The study of interacting spin systems is of fundamental importance for modern condensed-matter physics. On frustrated lattices, magnetic exchange interactions cannot be simultaneously satisfied, and often give rise to competing exotic ground states1. The frustrated two-dimensional Shastry–Sutherland lattice2 realized by SrCu2(BO3)2 (refs 3,4) is an important test case for our understanding of quantum magnetism. It was constructed to have an exactly solvable 2-spin dimer singlet ground state within a certain range of exchange parameters and frustration. While the exact dimer state and the antiferromagnetic order at both ends of the phase diagram are well known, the ground state and spin correlations in the intermediate frustration range have been widely debated2,4,5,6,7,8,9,10,11,12,13,14. We report here the first experimental identification of the conjectured plaquette singlet intermediate phase in SrCu2(BO3)2. It is observed by inelastic neutron scattering after pressure tuning to 21.5 kbar. This gapped singlet state leads to a transition to long-range antiferromagnetic order above 40 kbar, consistent with the existence of a deconfined quantum critical point.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.


  1. 1.

    & in High Magnetic Fields (eds Berthier, C., Lvy, L. & Martinez, G.) 161–190 (Lecture Notes in Physics, 595, Springer, 2001).

  2. 2.

    & Exact ground state of a quantum mechanical antiferromagnet. Physica B+C 108, 1069–1070 (1981).

  3. 3.

    et al. Exact dimer ground state and quantized magnetization plateaus in the two-dimensional spin system SrCu2(BO3)2. Phys. Rev. Lett. 82, 3168–3171 (1999).

  4. 4.

    & Theory of the orthogonal dimer Heisenberg spin model for SrCu2(BO3)2. J. Phys. Condens. Matter 15, R327 (2003).

  5. 5.

    & First-order transition between magnetic order and valence bond order in a 2D frustrated Heisenberg model. Europhys. Lett. 34, 145–150 (1996).

  6. 6.

    , & Series expansions for a Heisenberg antiferromagnetic model for SrCu2(BO3)2. Phys. Rev. B 60, 6608–6616 (1999).

  7. 7.

    , , & Exact demonstration of magnetization plateaus and first-order Dimer-Néel phase transitions in a modified Shastry–Sutherland model for SrCu2(BO3)2. Phys. Rev. Lett. 84, 1808–1811 (2000).

  8. 8.

    , , & Dispersion and symmetry of bound states in the Shastry–Sutherland model. Phys. Rev. Lett. 85, 3958–3961 (2000).

  9. 9.

    & Quantum phase transitions in the Shastry–Sutherland model for SrCu2(BO3)2. Phys. Rev. Lett. 84, 4461–4464 (2000).

  10. 10.

    , & Competing spin-gap phases in a frustrated quantum spin system in two dimensions. J. Phys. Soc. Jpn 70, 1369–1374 (2001).

  11. 11.

    , & Phase diagram of the Shastry–Sutherland antiferromagnet. Phys. Rev. B 65, 014408 (2001).

  12. 12.

    , & Phase diagram of the quadrumerized Shastry–Sutherland model. Phys. Rev. B 66, 014401 (2002).

  13. 13.

    & Phase transitions in the Shastry–Sutherland lattice. Phys. Rev. B 72, 094436 (2005).

  14. 14.

    & Identifying topological order in the Shastry–Sutherland model via entanglement entropy. Phys. Rev. B 90, 201108(R) (2014).

  15. 15.

    & On next nearest neighbor interaction in linear chain. I. J. Math. Phys. 10, 1388–1398 (1969).

  16. 16.

    et al. Fractional excitations in the square-lattice quantum antiferromagnet. Nat. Phys. 11, 62–68 (2015).

  17. 17.

    & Magnetization plateaus of the Shastry–Sutherland model for SrCu2(BO3)2: spin-density wave, supersolid, and bound states. Phys. Rev. B 62, 15067–15078 (2000).

  18. 18.

    , & Theory of magnetization plateaux in the Shastry–Sutherland model. Phys. Rev. Lett. 101, 250402 (2008).

  19. 19.

    et al. Magnetization of SrCu2(BO3)2 in Ultrahigh Magnetic Fields up to 118 T. Phys. Rev. Lett. 111, 137204 (2013).

  20. 20.

    & Tensor network study of the Shastry–Sutherland model in zero magnetic field. Phys. Rev. B 87, 115144 (2013).

  21. 21.

    , , , & Deconfined quantum critical points. Science 303, 1490–1494 (2004).

  22. 22.

    et al. Quantum and classical criticality in a dimerized quantum antiferromagnet. Nat. Phys. 10, 373–379 (2014).

  23. 23.

    , , , & Quantum phase transitions in the orthogonal dimer system SrCu2(BO3)2. Physica B 329–333, 1020–1023 (2003).

  24. 24.

    et al. High-field and high-pressure ESR measurements of SrCu2(BO3)2. J. Phys. Conf. Ser. 150, 042171 (2009).

  25. 25.

    et al. A novel ordered phase in SrCu2(BO3)2 under high pressure. J. Phys. Soc. Jpn. 76, 073710 (2007).

  26. 26.

    et al. Continuous and discontinuous quantum phase transitions in a model two-dimensional magnet. Proc. Natl Acad. Sci. USA 109, 2286–2289 (2012).

  27. 27.

    et al. Crystal structure and lattice dynamics of at high pressures. Physica B 359–361, 980–982 (2005).

  28. 28.

    et al. Temperature dependence of the pressure induced monoclinic distortion in the spin Shastry–Sutherland compound SrCu2(BO3)2. Solid State Commun. 186, 13–17 (2014).

  29. 29.

    et al. Emergence of long-range order in sheets of magnetic dimers. Proc. Natl Acad. Sci. USA 111, 14372–14377 (2014).

  30. 30.

    Novel States in Magnetic Materials under Extreme Conditions. A High Pressure Neutron Scattering Study of the Shastry–Sutherland Compound SrCu2(BO3)2 PhD thesis, ETH Zurich (2010).

  31. 31.

    et al. Bose-Einstein condensation of the triplet states in the magnetic insulator TlCuCl3. Nature 423, 62–65 (2003).

  32. 32.

    et al. Crystallization of spin superlattices with pressure and field in the layered magnet SrCu2(BO3)2. Nat. Commun. 7, 11956 (2016).

  33. 33.

    & PANDA: Cold three axes spectrometer. J. Large-Scale Res. Facil. 1, A12 (2015).

  34. 34.

    Techniques in High Pressure Neutron Scattering (CRC Press, Taylor and Francis, 2013).

  35. 35.

    et al. Correlated decay of triplet excitations in the Shastry–Sutherland compound SrCu2(BO3)2. Phys. Rev. Lett. 113, 067201 (2014).

  36. 36.

    Phonon dispersion curves by inelastic neutron scattering to 12 GPa. Z. Kristallogr. 216, 420–429 (2001).

  37. 37.

    et al. Neutron scattering investigation on quantum spin system SrCu2(BO3)2. Prog. Theor. Phys. Suppl. 159, 22–32 (2005).

  38. 38.

    , & First-order quantum phase transition in the orthogonal-dimer spin chain. Phys. Rev. B 62, 5558–5563 (2000).

Download references


We thank A. Magee for her contributions to the susceptibility measurements, M. Merlini and M. Hanfland for support during high-pressure X-ray diffraction experiments at the ESRF, and M. Ay and P. Link for assistance during neutron scattering experiments. We acknowledge F. Mila and B. Normand for many useful discussions. We also thank CamCool Research Ltd for supplying the pressure cells for the SQUID measurements. This work is based on experiments performed at the Swiss spallation neutron source SINQ, Paul Scherrer Institute, Villigen, Switzerland, at the FRM-2, Munich, Germany, and at the ILL, Grenoble, France. We thank the Swiss National Science Foundation SNF and the Royal Society (UK) for financial support. The work in London and Cambridge was supported by the EPSRC. J.L.J. acknowledges the Science Without Borders program of CNPq/MCTI-Brazil and C.P. acknowledges financial support from the National Research Foundation (NRF) of Singapore, through NRF Investigatorship (Reference No. NRF-NRFI2015-04).

Author information


  1. Laboratory for Quantum Magnetism, Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland

    • M. E. Zayed
    • , J. Larrea J.
    •  & H. M. Rønnow
  2. Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland

    • M. E. Zayed
    • , Ch. Rüegg
    • , Th. Strässle
    •  & V. Pomjakushin
  3. Department of Physics, Carnegie Mellon University in Qatar, Education City, PO Box 24866, Doha, Qatar

    • M. E. Zayed
  4. Department of Quantum Matter Physics, University of Geneva, 1211 Geneva 4, Switzerland

    • Ch. Rüegg
  5. London Centre for Nanotechnology and Department of Physics and Astronomy, University College London, London WC1E 6BT, UK

    • Ch. Rüegg
    • , M. Ellerby
    •  & D. F. McMorrow
  6. Centro Brasileiro de Pesquisas Fisicas, Rua Doutor Xavier Sigaud 150, CEP 2290-180, Rio de Janeiro, Brazil

    • J. Larrea J.
  7. Institut für Theoretische Physik, Universität Innsbruck, 6020 Innsbruck, Austria

    • A. M. Läuchli
  8. Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK

    • C. Panagopoulos
    •  & S. S. Saxena
  9. Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore

    • C. Panagopoulos
  10. IMPMC; CNRS–UMR 7590, Université Pierre et Marie Curie, 75252 Paris, France

    • S. Klotz
    •  & G. Hamel
  11. Institute for Nuclear Research, Russian Academy of Sciences, prospekt 60-letiya Oktyabrya 7a, Moscow 117312, Russia

    • R. A. Sadykov
  12. Vereshchagin Institute for High Pressure Physics, Russian Academy of Sciences, 108840, Moscow, Troitsk, Russia

    • R. A. Sadykov
  13. Institut Laue-Langevin, 71 avenue des Martyrs - CS 20156- 38042 Grenoble Cedex 9, France

    • M. Boehm
    •  & M. Jiménez–Ruiz
  14. Jülich Centre for Neutron Science (JCNS) at Heinz Maier-Leibnitz Zentrum (MLZ), Forschungszentrum Jülich GmbH, Lichtenbergstr. 1, 85748 Garching, Germany

    • A. Schneidewind
  15. Laboratory for Scientific Developments and Novel Materials, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland

    • E. Pomjakushina
    • , M. Stingaciu
    •  & K. Conder


  1. Search for M. E. Zayed in:

  2. Search for Ch. Rüegg in:

  3. Search for J. Larrea J. in:

  4. Search for A. M. Läuchli in:

  5. Search for C. Panagopoulos in:

  6. Search for S. S. Saxena in:

  7. Search for M. Ellerby in:

  8. Search for D. F. McMorrow in:

  9. Search for Th. Strässle in:

  10. Search for S. Klotz in:

  11. Search for G. Hamel in:

  12. Search for R. A. Sadykov in:

  13. Search for V. Pomjakushin in:

  14. Search for M. Boehm in:

  15. Search for M. Jiménez–Ruiz in:

  16. Search for A. Schneidewind in:

  17. Search for E. Pomjakushina in:

  18. Search for M. Stingaciu in:

  19. Search for K. Conder in:

  20. Search for H. M. Rønnow in:


M.E.Z., C.R. and H.M.R. designed the research, performed the experiments and analysed the data. A.M.L. computed the magnetic susceptibility by exact diagonalization. C.P., S.S.S. and M.E. helped with susceptibility experiments. T.S., S.K., G.H. and R.A.S. provided neutron high-pressure techniques. M.B., M.J.-R., A.S., V.P. and T.S. provided support for neutron experiments. E.P., M.S. and K.C. synthesized the SrCu2(BO3)2 samples. J.L.J. and D.F.M. contributed to interpretation of the data. M.E.Z., C.R. and H.M.R. wrote the manuscript with contributions from all co-authors.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to M. E. Zayed.

Supplementary information

PDF files

  1. 1.

    Supplementary information

    Supplementary information

About this article

Publication history






Further reading