Quantum criticality among entangled spin chains

Article metrics

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.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Comparison of the TH 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.

References

  1. 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).

  2. 2.

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

  3. 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).

  4. 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).

  5. 5.

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

  6. 6.

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

  7. 7.

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

  8. 8.

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

  9. 9.

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

  10. 10.

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

  11. 11.

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

  12. 12.

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

  13. 13.

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

  14. 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. 15.

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

  16. 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).

  17. 17.

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

  18. 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).

  19. 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).

  20. 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).

  21. 21.

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

  22. 22.

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

  23. 23.

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

  24. 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).

  25. 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).

  26. 26.

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

  27. 27.

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

  28. 28.

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

  29. 29.

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

  30. 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

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.

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

Verify currency and authenticity via CrossMark

Further reading