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.

  • Article
  • Published:

Quantum tricritical points in NbFe2

Nature Physics volume 14, pages 62–67 (2018)Cite this article

Subjects

This article has been updated

Abstract

Quantum critical points (QCPs) emerge when a second-order phase transition is suppressed to zero temperature. In metals the quantum fluctuations at such a QCP can give rise to new phases, including unconventional superconductivity. Whereas antiferromagnetic QCPs have been studied in considerable detail, ferromagnetic (FM) QCPs are much harder to access. In almost all metals FM QCPs are avoided through either a change to first-order transitions or through an intervening spin-density-wave (SDW) phase. Here, we study the prototype of the second case, NbFe2. We demonstrate that the phase diagram can be modelled using a two-order-parameter theory in which the putative FM QCP is buried within a SDW phase. We establish the presence of quantum tricritical points (QTCPs) at which both the uniform and finite wavevector susceptibility diverge. The universal nature of our model suggests that such QTCPs arise naturally from the interplay between SDW and FM order and exist generically near a buried FM QCP of this type. Our results promote NbFe2 as the first example of a QTCP, which has been proposed as a key concept in a range of narrow-band metals, including the prominent heavy-fermion compound YbRh2Si2.

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: Magnetic transitions in Nb1−yFe2+y in zero magnetic field.
Figure 2: Temperature–magnetic field phase diagrams for the composition series Nb1−yFe2+y.
Figure 3: Schematic phase diagram based on the model free energy in equation (1), as applied to Nb1−yFe2+y.
Figure 4: Two-order-parameter analysis of the magnetization in Nb1−yFe2+y.
Figure 5: Overall composition–magnetic field–temperature phase diagram for the Nb1−yFe2+y system.

Similar content being viewed by others

Change history

  • 06 November 2017

    In the version of this Article originally published, one of the author names was incorrect, and should have read Max Hirschberger.

References

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

    Book  Google Scholar 

  2. Lonzarich, G. G. in Electron (ed. Springford, M.) (Cambridge Univ. Press, 1997).

    Google Scholar 

  3. Löhneysen, H. v., Rosch, A., Vojta, M. & Wölfle, P. Fermi-liquid instabilities at magnetic quantum phase transitions. Rev. Mod. Phys. 79, 1015–1075 (2007).

    Article  ADS  Google Scholar 

  4. Brando, M., Belitz, D., Grosche, F. M. & Kirkpatrick, T. R. Metallic quantum ferromagnets. Rev. Mod. Phys. 88, 025006 (2016).

    Article  ADS  Google Scholar 

  5. 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  Google Scholar 

  6. 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 

  7. Smith, R. P. et al. Marginal breakdown of the Fermi-liquid state on the border of metallic ferromagnetism. Nature 455, 1220–1223 (2008).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. Belitz, D., Kirkpatrick, T. R. & Vojta, T. First order transitions and multicritical points in weak itinerant ferromagnets. Phys. Rev. Lett. 82, 4707–4710 (1999).

    Article  ADS  Google Scholar 

  10. Pfleiderer, C., MeMullan, G. & Lonzarich, G. Critical behaviour at the transition from a magnetic to a nonmagnetic metallic state in MnSi as a function of hydrostatic pressure. Phys. B 199–200, 634–636 (1994).

    Article  ADS  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  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  14. Chubukov, A. V., Pepin, C. & Rech, J. Instability of the quantum-critical point of itinerant ferromagnets. Phys. Rev. Lett. 92, 147003 (2004).

    Article  ADS  Google Scholar 

  15. Conduit, G. J., Green, A. G. & Simons, B. D. Inhomogeneous phase formation on the border of itinerant ferromagnetism. Phys. Rev. Lett. 103 (2009).

  16. Pedder, C. J., Krüger, F. & Green, A. G. Resummation of fluctuations near ferromagnetic quantum critical points. Phys. Rev. B 88, 165109 (2013).

    Article  ADS  Google Scholar 

  17. Moroni-Klementowicz, D. et al. Magnetism in Nb1−yFe2+y: composition and magnetic field dependence. Phys. Rev. B 79, 224410 (2009).

    Article  ADS  Google Scholar 

  18. Taufour, V. et al. Ferromagnetic quantum critical point avoided by the appearance of another magnetic phase in LaCrGe3 under pressure. Phys. Rev. Lett. 117, 037207 (2016).

    Article  ADS  Google Scholar 

  19. Abdul-Jabbar, G. et al. Modulated magnetism in PrPtAl. Nat. Phys. 11, 321–327 (2015).

    Article  Google Scholar 

  20. Kotegawa, H. et al. Pressure–temperature–magnetic field phase diagram of ferromagnetic Kondo lattice CeRuPO. J. Phys. Soc. Jpn 82, 123711 (2013).

    Article  ADS  Google Scholar 

  21. Lausberg, S. et al. Avoided ferromagnetic quantum critical point: unusual short-range ordered state in CeFePO. Phys. Rev. Lett. 109, 216402 (2012).

    Article  ADS  Google Scholar 

  22. Lausberg, S. et al. Doped YbRh2Si2: not only ferromagnetic correlations but ferromagnetic order. Phys. Rev. Lett. 110, 256402 (2013).

    Article  ADS  Google Scholar 

  23. Shiga, M. & Nakamura, Y. Magnetic-properties of stoichiometric and off-stoichiometric NbFe2 . J. Phys. Soc. Jpn 56, 4040–4046 (1987).

    Article  ADS  Google Scholar 

  24. Yamada, Y. & Sakata, A. Weak antiferromagnetism in NbFe2 . J. Phys. Soc. Jpn 57, 46–49 (1988).

    Article  ADS  Google Scholar 

  25. Crook, M. R. & Cywinski, R. Magnetic transitions in Nb1−yFe2+y . J. Magn. Magn. Mater. 140–144, 71–72 (1995).

    Article  ADS  Google Scholar 

  26. Rauch, D. et al. Spectroscopic study of the magnetic ground state of Nb1−yFe2+y . Phys. Rev. B 91, 174404 (2015).

    Article  ADS  Google Scholar 

  27. Niklowitz, P. G. et al. Ultra-small moment incommensurate spin density wave order masking a ferromagnetic quantum critical point in NbFe2 . Preprint at http://arXiv.org/abs/1704.08379 (2017).

  28. Moriya, T. & Usami, K. Coexistence of ferromagnetism and antiferromagnetism and phase-transitions in itinerant electron-systems. Solid State Commun. 23, 935–938 (1977).

    Article  ADS  Google Scholar 

  29. Lawrie, I. D. & Sarbach, S. in Phase Transitions and Critical Phenomena Vol. 9 (eds Domb, C., Green, M. S. & Lebowitz, J. L.) 1 (Academic, 1984).

    Google Scholar 

  30. Rost, A. W., Perry, R. S., Mercure, J.-F., Mackenzie, A. P. & Grigera, S. A. Entropy landscape of phase formation associated with quantum criticality in Sr3Ru2O7 . Science 325, 1360–1363 (2009).

    Article  ADS  Google Scholar 

  31. Vojta, T., Belitz, D., Kirkpatrick, T. & Narayanan, R. Quantum critical behavior of itinerant ferromagnets. Ann. Phys. 8, 593–602 (1999).

    Article  Google Scholar 

  32. Misawa, T., Yamaji, Y. & Imada, M. YbRh2Si2: quantum tricritical behavior in itinerant electron systems. J. Phys. Soc. Jpn 77, 093712 (2008).

    Article  ADS  Google Scholar 

  33. Oliver, G. T. & Schofield, A. J. Quantum multicriticality. Preprint at http://arXiv.org/abs/1506.03021 (2015).

  34. Misawa, T., Yamaji, Y. & Imada, M. Spin fluctuation theory for quantum tricritical point arising in proximity to first-order phase transitions: applications to heavy-fermion systems, YbRh2Si2, CeRu2Si2, and β-YbAlB4 . J. Phys. Soc. Jpn 78, 084707 (2009).

    Article  ADS  Google Scholar 

  35. Friedemann, S. et al. Ordinary and intrinsic anomalous Hall effects in Nb1−yFe2+y . Phys. Rev. B 87, 024410 (2013).

    Article  ADS  Google Scholar 

  36. Küchler, R., Bauer, T., Brando, M. & Steglich, F. A compact and miniaturized high resolution capacitance dilatometer for measuring thermal expansion and magnetostriction. Rev. Sci. Instrum. 83, 095102 (2012).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank G. G. Lonzarich, A. Schofield and P. Niklowitz for helpful discussions. This work was supported by the EPSRC UK under grant No EP/K012894, the Alexander-van-Humboldt foundation, FOR 960 Quantum Phase Transitions project P4, and DFG Transregio 80 (TRR80) project E1.

Author information

Author notes

  1. Max Hirschberger

    Present address: RIKEN Center for Emergent Matter Science (CEMS), Wako, 351-0198, Japan

Authors and Affiliations

  1. HH Wills Laboratory, University of Bristol, Bristol BS8 1TL, UK

    Sven Friedemann

  2. Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK

    Sven Friedemann, Max Hirschberger & F. Malte Grosche

  3. Department of Physics, Royal Holloway, University of London, Egham TW20 0EX, UK

    Will J. Duncan

  4. Physik-Department, Technische Universität München, James Franck Straße, 85748 Garching, Germany

    Max Hirschberger, Andreas Neubauer & Christian Pfleiderer

  5. MPI-CPfS, Nöthnitzer Strasse, 01189 Dresden, Germany

    Thomas W. Bauer, Robert Küchler & Manuel Brando

Authors
  1. Sven Friedemann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Will J. Duncan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Max Hirschberger
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Thomas W. Bauer
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Robert Küchler
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Andreas Neubauer
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Manuel Brando
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Christian Pfleiderer
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. F. Malte Grosche
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Magnetic measurements were conducted by S.F., W.J.D., M.H., and F.M.G. Resistivity was measured by S.F. and M.H. and thermal expansion by T.W.B., R.K., and M.B. Samples were grown by W.J.D., A.N., F.M.G., and C.P. The data were analysed and modelled by S.F., M.B. and F.M.G. The manuscript was prepared by S.F. and F.M.G. with the help of M.B. and C.P. The project was devised and led by F.M.G.

Corresponding author

Correspondence to Sven Friedemann.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 497 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Friedemann, S., Duncan, W., Hirschberger, M. et al. Quantum tricritical points in NbFe2. Nature Phys 14, 62–67 (2018). https://doi.org/10.1038/nphys4242

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys4242

This article is cited by

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