Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Hall-effect evolution across a heavy-fermion quantum critical point


A quantum critical point (QCP) develops in a material at absolute zero when a new form of order smoothly emerges in its ground state. QCPs are of great current interest because of their singular ability to influence the finite temperature properties of materials. Recently, heavy-fermion metals have played a key role in the study of antiferromagnetic QCPs. To accommodate the heavy electrons, the Fermi surface of the heavy-fermion paramagnet is larger than that of an antiferromagnet1,2,3. An important unsolved question is whether the Fermi surface transformation at the QCP develops gradually, as expected if the magnetism is of spin-density-wave (SDW) type4,5, or suddenly, as expected if the heavy electrons are abruptly localized by magnetism6,7,8. Here we report measurements of the low-temperature Hall coefficient (RH)—a measure of the Fermi surface volume—in the heavy-fermion metal YbRh2Si2 upon field-tuning it from an antiferromagnetic to a paramagnetic state. RH undergoes an increasingly rapid change near the QCP as the temperature is lowered, extrapolating to a sudden jump in the zero temperature limit. We interpret these results in terms of a collapse of the large Fermi surface and of the heavy-fermion state itself precisely at the QCP.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Temperature dependence of the Hall effect of YbRh2Si2.
Figure 2: Magnetic field dependence of the Hall effect of YbRh2Si2.
Figure 3: Temperature–field phase diagrams of YbRh2Si2.


  1. 1

    Martin, R. M. Fermi-surface sum rule and its consequences for periodic Kondo and mixed-valence systems. Phys. Rev. Lett. 48, 362–365 (1982)

    ADS  CAS  Article  Google Scholar 

  2. 2

    Fulde, P. in Narrow-Band Phenomena—Influence of Electrons with both Band and Localized Character (ed. Fuggle, J. C.) 27–29 (Plenum, New York, 1988)

    Google Scholar 

  3. 3

    Oshikawa, M. Topological approach to Luttinger's theorem and Fermi surface of a Kondo lattice. Phys. Rev. Lett. 84, 3370–3373 (2000)

    ADS  CAS  Article  Google Scholar 

  4. 4

    Hertz, J. A. Quantum critical phenomena. Phys. Rev. B 14, 1165–1184 (1976)

    ADS  CAS  Article  Google Scholar 

  5. 5

    Millis, A. J. Effect of a nonzero temperature on quantum critical points in itinerant fermion systems. Phys. Rev. B 48, 7183–7196 (1993)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Schröder, A. et al. Onset of antiferromagnetism in heavy-fermion metals. Nature 407, 351–355 (2000)

    ADS  Article  Google Scholar 

  7. 7

    Coleman, P., Pépin, C., Si, Q. & Ramazashvili, R. How do Fermi liquids get heavy and die? J. Phys. Condens. Matter 13, R723–R738 (2001)

    ADS  CAS  Article  Google Scholar 

  8. 8

    Si, Q., Rabello, S., Ingersent, K. & Smith, J. L. Locally critical quantum phase transitions in strongly correlated metals. Nature 413, 804–808 (2001)

    ADS  CAS  Article  Google Scholar 

  9. 9

    Trovarelli, O. et al. YbRh2Si2: Pronounced non-Fermi-liquid effects above a low-lying magnetic phase transition. Phys. Rev. Lett 85, 626–629 (2000)

    ADS  CAS  Article  Google Scholar 

  10. 10

    Ishida, K. et al. YbRh2Si2: Spin fluctuations in the vicinity of a quantum critical point at low magnetic fields. Phys. Rev. Lett. 89, 107202 (2002)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Ishida, K. et al. Low-temperature magnetic order and spin dynamics in YbRh2Si2 . Phys. Rev. B 68, 184401 (2003)

    ADS  Article  Google Scholar 

  12. 12

    Gegenwart, P. et al. Magnetic-field induced quantum critical point in YbRh2Si2 . Phys. Rev. Lett. 89, 056402 (2002)

    ADS  CAS  Article  Google Scholar 

  13. 13

    Küchler, R. et al. Low-temperature thermal expansion and magnetostriction of YbRh2(Si1-xGex)2 (x = 0 and 0.05). J. Magn. Magn. Mater. 272–276, 229–230 (2004)

    ADS  Article  Google Scholar 

  14. 14

    Custers, J. et al. The break-up of heavy electrons at a quantum critical point. Nature 424, 524–527 (2003)

    ADS  CAS  Article  Google Scholar 

  15. 15

    Stewart, G. R. Non-Fermi-liquid behavior in d- and f-electron metals. Rev. Mod. Phys. 73, 797–855 (2001)

    ADS  CAS  Article  Google Scholar 

  16. 16

    Senthil, T., Vojta, M. & Sachdev, S. Weak magnetism and non-Fermi liquids near heavy-fermion critical points. Phys. Rev. B 69, 035111 (2004)

    ADS  Article  Google Scholar 

  17. 17

    Paschen, S. et al. Hall effect of the NFL compound YbRh2Si2 . Acta Phys. Polon. B 34, 359–362 (2003)

    CAS  Google Scholar 

  18. 18

    Paschen, S. et al. Anomalous Hall effect in YbRh2Si2 . Physica B (in the press)

  19. 19

    Anderson, P. W. Hall effect in the two-dimensional Luttinger liquid. Phys. Rev. Lett. 67, 2092–2094 (1991)

    ADS  CAS  Article  Google Scholar 

  20. 20

    Nakajima, Y. et al. Normal-state Hall angle and magnetoresistance in quasi-2D heavy fermion CeCoIn5 near a quantum critical point. J. Phys. Soc. Jpn 73, 5–8 (2004)

    ADS  CAS  Article  Google Scholar 

  21. 21

    Custers, J. Quantum-Critical Behavior in the Heavy-Fermion Compounds YbRh2Si2 and CeIn3-xSnx. PhD thesis, TU Dresden (2004)

    Google Scholar 

  22. 22

    Lee, M., Husmann, A., Rosenbaum, T. F. & Aeppli, G. High resolution study of magnetic ordering at absolute zero. Phys. Rev. Lett. 92, 187201 (2004)

    ADS  CAS  Article  Google Scholar 

  23. 23

    Haldane, F. D. M. ‘Luttinger liquid theory’ of one-dimensional quantum fluids: I. Properties of the Luttinger model and their extension to the general 1D interacting spinless Fermi gas. J. Phys. C 14, 2585–2609 (1981)

    ADS  Article  Google Scholar 

  24. 24

    Varma, C. M., Littlewood, P. B., Schmitt-Rink, S., Abrahams, E. & Ruckenstein, A. E. Phenomenology of the normal state of Cu-O high-temperature superconductors. Phys. Rev. Lett. 63, 1996–1999 (1989)

    ADS  CAS  Article  Google Scholar 

  25. 25

    Valla, T. et al. Evidence for quantum critical behaviour in the optimally doped cuprate Bi2Sr2CaCu2O8+δ . Science 285, 2110–2113 (1999)

    CAS  Article  Google Scholar 

  26. 26

    Yeh, A. et al. Quantum phase transition in a common metal. Nature 419, 459–462 (2002)

    ADS  CAS  Article  Google Scholar 

  27. 27

    Balakirev, F. F. et al. Signature of optimal doping in Hall-effect measurements on a high-temperature superconductor. Nature 424, 912–915 (2003)

    ADS  CAS  Article  Google Scholar 

  28. 28

    Fert, A. & Levy, P. M. Theory of the Hall effect in heavy-fermion compounds. Phys. Rev. B 36, 1907–1916 (1987)

    ADS  CAS  Article  Google Scholar 

  29. 29

    Kontani, H., Miyazawa, M. & Yamada, K. Theory of anomalous Hall effect in a heavy fermion system with a strong anisotropic crystal field. J. Phys. Soc. Jpn 66, 2252–2255 (1997)

    ADS  CAS  Article  Google Scholar 

  30. 30

    Norman, M. R., Si, Q., Bazaliy, Y. B. & Ramazashvili, R. Hall effect in nested antiferromagnets near the quantum critical point. Phys. Rev. Lett. 90, 116601 (2003)

    ADS  CAS  Article  Google Scholar 

Download references


We acknowledge discussions with P. Bühler, J. Custers, C. Langhammer, C. Pépin, A. Rosch, A. Schofield, M. Vojta, A. Tsvelik and F. Weickert. Part of the work at Dresden was supported by the Fonds der Chemischen Industrie. P.C. and Q.S. are supported by the National Science Foundation. The work at Rice University was partially supported by the Welch Foundation and TCSAM.

Author information



Corresponding author

Correspondence to S. Paschen.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Supplementary information

Supplementary Methods 1

Proof that the longitudinal field B2 produces essentially no Hall response. (PDF 32 kb)

Supplementary Methods 2

Determination of the orbital part of the differential Hall coefficient (Equation 2) within the Kubo formalism. (PDF 44 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Paschen, S., Lühmann, T., Wirth, S. et al. Hall-effect evolution across a heavy-fermion quantum critical point. Nature 432, 881–885 (2004).

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing