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
  • Letter
  • Open Access

Magnetic phase diagram of YbRh2Si2: The influence of hyperfine interactions

J. Knapp1,2,*, L. V. Levitin1,†, J. Nyéki1, B. Cowan1, M. Brando2, C. Geibel2, K. Kliemt3, C. Krellner3, and J. Saunders1,‡

  • *Contact author: jan.knapp@rhul.ac.uk
  • †Contact author: l.v.levitin@rhul.ac.uk
  • ‡Contact author: j.saunders@rhul.ac.uk

Phys. Rev. Research 7, L042043 – Published 25 November, 2025

DOI: https://doi.org/10.1103/yl3t-1gj5

Abstract

We report the determination of the magnetic phase diagram of the heavy fermion metal YbRh2Si2 in magnetic fields up to 70 mT applied perpendicular to the crystallographic c axis. By a combination of heat capacity, magnetocaloric, and magnetoresistance measurements, we map two antiferromagnetic phases: the electronic AFM1 below 70 mK and electronuclear AFM2 below 1.5 mK. The measurements extend into the microkelvin regime to explore the quantum phase transitions in this system. We demonstrate how the hyperfine interaction significantly modifies the phase diagram and the putative field-tuned quantum critical point. The determination of the rich magnetic properties of YbRh2Si2 is essential to understanding the interplay of the two magnetic orders and superconductivity in this compound.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (57)

  1. P. Gegenwart, J. Custers, C. Geibel, K. Neumaier, T. Tayama, K. Tenya, O. Trovarelli, and F. Steglich, Magnetic-field induced quantum critical point in YbRh2Si2, Phys. Rev. Lett. 89, 056402 (2002).
  2. J. Custers, P. Gegenwart, K. Neumaier, H. Wilhelm, N. Oeschler, K. Ishida, Y. Kitaoka, C. Geibel, and F. Steglich, Quantum criticality in YbRh2Si2, J. Phys.: Condens. Matter 15, S2047 (2003).
  3. H. Pfau, S. Hartmann, U. Stockert, P. Sun, S. Lausberg, M. Brando, S. Friedemann, C. Krellner, C. Geibel, S. Wirth, S. Kirchner, E. Abrahams, Q. Si, and F. Steglich, Thermal and electrical transport across a magnetic quantum critical point, Nature (London) 484, 493 (2012).
  4. P. Gegenwart, T. Westerkamp, C. Krellner, Y. Tokiwa, S. Paschen, C. Geibel, F. Steglich, E. Abrahams, and Q. Si, Multiple energy scales at a quantum critical point, Science 315, 969 (2007).
  5. P. Gegenwart, Q. Si, and F. Steglich, Quantum criticality in heavy-fermion metals, Nat. Phys. 4, 186 (2008).
  6. S. Friedemann, T. Westerkamp, M. Brando, N. Oeschler, S. Wirth, P. Gegenwart, C. Krellner, C. Geibel, and F. Steglich, Detaching the antiferromagnetic quantum critical point from the Fermi-surface reconstruction in YbRh2Si2, Nat. Phys. 5, 465 (2009).
  7. G. Knebel, R. Boursier, E. Hassinger, G. Lapertot, P. G. Niklowitz, A. Pourret, B. Salce, J. P. Sanchez, I. Sheikin, P. Bonville, H. Harima, and J. Flouquet, Localization of 4f state in YbRh2Si2 under magnetic field and high pressure: Comparison with CeRh2Si2, J. Phys. Soc. Jpn. 75, 114709 (2006).
  8. Z. F. Weng, M. Smidman, L. Jiao, X. Lu, and H. Q. Yuan, Multiple quantum phase transitions and superconductivity in Ce-based heavy fermions, Rep. Prog. Phys. 79, 094503 (2016).
  9. S. Nakatsuji, K. Kuga, Y. Machida, T. Tayama, T. Sakakibara, Y. Karaki, H. Ishimoto, S. Yonezawa, Y. Maeno, E. Pearson, G. G. Lonzarich, L. Balicas, H. Lee, and Z. Fisk, Superconductivity and quantum criticality in the heavy-fermion system β−YbAlB4, Nat. Phys. 4, 603 (2008).
  10. E. Schuberth, M. Tippmann, L. Steinke, S. Lausberg, A. Steppke, M. Brando, C. Krellner, C. Geibel, R. Yu, Q. Si, and F. Steglich, Emergence of superconductivity in the canonical heavy-electron metal YbRh2Si2, Science 351, 485 (2016).
  11. D. Nguyen, A. Sidorenko, M. Taupin, G. Knebel, G. Lapertot, E. Schuberth, and S. Paschen, Superconductivity in an extreme strange metal, Nat. Commun. 12, 4341 (2021).
  12. L. V. Levitin, J. Knapp, P. Knappová, M. Lucas, J. Nyéki, P. Heikkinen, V. Antonov, A. Casey, A. F. Ho, P. Coleman, C. Geibel, A. Steppke, K. Kliemt, C. Krellner, M. Brando, and J. Saunders, Odd-parity superconductivity underpinned by antiferromagnetism in heavy fermion metal YbRh2Si2, arXiv:2502.06420.
  13. J. Knapp, L. Levitin, J. Nyéki, A. 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).
  14. J. Knapp, L. V. Levitin, J. Nyéki, M. Brando, and J. Saunders, Precise calorimetry of small metal samples using noise thermometry, J. Low Temp. Phys. 217, 638 (2024).
  15. S. Friedemann, S. Wirth, N. Oeschler, C. Krellner, C. Geibel, F. Steglich, S. MaQuilon, Z. Fisk, S. Paschen, and G. Zwicknagl, Hall effect measurements and electronic structure calculations on YbRh2Si2 and its reference compounds LuRh2Si2 and YbIr2Si2, Phys. Rev. B 82, 035103 (2010).
  16. K. Kummer, S. Patil, A. Chikina, M. Güttler, M. Höppner, A. Generalov, S. Danzenbächer, S. Seiro, A. Hannaske, C. Krellner, Y. Kucherenko, M. Shi, M. Radovic, E. Rienks, G. Zwicknagl, K. Matho, J. W. Allen, C. Laubschat, C. Geibel, and D. V. Vyalikh, Temperature-independent fermi surface in the Kondo lattice YbRh2Si2, Phys. Rev. X 5, 011028 (2015).
