological paramagnetic excitons of localized f electrons on the honeycomb lattice, Phys. Rev. B 108, 045143 (2023).
  5. P. Thalmeier and A. Akbari, Induced quantum magnetism in crystalline electric field singlet ground state models: Thermodynamics and excitations, Phys. Rev. B 109, 115110 (2024).
  6. P. Thalmeier, Magnetocalorics of singlet ground state induced moment magnets, Phys. Rev. B 112, 104417 (2025).
  7. T. Takimoto and P. Thalmeier, Theory of induced quadrupolar order in tetragonal YbRu2Ge2, Phys. Rev. B 77, 045105 (2008).
  8. K. Haule and G. Kotliar, Complex Landau-Ginzburg theory of the hidden order in URu2Si2, Europhys. Lett. 89, 57006 (2010).
  9. J. Jensen and A. R. Mackintosh, Rare Earth Magnetism (Clarendon Press, Oxford, 1991).
  10. A. Steppke, M. Brando, N. Oeschler, C. Krellner, C. Geibel, and F. Steglich, Nuclear contribution to the specific heat of Yb(Rh0.93Co0.07)2Si2, Phys. Stat. Sol. (B) 247, 737 (2010).
  11. L. Steinke, K. Mitsumoto, C. F. Miclea, F. Weickert, A. Dönni, M. Akatsu, Y. Nemoto, T. Goto, H. Kitazawa, P. Thalmeier, and M. Brando, Role of hyperfine coupling in magnetic and quadrupolar ordering of Pr3Pd20Si6, Phys. Rev. Lett. 111, 077202 (2013).
  12. J. Knapp, L. V. Levitin, J. Nyéki, A. F. Ho, B. Cowan, J. Saunders, M. Brando, C. Geibel, K. Kliemt, and C. Krellner, Electronuclear transition into a spatially modulated magnetic state in YbRh2Si2, Phys. Rev. Lett. 130, 126802 (2023).
  13. J. Knapp, L. V. Levitin, J. Nyéki, B. Cowan, M. Brando, C. Geibel, K. Kliemt, C. Krellner, and J. Saunders, Magnetic phase diagram of YbRh2Si2: The influence of hyperfine interactions, Phys. Rev. Res. 7, L042043 (2025).
  14. S. Gabani, I. Curlik, F. Akbar, M. Giovannini, and J. G. Sereni, Hyperfine electro-nuclear coupling at the quantum criticality of YbCu4Zn, arXiv:2506.18192.
  15. Y. Aoki, T. Namiki, S. R. Saha, T. Tayama, T. Sakakibara, R. Shiina, H. Shiba, H. Sugawara, and H. Sato, f-electron-nuclear hyperfine-coupled multiplets in the unconventional charge order phase of filled skutterudite PrRu4P12, J. Phys. Soc. Jpn. 80, 054704 (2011).
  16. T. Kitazawa, Y. Shimura, T. Onimaru, S. Tsuchida, K. Kubo, Y. Haga, H. Sakai, Y. Tokiwa, S. Kambe, and Y. Tokunaga, Paramagnetic electron-nuclear spin entanglement in HoCo2Zn20 Phys. Rev. Res. 8, 023009 (2026).
  17. H. Eisenlohr and M. Vojta, Limits to magnetic quantum criticality from nuclear spins, Phys. Rev. B 103, 064405 (2021).
  18. K. Andres, Combined electron-nuclear magnetic-ordering phenomena in singlet-ground-state systems, Phys. Rev. B 7, 4295 (1973).
  19. T. Murao, Effective nuclear spin Hamiltonian for magnetically ordered singlet ground state system, J. Phys. Soc. Jpn. 46, 40 (1979).
  20. M. Kubota, H. R. Folle, C. Buchal, R. M. Mueller, and F. Pobell, Nuclear magnetic ordering in PrNi5 at 0.4 mK, Phys. Rev. Lett. 45, 1812 (1980).
  21. T. Murao, Magnetism of a nucleus-electron complex system in the vicinity of the threshold, J. Phys. Soc. Jpn. 50, 3240 (1981).
  22. H. B. Møller, J. Z. Jensen, M. Wulff, A. R. Mackintosh, O. D. McMasters, and K. A. Gschneidner, Hyperfine interactions, magnetic impurities, and ordering in praseodymium, Phys. Rev. Lett. 49, 482 (1982).
  23. T. Miki, M. Yanaka, M. Nakagawa, D. Kim, O. Ishikawa, T. Hata, H. Ishii, T. Kodama, and Y. Ōnuki, Electrical resistivity anomaly at the nuclear magnetic ordering in a Van Vleck paramagnet PrCu6, Phys. Rev. Lett. 69, 375 (1992).
  24. T. Zajarniuk, A. Szewczyk, P. Wiśniewski, M. U. Gutowska, R. Puzniak, H. Szymczak, I. Gudim, V. A. Bedarev, M. I. Pashchenko, P. Tomczak, and W. Szuszkiewicz, Quantum versus classical nature of the low-temperature magnetic phase transition in TbAl3(BO3)4, Phys. Rev. B 105, 094418 (2022).
  25. F. Bangma, L. Levitin, M. Lucas, A. Casey, J. Nyeki, I. Broeders, A. Sutton, B. Andraka, S. Julian, J. Saunders, and A. McCollam, Diverse influences of hyperfine interactions on strongly correlated electron states, arXiv:2305.17088.
  26. M. P. Zic, C. Huan, N. Silva, Y. Li, M. W. Meisel, and I. R. Fisher, Electro-nuclear quantum phase transition in TmVO4, arXiv:2509.11489.
  27. P. Santini and G. Amoretti, Crystal field model of the magnetic properties of URu2Si2, Phys. Rev. Lett. 73, 1027 (1994).
  28. P. Thalmeier, Dual model for magnetic excitations and superconductivity in UPd2Al3, Eur. Phys. J. B 27, 29 (2002).
  29. M. Sundermann, M. W. Haverkort, S. Agrestini, A. Al-Zein, M. M. Sala, Y. Huang, M. Golden, A. de Visser, P. Thalmeier, L. H. Tjeng, and A. Severing, Direct bulk-sensitive probe of 5f symmetry in URu2Si2, Proc. Natl. Acad. Sci. USA 113, 13989 (2016).
  30. G. Frossati, J. M. Mignot, D. Thoulouze, and R. Tournier, Van Vleck-like electronuclear susceptibility of Yb171 in Au at very low temperature, Phys. Rev. Lett. 36, 203 (1976).
  31. M. Kofu, O. Yamamuro, T. Kajiwara, Y. Yoshimura, M. Nakano, K. Nakajima, S. Ohira-Kawamura, T. Kikuchi, and Y. Inamura, Hyperfine structure of magnetic excitations in a Tb-based single-molecule magnet studied by high-resolution neutron spectroscopy, Phys. Rev. B 88, 064405 (2013).
  32. D. Giglberger and S. Penselin, Ground-state hyperfine structure and nuclear magnetic moment of thulium-169, Z. Phys. 199, 244 (1967).
  33. A. Abragam, Principles of Nuclear Magnetism (Oxford University Press, Oxford, 1961).
  34. P. S. Savchenkov, E. S. Clementyev, P. A. Alekseev, and V. N. Lazukov, Induced magnetism and “magnetic hole” in singlet ground state system PrNi, J. Magn. Magn. Mater. 489, 165413 (2019).
  35. B. R. Cooper and O. Vogt, Transition from Van Vleck paramagnetism to induced antiferromagnetism in TbζY1−ζSb, Phys. Rev. B 1, 1218 (1970).
  36. A. Marino, M. Sundermann, D. S. Christovam, A. Amorese, C.-F. Chang, P. Dolmantas, A. H. Said, H. Gretarsson, B. Keimer, M. W. Haverkort, A. V. Andreev, L. Havela, P. Thalmeier, L. H. Tjeng, and A. Severing, Singlet magnetism in intermetallic UGa2 unveiled by inelastic x-ray scattering, Phys. Rev. B 108, 045142 (2023).
  37. R. J. Birgeneau, J. Als-Nielsen, and E. Bucher, Neutron scattering from fcc Pr and Pr3Tl, Phys. Rev. B 6, 2724 (1972).
  38. K. Andres, E. Bucher, J. P. Maita, and A. S. Cooper, Observation of cooperative nuclear magnetic order in PrCu2 below 54 mK, Phys. Rev. Lett. 28, 1652 (1972).
  39. W. J. L. Buyers, T. M. Holden, and A. Perreault, Temperature dependence of magnetic excitations in singlet-ground-state systems. II. Excited-state spin waves near the Curie temperature in Pr3Tl, Phys. Rev. B 11, 266 (1975).
  40. R. Wawrzyńczak, B. Tomasello, P. Manuel, D. Khalyavin, M. D. Le, T. Guidi, A. Cervellino, T. Ziman, M. Boehm, G. J. Nilsen, and T. Fennell, Magnetic order and single-ion anisotropy Tb3Ga5O12, Phys. Rev. B 100, 094442 (2019).
  41. J. Hamman and P. Manneville, Ordre magnétique électronique induit par les interactions hyperfines dans les grenats de gallium-holmium et de gallium-terbium, J. Phys. France 34, 615 (1973).
  42. S. Kawarazaki, Y. Kobashi, M. Sato, and Y. Miyako, Observation of the singlet-singlet crystal-field excitons in PrCu2 by inelastic neutron scattering, J. Phys.: Condens. Matter 7, 4051 (1995).
  43. R. J. Radwanski, R. Michalski, and Z. Ropka, From atomic physics to solid-state physics: Magnetism and electronic structure of PrNi5, ErNi5, LaCoO3 and UPd2Al3, Acta Phys. Pol. B 31, 3079 (2000).
  44. K. Sugiyama, M. Nakashima, A. Koyanagi, S. Araki, K. Kindo, T. Hata, R. Settai, and Y. Ōnuki, High-field magnetization of PrCu6 and PrNi5 with the singlet ground state, J. Phys. Soc. Jpn. 67, 2553 (1998).
  45. P. Ahmet, M. Abliz, R. Settai, K. Sugiyama, Y. Ōnuki, T. Takeuchi, K. Kindo, and S. Takayanagi, Crystalline electric field and metamagnetic transition of PrCu2, J. Phys. Soc. Jpn. 65, 1077 (1996).

Outline

Information

Phys. Rev. B 114, 084411– Published 14 August, 2026
  • Received 12 December 2025
  • Revised 8 May 2026
  • Accepted 13 July 2026
Crossmark - Check for updates button
Creative Commons Logo

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. Open access publication funded by Max Planck Society.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation