Skip to main content

Thank you for visiting nature.com. 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.

  • Letter
  • Published:

Marginal breakdown of the Fermi-liquid state on the border of metallic ferromagnetism

Nature volume 455, pages 1220–1223 (2008)Cite this article

Abstract

For the past half century, our understanding of how the interactions between electrons affect the low-temperature properties of metals has been based on the Landau theory of a Fermi liquid1. In recent times, however, there have been an increasingly large number of examples in which the predictions of the Fermi-liquid theory appear to be violated2. Although the qualitative reasons for the breakdown are generally understood, the specific quantum states that replace the Fermi liquid remain in many cases unclear. Here we describe an example of such a breakdown where the non-Fermi-liquid properties can be interpreted. We show that the thermal and electrical resistivities in high-purity samples of the d-electron metal ZrZn2 at low temperatures have T and T5/3 temperature dependences, respectively: these are the signatures of the ‘marginal’ Fermi-liquid state3,4,5,6,7, expected to arise from effective long-range spin–spin interactions in a metal on the border of metallic ferromagnetism in three dimensions3,5. The marginal Fermi liquid provides a link between the conventional Fermi liquid and more exotic non-Fermi-liquid states that are of growing interest in condensed matter physics. The idea of a marginal Fermi liquid has also arisen in other contexts—for example, in the phenomenology of the normal state of the copper oxide superconductors7, and in studies of relativistic plasmas and of nuclear matter3,4,6.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Evidence for the marginal Fermi-liquid state in ZrZn2.
Figure 2: Predicted phase diagram of ZrZn2.
Figure 3: Resistivity of ZrZn 2 just below the critical pressure.
Figure 4: Pressure dependence of TC and the resistivity exponent in ZrZn2.

Similar content being viewed by others

References

  1. Landau, L. D. Collected Papers (ed. Ter Haas, D.) Ch. 90, 91 (Pergamon, 1965)

    Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  3. Baym, G. & Pethick, C. Landau Fermi Liquid Theory Ch. 3 (Wiley, 1991)

    Book  Google Scholar 

  4. Holstein, T., Norton, R. E. & Pincus, P. de Haas-van Alphen effect and the specific heat of an electron gas. Phys. Rev. B 8, 2649–2656 (1973)

    Article  ADS  Google Scholar 

  5. Dzyaloshinskii, I. E. & Kondratenko, P. S. Theory of weak ferromagnetism in a Fermi fluid. Sov. Phys. JETP 43, 1036–1054 (1976)

    ADS  Google Scholar 

  6. Reizer, M. & Yu Effective electron-electron interaction in metals and superconductors. Phys. Rev. B 39, 1602–1608 (1989)

    Article  ADS  CAS  Google Scholar 

  7. 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)

    Article  ADS  CAS  Google Scholar 

  8. Moriya, T. Spin Fluctuations in Itinerant Electron Magnetism (Springer, 1985)

    Book  Google Scholar 

  9. Lonzarich, G. G. in Electron (ed. Springford, M.) 109–147 (Cambridge Univ. Press, 1997)

    Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  11. Pfleiderer, C., McMullan, G. J., Julian, S. R. & Lonzarich, G. G. Magnetic quantum phase transition in MnSi under hydrostatic pressure. Phys. Rev. B 55, 8330–8338 (1997)

    Article  ADS  CAS  Google Scholar 

  12. Pfleiderer, C., Julian, S. R. & Lonzarich, G. G. Non-Fermi liquid nature of the normal state of itinerant-electron ferromagnets. Nature 414, 427–430 (2001)

    Article  ADS  CAS  Google Scholar 

  13. Nicklas, M. et al. Non-Fermi-liquid behaviour at a ferromagnetic quantum critical point in NixPd1-x . Phys. Rev. Lett. 82, 4268–4271 (1999)

    Article  ADS  CAS  Google Scholar 

  14. Kuchler, R. et al. Thermal expansion and Gruneisen ratio near quantum critical points. Physica B 378–380, 36–39 (2006)

    Article  ADS  Google Scholar 

  15. Uhlarz, M., Pfleiderer, C. & Hayden, S. M. Quantum phase transitions in the itinerant ferromagnet ZrZn2 . Phys. Rev. Lett. 93, 256404 (2004)

    Article  ADS  CAS  Google Scholar 

  16. Yates, S. J. C., Santi, G., Hayden, S. M., Meeson, P. J. & Dugdale, S. B. Heavy quasiparticles in the ferromagnetic superconductor ZrZn2 . Phys. Rev. Lett. 90, 057003 (2003)

    Article  ADS  CAS  Google Scholar 

  17. Lonzarich, G. G., Bernhoeft, N. R. & Paul, D. M. Spin density fluctuations in magnetic metals. Physica B 156–157, 699–705 (1989)

    Article  ADS  Google Scholar 

  18. Bernhoeft, N. R., Law, S. A. & Lonzarich, G. G. Magnetic excitations in ZrZn2 at low energies and long wavelengths. Phys. Scripta 38, 191–193 (1988)

    Article  ADS  CAS  Google Scholar 

  19. Yelland, E. A. et al. Ferromagnetic properties of ZrZn2 . Phys. Rev. B 72, 184436 (2005)

    Article  ADS  Google Scholar 

  20. Sokolov, D. A., Aronson, M. C., Gannon, W. & Fisk, Z. Critical phenomena and the quantum critical point of ferromagnetic Zr1-xNbxZn2 . Phys. Rev. Lett. 96, 116404 (2006)

    Article  ADS  CAS  Google Scholar 

  21. Takashima, S. et al. Robustness of non-Fermi-liquid behavior near the ferromagnetic critical point in clean ZrZn2 . J. Phys. Soc. Jpn 76, 043704 (2007)

    Article  ADS  Google Scholar 

  22. Niklowitz, P. G. et al. Spin-fluctuation-dominated electrical transport of Ni3Al at high pressure. Phys. Rev. B 72, 024424 (2005)

    Article  ADS  Google Scholar 

  23. Brando, M. et al. Logarithmic Fermi-liquid breakdown in NbFe2 . Phys. Rev. Lett. 101, 026401 (2008)

    Article  ADS  CAS  Google Scholar 

  24. Thessieu, C. et al. Field dependence of the magnetic quantum phase transition in MnSi. J. Phys. Condens. Matter 9, 6677–6687 (1997)

    Article  ADS  CAS  Google Scholar 

  25. Doiron-Leyraud, N. et al. Fermi liquid breakdown of the paramagnetic phase of a pure metal. Nature 425, 595–599 (2003)

    Article  ADS  CAS  Google Scholar 

  26. Zhou, J. S., Goodenough, J. B. & Dabrowski, B. Pressure induced non-Fermi liquid behaviour of PrNiO3 . Phys. Rev. Lett. 94, 226602 (2005)

    Article  ADS  Google Scholar 

  27. Pfleiderer, C. et al. Partial order in the non-Fermi-liquid phase of MnSi. Nature 427, 227–231 (2004)

    Article  ADS  CAS  Google Scholar 

  28. Chubukov, A. V., Maslov, D. L. & Millis, A. J. Nonanalytic corrections to the specific heat of a three-dimensional Fermi liquid. Phys. Rev. B 73, 045128 (2006)

    Article  ADS  Google Scholar 

  29. Chitov, C. Y. & Millis, A. J. First temperature corrections to the Fermi-liquid fixed point in two dimensions. Phys. Rev. B 64, 054414 (2001)

    Article  ADS  Google Scholar 

  30. Belitz, D., Kirkpatrick, T. R. & Vojta, T. Nonanalytic behaviour of the spin susceptibility in clean Fermi systems. Phys. Rev. B 55, 9452–9462 (1997)

    Article  ADS  CAS  Google Scholar 

  31. Gehring, G. A. Pressure induced quantum phase transitions. Europhys. Lett. (in the press); preprint at 〈http://arxiv.org/abs/0711.2586〉 (2007)

  32. Jeong, T., Kyker, A. & Pickett, W. E. Fermi velocity spectrum and incipient magnetism in TiBe2 . Phys. Rev. B 73, 115106 (2006)

    Article  ADS  Google Scholar 

  33. Ueda, K. & Moriya, T. Contribution of spin fluctuations to the electrical and thermal resistivities of weakly and nearly ferromagnetic metals. J. Phys. Soc. Jpn 39, 605–615 (1975)

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

We acknowledge financial support from the Royal Society, the EPSRC and St Catharine’s College, Cambridge, and the Ministry of Education, Culture, Sports, Science and Technology of Japan (Grants-in-Aid for Scientific Research on Priority Areas and (S) from MEXT, Japan). We thank S. E. Rowley and I. R. Walker for experimental help and S. E. Rowley, C. M. Varma and P. B. Littlewood for discussions.

Author Contributions R.P.S. set up, performed and analysed the resistivity measurements at ambient pressure and under pressure, and carried out the model calculations. M.S. set up, performed and analysed the thermal conductivity measurements. S.S.S. assisted with measurements under pressure. N.K., S.T., M.N. and H.T. grew the ZrZn2 crystals for the study. G.G.L and N.K. designed the study. R.P.S. and G.G.L. wrote the paper. M.S. assisted in writing the paper.

Author information

Authors and Affiliations

  1. Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, UK ,

    R. P. Smith, M. Sutherland, G. G. Lonzarich & S. S. Saxena

  2. Center for Low Temperature Science, Tohoku University, Sendai, Miyagi 980-8578, Japan ,

    N. Kimura

  3. Department of Advanced Materials Science, University of Tokyo, Kashiwa, Chiba 277-8561, Tokyo, Japan,

    S. Takashima, M. Nohara & H. Takagi

  4. RIKEN, 2-1 Hirosawa Wako, Saitama 351-0198, Japan

    H. Takagi

Authors
  1. R. P. Smith
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Sutherland
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. G. Lonzarich
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. S. Saxena
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. N. Kimura
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. S. Takashima
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. M. Nohara
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. H. Takagi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. P. Smith.

Supplementary information

Supplementary Information

This file contains supplementary Information and Supplementary Figures 1-8 with Legends (PDF 579 kb)

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Cite this article

Smith, R., Sutherland, M., Lonzarich, G. et al. Marginal breakdown of the Fermi-liquid state on the border of metallic ferromagnetism. Nature 455, 1220–1223 (2008). https://doi.org/10.1038/nature07401

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature07401

This article is cited by

Comments

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.

Search

Advanced search

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