  17. G. Zwicknagl, The utility of band theory in strongly correlated electron systems, Rep. Prog. Phys. 79, 124501 (2016).
  18. Y. Li, Q. Wang, Y. Xu, W. Xie, and Y. F. Yang, Nearly degenerate px+ipy and dx2−y2 pairing symmetry in the heavy fermion superconductor YbRh2Si2, Phys. Rev. B 100, 085132 (2019).
  19. M. Güttler, K. Kummer, K. Kliemt, C. Krellner, S. Seiro, C. Geibel, C. Laubschat, Y. Kubo, Y. Sakurai, D. V. Vyalikh, and A. Koizumi, Visualizing the Kondo lattice crossover in YbRh2Si2 with Compton scattering, Phys. Rev. B 103, 115126 (2021).
  20. K. Ishida, D. E. MacLaughlin, B. L. Young, K. Okamoto, Y. Kawasaki, Y. Kitaoka, G. J. Nieuwenhuys, R. H. Heffner, O. O. Bernal, W. Higemoto, A. Koda, R. Kadono, O. Trovarelli, C. Geibel, and F. Steglich, Low-temperature magnetic order and spin dynamics in YbRh2Si2, Phys. Rev. B 68, 184401 (2003).
  21. S. Hamann, J. Zhang, D. Jang, A. Hannaske, L. Steinke, S. Lausberg, L. Pedrero, C. Klingner, M. Baenitz, F. Steglich, C. Krellner, C. Geibel, and M. Brando, Evolution from ferromagnetism to antiferromagnetism in Yb(Rh1−xCox)Si2, Phys. Rev. Lett. 122, 077202 (2019).
  22. Q. Si, S. Rabello, K. Ingersent, and J. L. Smith, Locally critical quantum phase transitions in strongly correlated metals, Nature (London) 413, 804 (2001).
  23. P. Coleman and A. J. Schofield, Quantum criticality, Nature (London) 433, 226 (2005).
  24. Q. Si and F. Steglich, Heavy fermions and quantum phase transitions, Science 329, 1161 (2010).
  25. F. Steglich, Heavy fermions: Superconductivity and its relationship to quantum criticality, Philos. Mag. 94, 3259 (2014).
  26. M. H. Schubert, Y. Tokiwa, S. H. Hübner, M. Mchalwat, E. Blumenröther, H. S. Jeevan, and P. Gegenwart, Tuning low-energy scales in YbRh2Si2 by non-isoelectronic substitution and pressure, Phys. Rev. Res. 1, 032004(R) (2019).
  27. S. Paschen and Q. Si, Quantum phases driven by strong correlations, Nat. Rev. Phys. 3, 9 (2020).
  28. E. Schuberth, S. Wirth, and F. Steglich, Nuclear-order-induced quantum criticality and heavy-fermion superconductivity at ultra-low temperatures in YbRh2Si2, Front. Electron. Mater. 2, 869495 (2022).
  29. E. Abrahams and P. Wölfle, Critical quasiparticle theory applied to heavy fermion metals near an antiferromagnetic quantum phase transition, Proc. Natl. Acad. Sci. USA 109, 3238 (2012).
  30. E. Abrahams, J. Schmalian, and P. Wölfle, Strong-coupling theory of heavy-fermion criticality, Phys. Rev. B 90, 045105 (2014).
  31. P. Wölfle and E. Abrahams, Spin-flip scattering of critical quasiparticles and the phase diagram of YbRh2Si2, Phys. Rev. B 92, 155111 (2015).
  32. S. Watanabe and K. Miyake, Quantum valence criticality as an origin of unconventional critical phenomena, Phys. Rev. Lett. 105, 186403 (2010).
  33. L. Steinke, E. Schuberth, S. Lausberg, M. Tippmann, A. Steppke, C. Krellner, C. Geibel, F. Steglich, and M. Brando, Ultra-low temperature ac susceptibility of the heavy-fermion superconductor YbRh2Si2, J. Phys.: Conf. Ser. 807, 052007 (2017).
  34. See Supplemental Material at http://link.aps.org/supplemental/10.1103/yl3t-1gj5 for details of the hyperfine fields calculation, the hyperfine Schottky model, the thermodynamics of the magnetocaloric sweeps, the phase boundaries and critical exponents, and the investigation of hysteresis and preparation condition dependence, which also includes Ref.  [57].
  35. M. Garst and A. Rosch, Sign change of the Grüneisen parameter and magnetocaloric effect near quantum critical points, Phys. Rev. B 72, 205129 (2005).
  36. S. Sosin, L. Prozorova, A. Smirnov, A. Golov, I. Berkutov, O. Petrenko, G. Balakrishnan, and M. Zhitomirsky, Magnetocaloric effect in pyrochlore antiferromagnet Gd2Ti2O7, Phys. Rev. B 71, 094413 (2005).
  37. K. A. Gschneidner Jr., V. K. Pecharsky, and A. O. Tsokol, Recent developments in magnetocaloric materials, Rep. Prog. Phys. 68, 1479 (2005).
  38. V. Pecharsky, K. Gschneidner, A. Pecharsky, and A. Tishin, Thermodynamics of the magnetocaloric effect, Phys. Rev. B 64, 144406 (2001).
  39. V. K. Pecharsky and K. A. Gschneidner Jr., Giant magnetocaloric effect in Gd5(Si2Ge2), Phys. Rev. Lett. 78, 4494 (1997).
  40. C. Krellner, S. Hartmann, A. Pikul, N. Oeschler, J. G. Donath, C. Geibel, F. Steglich, and J. Wosnitza, Violation of critical universality at the antiferromagnetic phase transition of YbRh2Si2, Phys. Rev. Lett. 102, 196402 (2009).
  41. I. Nowik and S. Ofer, Mössbauer studies of Yb170 in several paramagnetic salts, J. Phys. Chem. Solids 29, 2117 (1968).
  42. J. Plessel, M. M. Abd–Elmeguid, J. P. Sanchez, G. Knebel, C. Geibel, O. Trovarelli, and F. Steglich, Unusual behavior of the low-moment magnetic ground state of YbRh2Si2 under high pressure, Phys. Rev. B 67, 180403(R) (2003).
  43. J. Flouquet and W. D. Brewer, Hyperfine interaction studies of local moments in metals, Phys. Scr. 11, 199 (1975).
  44. J. Flouquet, Kondo coupling, hyperfine and exchange interactions, J. Phys. Colloq. 39, C6-1493 (1978).
  45. P. Bonville, B. Canaud, J. Hammann, J. A. Hodges, P. Imbert, G. Jéhanno, A. Severing, and Z. Fisk, Magnetic ordering and hybridisation in YbAuCu4, J. Phys. I 2, 459 (1992).
  46. P. Bonville, J. A. Hodges, P. Imbert, G. Jéhanno, D. Jaccard, and J. Sierro, Magnetic ordering and paramagnetic relaxation of Yb3+ in YbNi2Si2, J. Magn. Magn. Mater. 97, 178 (1991).
  47. P. Bonville, P. Imbert, G. Jéhanno, F. Gonzalez–Jimenez, and F. Hartmann–Boutron, Emission Mössbauer spectroscopy and relaxation measurements in hyperfine levels out of thermal equilibrium: Very-low-temperature experiments on the Kondo alloy AuYb170, Phys. Rev. B 30, 3672 (1984).
  48. J. Kondo, Internal magnetic field in rare earth metals, J. Phys. Soc. Jpn. 16, 1690 (1961).
  49. The measured susceptibility leads to the enhancement of the magnetic induction B=(1+χ)Bext inside YbRh2Si2 over the external field Bext by about 20%. This effect should be incorporated in future theoretical models of the magnetism in YbRh2Si2.
  50. M. A. Continentino, Universality in heavy fermions, Phys. Rev. B 57, 5966 (1998).
  51. P. Chandra, P. Coleman, M. A. Continentino, and G. G. Lonzarich, Quantum annealed criticality: A scaling description, Phys. Rev. Res. 2, 043440 (2020).
  52. H. Eisenlohr and M. Vojta, Limits to magnetic quantum criticality from nuclear spins, Phys. Rev. B 103, 064405 (2021).
  53. D. Bitko, T. F. Rosenbaum, and G. Aeppli, Quantum critical behavior for a model magnet, Phys. Rev. Lett. 77, 940 (1996).
  54. M. Libersky, R. D. McKenzie, D. M. Silevitch, P. C. E. Stamp, and T. F. Rosenbaum, Direct observation of collective electronuclear modes about a quantum critical point, Phys. Rev. Lett. 127, 207202 (2021).
  55. J. Banda, D. Hafner, J. F. Landaeta, E. Hassinger, K. Mitsumoto, M. Giovannini, J. G. Sereni, C. Geibel, and M. Brando, Electronuclear quantum criticality, arXiv:2308.15294.
  56. 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.
  57. K. Andres and O. V. Lounasmaa, Recent progress in nuclear cooling, in Progress in Low Temperature Physics (North Holland Publishing Company, Amsterdam, 1982), Chap. 4, pp. 221–287.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation