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
  • Editors' Suggestion
  • Open Access

Evolution of Electron Spin Resonance through a Metallic Quantum Critical Phase Diagram

Marc Scheffler1,*, Jörg Sichelschmidt2,*, Conrad Clauss1, Mojtaba Javaheri Rahim1, Boris I. Kochelaev2,†, Cornelius Krellner2,3, Christoph Geibel2, Frank Steglich2,4, and Martin Dressel1

  • *These authors contributed equally to this work.
  • †Deceased.

Phys. Rev. Lett. 137, 136506 – Published 25 September, 2026

DOI: https://doi.org/10.1103/y227-dk8f

Abstract

In the heavy-fermion metal YbRh2Si2, quantum criticality at a suppressed antiferromagnetic order is governed by the interplay of local magnetic moments and itinerant conduction electrons. We demonstrate how this can be investigated by a new experimental approach that enables the observation of electron spin resonance (ESR) across a broad range of frequencies and fields at very low temperatures. This allowed us to cover a large part of the phase diagram from the paramagnetic Fermi-liquid phase to the phase with antiferromagnetic order and including the quantum-critical regime. Both the ESR g factor and the linewidth present distinct behaviors in these three regimes, providing further insight into the physics across a quantum critical point. Notably, when cooling down at a field directly toward the quantum critical point, both g factor and linewidth continuously decrease. Furthermore, we observe a very good matching of the g-factor behavior upon field tuning and temperature tuning toward the quantum-critical point. We analyze and discuss the results in the context of present theories on ESR in strongly correlated electron systems.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (72)

  1. P. Gegenwart, Q. Si, and F. Steglich, Nat. Phys. 4, 186 (2008).
  2. Q. Si and F. Steglich, Science 329, 1161 (2010).
  3. O. Trovarelli, C. Geibel, S. Mederle, C. Langhammer, F. M. Grosche, P. Gegenwart, M. Lang, G. Sparn, and F. Steglich, Phys. Rev. Lett. 85, 626 (2000).
  4. S. Paschen, T. Lühmann, S. Wirth, P. Gegenwart, O. Trovarelli, C. Geibel, F. Steglich, P. Coleman, and Q. Si, Nature (London) 432, 881 (2004).
  5. P. Gegenwart, T. Westerkamp, C. Krellner, Y. Tokiwa, S. Paschen, C. Geibel, F. Steglich, E. Abrahams, and Q. Si, Science 315, 969 (2007).
  6. K. Kummer et al., Phys. Rev. X 5, 011028 (2015).
  7. S. Paschen, S. Friedemann, S. Wirth, F. Steglich, S. Kirchner, and Q. Si, J. Magn. Magn. Mater. 400, 17 (2016).
  8. P. Wölfle and E. Abrahams, Phys. Rev. B 92, 155111 (2015).
  9. M.-H. Schubert, Y. Tokiwa, S.-H. Hübner, M. Mchalwat, E. Blumenröther, H. S. Jeevan, and P. Gegenwart, Phys. Rev. Res. 1, 032004(R) (2019).
  10. P. Gegenwart, J. Custers, Y. Tokiwa, C. Geibel, and F. Steglich, Phys. Rev. Lett. 94, 076402 (2005).
  11. 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, Nature (London) 484, 493 (2012).
  12. H. Pfau, R. Daou, S. Lausberg, H. R. Naren, M. Brando, S. Friedemann, S. Wirth, T. Westerkamp, U. Stockert, P. Gegenwart, C. Krellner, C. Geibel, G. Zwicknagl, and F. Steglich, Phys. Rev. Lett. 110, 256403 (2013).
  13. F. Steglich, H. Pfau, S. Lausberg, S. Hamann, P. Sun, U. Stockert, M. Brando, S. Friedemann, C. Krellner, C. Geibel, S. Wirth, S. Kirchner, E. Abrahams, and Q. Si, J. Phys. Soc. Jpn. 83, 061001 (2014).
  14. A different conclusion is drawn by Taupin et al. [15], cf. also Ref. [16].

  15. M. Taupin, G. Knebel, T. D. Matsuda, G. Lapertot, Y. Machida, K. Izawa, J.-P. Brison, and J. Flouquet, Phys. Rev. Lett. 115, 046402 (2015).
  16. E. Schuberth, S. Wirth, and F. Steglich, Front. Electron. Mater. 2, 869495 (2022).
  17. P. Gegenwart, J. Custers, C. Geibel, K. Neumaier, T. Tayama, K. Tenya, O. Trovarelli, and F. Steglich, Phys. Rev. Lett. 89, 056402 (2002).
  18. J. Custers, P. Gegenwart, H. Wilhelm, K. Neumaier, Y. Tokiwa, O. Trovarelli, C. Geibel, F. Steglich, C. Pépin, and P. Coleman, Nature (London) 424, 524 (2003).
  19. D. Hafner, B. K. Rai, J. Banda, K. Kliemt, C. Krellner, J. Sichelschmidt, E. Morosan, C. Geibel, and M. Brando, Phys. Rev. B 99, 201109(R) (2019).
  20. 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, Phys. Rev. Lett. 122, 077202 (2019).
  21. 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, Phys. Rev. B 68, 184401 (2003).
  22. E. Schuberth, M. Tippmann, L. Steinke, S. Lausberg, A. Steppke, M. Brando, C. Krellner, C. Geibel, R. Yu, Q. Si, and F. Steglich, Science 351, 485 (2016).
  23. J. Knapp, L. V. Levitin, J. Nyéki, A. F. Ho, B. Cowan, J. Saunders, M. Brando, C. Geibel, K. Kliemt, and C. Krellner, Phys. Rev. Lett. 130, 126802 (2023).
  24. D. H. Nguyen, A. Sidorenko, M. Taupin, G. Knebel, G. Lapertot, E. Schuberth, and S. Paschen, Nat. Commun. 12, 4341 (2021).
  25. 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, Nat. Phys. 22, 713 (2026).
  26. See Supplemental Material at http://link.aps.org/supplemental/10.1103/y227-dk8f including references [27–41] for experimental details, sample preparation, data analysis, and theoretical model.
  27. M. Göppl, A. Fragner, M. Baur, R. Bianchetti, S. Filipp, J. M. Fink, P. J. Leek, G. Puebla, L. Steffen, and A. Wallraff, J. Appl. Phys. 104, 113904 (2008).
  28. Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J.-F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, Phys. Rev. Lett. 105, 140502 (2010).
  29. D. Bothner, T. Gaber, M. Kemmler, D. Koelle, R. Kleiner, S. Wünsch, and M. Siegel, Phys. Rev. B 86, 014517 (2012).
  30. M. Javaheri Rahim, T. Lehleiter, D. Bothner, C. Krellner, D. Koelle, R. Kleiner, M. Dressel, and M. Scheffler, J. Phys. D 49, 395501 (2016).
  31. L. Bondorf, M. Beutel, M. Thiemann, M. Dressel, D. Bothner, J. Sichelschmidt, K. Kliemt, C. Krellner, and M. Scheffler, Physica (Amsterdam) 536B, 331 (2018).
  32. B. Miksch, A. Pustogow, M. J. Rahim, A. A. Bardin, K. Kanoda, J. A. Schlueter, R. Hübner, M. Scheffler, and M. Dressel, Science 372, 276 (2021).
  33. C. Krellner, S. Taube, T. Westerkamp, Z. Hossain, and C. Geibel, Philos. Mag. 92, 2508 (2012).
  34. C. Clauß, Dissertation, University of Stuttgart, 2014.
  35. K. Parkkinen, M. Dressel, K. Kliemt, C. Krellner, C. Geibel, F. Steglich, and M. Scheffler, Phys. Procedia 75, 340 (2015).
  36. M. Javaheri Rahim, Dissertation, University of Stuttgart, 2018.
  37. J. Wykhoff, J. Sichelschmidt, G. Lapertot, G. Knebel, J. Flouquet, I. I. Fazlishanov, H.-A. Krug von Nidda, C. Krellner, C. Geibel, and F. Steglich, Science Techn. Adv. Mat. 8, 389 (2007).
  38. M. E. Lines, Phys. Rev. 131, 540 (1963).
  39. M. E. Lines, Phys. Rev. 135, A1336 (1964).
  40. S. I. Belov, A. S. Kutuzov, and B. I. Kochelaev, J. Phys. Conf. Ser. 324, 012017 (2011).
  41. P. W. Anderson, Phys. Rev. 86, 694 (1952).
  42. S. Kimura, J. Sichelschmidt, J. Ferstl, C. Krellner, C. Geibel, and F. Steglich, Phys. Rev. B 74, 132408 (2006).
  43. C. Stock, C. Broholm, F. Demmel, J. Van Duijn, J. W. Taylor, H. J. Kang, R. Hu, and C. Petrovic, Phys. Rev. Lett. 109, 127201 (2012).
  44. S. Ernst, S. Kirchner, C. Krellner, C. Geibel, G. Zwicknagl, F. Steglich, and S. Wirth, Nature (London) 474, 362 (2011).
  45. S. Kambe, H. Sakai, Y. Tokunaga, G. Lapertot, T. D. Matsuda, G. Knebel, J. Flouquet, and R. E. Walstedt, Nat. Phys. 10, 840 (2014).
  46. D. Y. Usachov, G. Poelchen, I. I. Tupitsyn, K. A. Bokai, D. Glazkova, A. V. Tarasov, M. Mende, A. V. Fedorov, V. S. Stolyarov, C. Krellner, and D. V. Vyalikh, Phys. Rev. B 109, L241118 (2024).
  47. S. E. Barnes, Adv. Phys. 30, 801 (1981).
  48. B. Elschner and A. Loidl, Electron-Spin Resonance on Localized Magnetic Moments in Metals (Elsevier Science B.V., New York, 1997), Review 162, p. 221, https://doi.org/10.1016/S0168-1273(97)24007-9.
  49. J. Sichelschmidt, V. A. Ivanshin, J. Ferstl, C. Geibel, and F. Steglich, Phys. Rev. Lett. 91, 156401 (2003).
  50. C. Krellner, T. Förster, H. Jeevan, C. Geibel, and J. Sichelschmidt, Phys. Rev. Lett. 100, 066401 (2008).
  51. J. G. S. Duque, E. M. Bittar, C. Adriano, C. Giles, L. M. Holanda, R. Lora-Serrano, P. G. Pagliuso, C. Rettori, C. A. Perez, R. Hu, C. Petrovic, S. Maquilon, Z. Fisk, D. L. Huber, and S. B. Oseroff, Phys. Rev. B 79, 035122 (2009).
  52. J. Sichelschmidt, J. Wykhoff, T. Gruner, C. Krellner, C. Klingner, C. Geibel, F. Steglich, H.-A. Krug von Nidda, D. V. Zakharov, A. Loidl, and I. Fazlizhanov, Phys. Rev. B 81, 205116 (2010).
  53. T. Gruner, J. Sichelschmidt, C. Klingner, C. Krellner, C. Geibel, and F. Steglich, Phys. Rev. B 85, 035119 (2012).
  54. D. L. Huber, J. Phys. Condens. Matter 24, 226001 (2012).
  55. B. I. Kochelaev, Low Temp. Phys. 43, 76 (2017).
  56. B. I. Kochelaev, S. I. Belov, A. M. Skvortsova, A. S. Kutuzov, J. Sichelschmidt, J. Wykhoff, C. Geibel, and F. Steglich, Eur. Phys. J. B 72, 485 (2009).
  57. P. Wölfle and E. Abrahams, Phys. Rev. B 80, 235112 (2009).
  58. U. Schaufuß, V. Kataev, A. A. Zvyagin, B. Büchner, J. Sichelschmidt, J. Wykhoff, C. Krellner, C. Geibel, and F. Steglich, Phys. Rev. Lett. 102, 076405 (2009).
  59. J. Sichelschmidt, T. Kambe, I. Fazlishanov, D. Zakharov, H.-A. Krug von Nidda, J. Wykhoff, A. Skvortsova, S. Belov, A. Kutuzov, B. I. Kochelaev, V. Pashchenko, M. Lang, C. Krellner, C. Geibel, and F. Steglich, Phys. Status Solidi (b) 247, 747 (2010).
  60. M. Scheffler, K. Schlegel, C. Clauss, D. Hafner, C. Fella, M. Dressel, M. Jourdan, J. Sichelschmidt, C. Krellner, C. Geibel, and F. Steglich, Phys. Status Solidi B 250, 439 (2013).
  61. T. Förster, J. Sichelschmidt, C. Krellner, C. Geibel, and F. Steglich, J. Phys. Condens. Matter 22, 435603 (2010).
  62. I. Fazlizhanov, Z. Y. Seidov, H.-A. Krug von Nidda, C. Krellner, C. Klingner, L. Pedrero, S. Lausberg, M. Brando, C. Geibel, F. Steglich, and J. Sichelschmidt Phys. Rev. B 114, 115117 (2026).
  63. R. H. Taylor and B. R. Coles, J. Phys. F 5, 121 (1975).
  64. J. Sichelschmidt, K. Kliemt, M. Hofmann-Kliemt, and C. Krellner, Phys. Rev. B 97, 214424 (2018).
  65. C.-J. Yang, K. Kliemt, C. Krellner, J. Kroha, M. Fiebig, and S. Pal, Nat. Phys. 19, 1605 (2023).
  66. Previous ESR studies at much higher temperatures and magnetic fields have at most shown a slight slope change of g(T) at T* but no maximum [58]. Moreover, a linear relation between g and magnetic susceptibility has been identified [49] which clearly is not the case for temperatures near or below T*.

