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:

Quantum criticality among entangled spin chains

Nature Physics volume 14, pages 273–276 (2018)Cite this article

Subjects

Abstract

An important challenge in magnetism is the unambiguous identification of a quantum spin liquid1,2, of potential importance for quantum computing. In such a material, the magnetic spins should be fluctuating in the quantum regime, instead of frozen in a classical long-range-ordered state. While this requirement dictates systems3,4 wherein classical order is suppressed by a frustrating lattice5, an ideal system would allow tuning of quantum fluctuations by an external parameter. Conventional three-dimensional antiferromagnets can be tuned through a quantum critical point—a region of highly fluctuating spins—by an applied magnetic field. Such systems suffer from a weak specific-heat peak at the quantum critical point, with little entropy available for quantum fluctuations6. Here we study a different type of antiferromagnet, comprised of weakly coupled antiferromagnetic spin-1/2 chains as realized in the molecular salt K2PbCu(NO2)6. Across the temperature–magnetic field boundary between three-dimensional order and the paramagnetic phase, the specific heat exhibits a large peak whose magnitude approaches a value suggestive of the spinon Sommerfeld coefficient of isolated quantum spin chains. These results demonstrate an alternative approach for producing quantum matter via a magnetic-field-induced shift of entropy from one-dimensional short-range order to a three-dimensional quantum critical point.

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

Fig. 1: Comparison of the T–H phase diagram for the quasi-1D system K2PbCu(NO2)6 with the behaviour of a generic 3D antiferromagnet.
Fig. 2: Magnetic properties of K2PbCu(NO2)6 showing quasi-1D behaviour and antiferromagnetic order.
Fig. 3: Specific heat divided by temperature, C(T,H)/T, versus magnetic field for K2PbCu(NO2)6.
Fig. 4: The temperature dependence of C/T(H) peaks suggests an explanation based on spinons in 1D.

Similar content being viewed by others

References

  1. Nayak, C., Simon, S. H., Stern, A., Freedman, M. & Das Sarma, S. Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083–1159 (2008).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Kitaev, A. Anyons in an exactly solved model and beyond. Ann. Phys. 321, 2–111 (2006).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Helton, J. S. et al. Spin dynamics of the spin-1/2 Kagome lattice antiferromagnet ZnCu3(OH)6Cl2. Phys. Rev. Lett. 98, 107204 (2007).

    Article  ADS  Google Scholar 

  4. Yamashita, M. et al. Thermal-transport measurements in a quantum spin-liquid state of the frustrated triangular magnet kappa-(BEDT-TTF)2Cu2(CN)3. Nat. Phys. 5, 44–47 (2009).

    Article  Google Scholar 

  5. Ramirez, A. P. Strongly geometrically frustrated magnets. Annu. Rev. Mater. Sci. 24, 453–480 (1994).

    Article  ADS  Google Scholar 

  6. Wu, L. S. et al. Magnetic field tuning of antiferromagnetic Yb3Pt4. Phys. Rev. B 84, 134409 (2011).

    Article  ADS  Google Scholar 

  7. Bitko, D., Rosenbaum, T. F. & Aeppli, G. Quantum critical behavior for a model magnet. Phys. Rev. Lett. 77, 940–943 (1996).

    Article  ADS  Google Scholar 

  8. Ghosh, S., Rosenbaum, T. F., Aeppli, G. & Coppersmith, S. N. Entangled quantum state of magnetic dipoles. Nature 425, 48–51 (2003).

    Article  ADS  Google Scholar 

  9. Coldea, R. et al. Quantum criticality in an Ising chain: experimental evidence for emergent E-8 symmetry. Science 327, 177–180 (2010).

    Article  ADS  Google Scholar 

  10. Blote, H. W. J. Magnetically linear and quadratic hexanitrocuprates. J. Appl. Phys. 50, 1825–1827 (1979).

    Article  ADS  Google Scholar 

  11. Hammar, P. R. et al. Characterization of a quasi-one-dimensional spin-1/2 magnet which is gapless and paramagnetic for gμ B H less than or similar to J and k B T ≪ J. Phys. Rev. B 59, 1008–1015 (1999).

    Article  ADS  Google Scholar 

  12. Nikuni, T., Oshikawa, M., Oosawa, A. & Tanaka, H. Bose–Einstein condensation of dilute magnons in TlCuCl3. Phys. Rev. Lett. 84, 5868–5871 (2000).

    Article  ADS  Google Scholar 

  13. Jaime, M. et al. Magnetic-field-induced condensation of triplons in Han purple pigment BaCuSi2O6. Phys. Rev. Lett. 93, 087203 (2014).

    Article  ADS  Google Scholar 

  14. Dong, L., Besara, T., Henderson, A. & Siegrist, T. Gel growth of K2PbCu(NO2)6-elpasolite single crystals. Cryst. Growth Des. 17, 5170–5177 (2017).

  15. Noda, Y., Mori, M. & Yamada, Y. Successive Jahn–Teller phase-transitions in K2PbCu(NO2)6. J. Phys. Soc. Jpn 45, 954–966 (1978).

    Article  ADS  Google Scholar 

  16. McConnell, J. D. C. & Heine, V. Origin of incommensurate structure in the cooperative Jahn–Teller system K2PbCu(NO2)6. J. Phys. C 15, 2387–2402 (1982).

    Article  ADS  Google Scholar 

  17. Bonner, J. C. & Fisher, M. E. Linear magnetic chains with anisotropic coupling. Phys. Rev. 135, A640–A658 (1964).

    Article  ADS  Google Scholar 

  18. Okuda, K., Mollymoto, H., Miyako, Y., Mori, M. & Date, M. One-dimensional antiferromagnetism in Rb2PbCu(NO2)6. J. Phys. Soc. Jpn 53, 3616–3623 (1984).

    Article  ADS  Google Scholar 

  19. Kosterlitz, J. M., Nelson, D. R. & Fisher, M. E. Bicritical and tetracritical points in anisotropic antiferromagnetic systems. Phys. Rev. B 13, 412–432 (1976).

    Article  ADS  Google Scholar 

  20. Hijmans, J., Kopinga, K., Boersma, F. & Dejonge, W. J. M. Phase-diagrams of pseudo one-dimensional Heisenberg systems. Phys. Rev. Lett. 40, 1108–1111 (1978).

    Article  ADS  Google Scholar 

  21. Sakai, A. et al. Signature of frustrated moments in quantum critical CePd1–x Ni x Al. Phys. Rev. B 94, 220405 (2016).

    Article  ADS  Google Scholar 

  22. Tsvelik, A. M. Quantum Field Theory in Condensed Matter Physics (Cambridge Univ. Press, Cambridge, 1995).

    MATH  Google Scholar 

  23. Klumper, A. The spin-1/2 Heisenberg chain: thermodynamics, quantum criticality and spin-Peierls exponents. Eur. Phys. J. B 5, 677–685 (1998).

    Article  ADS  Google Scholar 

  24. Mennenga, G., Dejongh, L. J., Huiskamp, W. J. & Reedijk, J. Specific-heat and susceptibility of the 1-dimensional S = 1/2 Heisenberg-antiferromagnet Cu(Pyrazine) (NO3)2 - evidence for random exchange effects at low-temperatures. J. Magn. Magn. Mater. 44, 89–98 (1984).

    Article  ADS  Google Scholar 

  25. Dender, D. C., Hammar, P. R., Reich, D. H., Broholm, C. & Aeppli, G. Direct observation of field-induced incommensurate fluctuations in a one-dimensional S = 1/2 antiferromagnet. Phys. Rev. Lett. 79, 1750–1753 (1997).

    Article  ADS  Google Scholar 

  26. Scalapino, D. J., Imry, Y. & Pincus, P. Generalized Ginzburg–Landau theory of pseudo-one-dimensional systems. Phys. Rev. B 11, 2042–2048 (1975).

    Article  ADS  Google Scholar 

  27. Sandvik, A. W. Multichain mean-field theory of quasi-one-dimensional quantum spin systems. Phys. Rev. Lett. 83, 3069–3072 (1999).

    Article  ADS  Google Scholar 

  28. Starykh, O. A., Katsura, H. & Balents, L. Extreme sensitivity of a frustrated quantum magnet: Cs2CuCl4. Phys. Rev. B 82, (2010)

  29. Sebastian, S. E. et al. Dimensional reduction at a quantum critical point. Nature 441, 617–620 (2006).

    Article  ADS  Google Scholar 

  30. Heath, R. in CRC Handbook of Chemistry and Physics (ed. Weast, R.) (CRC Press, Boca Raton, FL, 1988).

Download references

Acknowledgements

This work was supported by NSF-DMR 1534741 (A.P.R.), NSF-DMR1506119 (L.B.) and NSF-DMR 1534818 (T.S., L.D.). The research at Georgia Tech was supported by Oak Ridge Associated Universities through the Ralph E. Powe Junior Faculty Enhancement Award (M.M.). The research at Oak Ridge National Laboratory’s High Flux Isotope Reactor was sponsored by the US Department of Energy, Office of Basic Energy Sciences, Scientific User Facilities Division. The research at the National High Magnetic Field Laboratory was supported by the NSF Collaborative Agreement DMR 1157490 and the State of Florida. We thank G. Aeppli, M. E. Fisher, D. Reich and C. M. Varma for their helpful insights.

Author information

Author notes

  1. N. Blanc and J. Trinh contributed equally to this work.

Authors and Affiliations

  1. UC Santa Cruz, Santa Cruz, CA, 95064, USA

    N. Blanc, J. Trinh & A. P. Ramirez

  2. FAMU-FSU College of Engineering, Tallahassee, FL, 32310, USA

    L. Dong & T. Siegrist

  3. National High Magnetic Field Laboratory, Tallahassee, FL, 32310, USA

    L. Dong & T. Siegrist

  4. School of Physics, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    X. Bai & M. Mourigal

  5. Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA

    A. A. Aczel

  6. Kavli Institute for Theoretical Physics, UC Santa Barbara, Santa Barbara, CA, 93106, USA

    L. Balents

Authors
  1. N. Blanc
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Trinh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. X. Bai
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. A. Aczel
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. M. Mourigal
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. L. Balents
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. T. Siegrist
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. A. P. Ramirez
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

A.P.R. designed the experiment, and with N.B. and J.T. collected and analysed specific-heat data. T.S. and L.D. grew crystals and analysed susceptibility data. X.B., A.A. and M.M. performed neutron scattering and magnetization measurements and analysed the data. L.B. provided theoretical interpretation of results.

Corresponding author

Correspondence to A. P. Ramirez.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Supplementary Information

Supplementary note 1, Supplementary Figures 1&2, and Supplementary Reference 1

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Blanc, N., Trinh, J., Dong, L. et al. Quantum criticality among entangled spin chains. Nature Phys 14, 273–276 (2018). https://doi.org/10.1038/s41567-017-0010-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-017-0010-y

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