- Editors' Suggestion
- Open Access
Evolution of Electron Spin Resonance through a Metallic Quantum Critical Phase Diagram
Phys. Rev. Lett. 137, 136506 – Published 25 September, 2026
DOI: https://doi.org/10.1103/y227-dk8f
Abstract
In the heavy-fermion metal , 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 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 factor and linewidth continuously decrease. Furthermore, we observe a very good matching of the -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.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (72)
- P. Gegenwart, Q. Si, and F. Steglich, Nat. Phys. 4, 186 (2008).
- Q. Si and F. Steglich, Science 329, 1161 (2010).
- 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).
- S. Paschen, T. Lühmann, S. Wirth, P. Gegenwart, O. Trovarelli, C. Geibel, F. Steglich, P. Coleman, and Q. Si, Nature (London) 432, 881 (2004).
- P. Gegenwart, T. Westerkamp, C. Krellner, Y. Tokiwa, S. Paschen, C. Geibel, F. Steglich, E. Abrahams, and Q. Si, Science 315, 969 (2007).
- K. Kummer et al., Phys. Rev. X 5, 011028 (2015).
- S. Paschen, S. Friedemann, S. Wirth, F. Steglich, S. Kirchner, and Q. Si, J. Magn. Magn. Mater. 400, 17 (2016).
- P. Wölfle and E. Abrahams, Phys. Rev. B 92, 155111 (2015).
- 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).
- P. Gegenwart, J. Custers, Y. Tokiwa, C. Geibel, and F. Steglich, Phys. Rev. Lett. 94, 076402 (2005).
- 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).
- 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).
- 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).
A different conclusion is drawn by Taupin et al. [15], cf. also Ref. [16].
- 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).
- E. Schuberth, S. Wirth, and F. Steglich, Front. Electron. Mater. 2, 869495 (2022).
- P. Gegenwart, J. Custers, C. Geibel, K. Neumaier, T. Tayama, K. Tenya, O. Trovarelli, and F. Steglich, Phys. Rev. Lett. 89, 056402 (2002).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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).
- D. H. Nguyen, A. Sidorenko, M. Taupin, G. Knebel, G. Lapertot, E. Schuberth, and S. Paschen, Nat. Commun. 12, 4341 (2021).
- 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).
- 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.
- 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).
- 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).
- D. Bothner, T. Gaber, M. Kemmler, D. Koelle, R. Kleiner, S. Wünsch, and M. Siegel, Phys. Rev. B 86, 014517 (2012).
- M. Javaheri Rahim, T. Lehleiter, D. Bothner, C. Krellner, D. Koelle, R. Kleiner, M. Dressel, and M. Scheffler, J. Phys. D 49, 395501 (2016).
- L. Bondorf, M. Beutel, M. Thiemann, M. Dressel, D. Bothner, J. Sichelschmidt, K. Kliemt, C. Krellner, and M. Scheffler, Physica (Amsterdam) 536B, 331 (2018).
- 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).
- C. Krellner, S. Taube, T. Westerkamp, Z. Hossain, and C. Geibel, Philos. Mag. 92, 2508 (2012).
- C. Clauß, Dissertation, University of Stuttgart, 2014.
- K. Parkkinen, M. Dressel, K. Kliemt, C. Krellner, C. Geibel, F. Steglich, and M. Scheffler, Phys. Procedia 75, 340 (2015).
- M. Javaheri Rahim, Dissertation, University of Stuttgart, 2018.
- 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).
- M. E. Lines, Phys. Rev. 131, 540 (1963).
- M. E. Lines, Phys. Rev. 135, A1336 (1964).
- S. I. Belov, A. S. Kutuzov, and B. I. Kochelaev, J. Phys. Conf. Ser. 324, 012017 (2011).
- P. W. Anderson, Phys. Rev. 86, 694 (1952).
- S. Kimura, J. Sichelschmidt, J. Ferstl, C. Krellner, C. Geibel, and F. Steglich, Phys. Rev. B 74, 132408 (2006).
- 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).
- S. Ernst, S. Kirchner, C. Krellner, C. Geibel, G. Zwicknagl, F. Steglich, and S. Wirth, Nature (London) 474, 362 (2011).
- S. Kambe, H. Sakai, Y. Tokunaga, G. Lapertot, T. D. Matsuda, G. Knebel, J. Flouquet, and R. E. Walstedt, Nat. Phys. 10, 840 (2014).
- 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).
- S. E. Barnes, Adv. Phys. 30, 801 (1981).
- 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.
- J. Sichelschmidt, V. A. Ivanshin, J. Ferstl, C. Geibel, and F. Steglich, Phys. Rev. Lett. 91, 156401 (2003).
- C. Krellner, T. Förster, H. Jeevan, C. Geibel, and J. Sichelschmidt, Phys. Rev. Lett. 100, 066401 (2008).
- 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).
- 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).
- T. Gruner, J. Sichelschmidt, C. Klingner, C. Krellner, C. Geibel, and F. Steglich, Phys. Rev. B 85, 035119 (2012).
- D. L. Huber, J. Phys. Condens. Matter 24, 226001 (2012).
- B. I. Kochelaev, Low Temp. Phys. 43, 76 (2017).
- 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).
- P. Wölfle and E. Abrahams, Phys. Rev. B 80, 235112 (2009).
- 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).
- 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).
- 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).
- T. Förster, J. Sichelschmidt, C. Krellner, C. Geibel, and F. Steglich, J. Phys. Condens. Matter 22, 435603 (2010).
- 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).
- R. H. Taylor and B. R. Coles, J. Phys. F 5, 121 (1975).
- J. Sichelschmidt, K. Kliemt, M. Hofmann-Kliemt, and C. Krellner, Phys. Rev. B 97, 214424 (2018).
- C.-J. Yang, K. Kliemt, C. Krellner, J. Kroha, M. Fiebig, and S. Pal, Nat. Phys. 19, 1605 (2023).
Previous ESR studies at much higher temperatures and magnetic fields have at most shown a slight slope change of at but no maximum [58]. Moreover, a linear relation between and magnetic susceptibility has been identified [49] which clearly is not the case for temperatures near or below .
- 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).
- 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).
- H. Hu, L. Chen, and Q. Si, Nat. Phys. 20, 1863 (2024).
- K. Ishida, K. Okamoto, Y. Kawasaki, Y. Kitaoka, O. Trovarelli, C. Geibel, and F. Steglich, Phys. Rev. Lett. 89, 107202 (2002).
- 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).
- 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).