  67. A. Kutuzov, A. Skvortsova, S. Belov, J. Sichelschmidt, J. Wykhoff, I. Eremin, C. Krellner, C. Geibel, and B. Kochelaev, J. Phys. Condens. Matter 20, 455208 (2008).
  68. Y. Wiemann, J. Simmendinger, C. Clauss, L. Bogani, D. Bothner, D. Koelle, R. Kleiner, M. Dressel, and M. Scheffler, Appl. Phys. Lett. 106, 193505 (2015).
  69. H. Hu, L. Chen, and Q. Si, Nat. Phys. 20, 1863 (2024).
  70. K. Ishida, K. Okamoto, Y. Kawasaki, Y. Kitaoka, O. Trovarelli, C. Geibel, and F. Steglich, Phys. Rev. Lett. 89, 107202 (2002).
  71. L. M. Holanda, J. M. Vargas, W. Iwamoto, C. Rettori, S. Nakatsuji, K. Kuga, Z. Fisk, S. B. Oseroff, and P. G. Pagliuso, Phys. Rev. Lett. 107, 026402 (2011).
  72. F. L. Pratt, P. J. Baker, S. J. Blundell, T. Lancaster, S. Ohira-Kawamura, C. Baines, Y. Shimizu, K. Kanoda, I. Watanabe, and G. Saito, Nature (London) 471, 612 (2011).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation