Topological triplon modes and bound states in a Shastry–Sutherland magnet

Abstract

The twin discoveries of the quantum Hall effect1, in the 1980s, and of topological band insulators2, in the 2000s, were landmarks in physics that enriched our view of the electronic properties of solids. In a nutshell, these discoveries have taught us that quantum mechanical wavefunctions in crystalline solids may carry nontrivial topological invariants which have ramifications for the observable physics. One of the side effects of the recent topological insulator revolution has been that such physics is much more widespread than was appreciated ten years ago. For example, while topological insulators were originally studied in the context of electron wavefunctions, recent work has initiated a hunt for topological insulators in bosonic systems: in photonic crystals3,4,5,6, in the vibrational modes of crystals7, and in the excitations of ordered magnets8. Using inelastic neutron scattering along with theoretical calculations, we demonstrate that, in a weak magnetic field, the dimerized quantum magnet SrCu2(BO3)2 is a bosonic topological insulator with topologically protected chiral edge modes of triplon excitations.

Access options

Rent or Buy article

from\$8.99

All prices are NET prices.

References

1. 1

Klitzing, K. v., Dorda, G. & Pepper, M. New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Phys. Rev. Lett. 45, 494–497 (1980).

2. 2

Hsieh, D. et al. A topological Dirac insulator in a quantum spin Hall phase. Nature 452, 970–974 (2008).

3. 3

Haldane, F. D. M. & Raghu, S. Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Phys. Rev. Lett. 100, 013904 (2008).

4. 4

Rechtsman, M. C. et al. Photonic Floquet topological insulators. Nature 496, 196–200 (2013).

5. 5

Khanikaev, A. B. et al. Photonic topological insulators. Nat. Mater. 12, 233–239 (2013).

6. 6

Lu, L., Joannopoulos, J. D. & Soljac̆ić, M. Topological photonics. Nat. Photon. 8, 821–829 (2014).

7. 7

Zhang, L., Ren, J., Wang, J.-S. & Li, B. Topological nature of the phonon Hall effect. Phys. Rev. Lett. 105, 225901 (2010).

8. 8

Chisnell, R. et al. Topological magnon bands in a kagome lattice ferromagnet. Phys. Rev. Lett. 115, 147201 (2015).

9. 9

Gozar, A. & Blumberg, G. in Collective Magnetic Excitations in SrCu2(BO3)2, Frontiers in Magnetic Materials (ed. Narlikar, A. V.) 735–754 (Springer, 2005).

10. 10

Kodama, K. et al. Magnetic superstructure in the two-dimensional quantum antiferromagnet SrCu2(BO3)2 . Science 298, 395–399 (2002).

11. 11

Corboz, P. & Mila, F. Crystals of bound states in the magnetization plateaus of the Shastry–Sutherland model. Phys. Rev. Lett. 112, 147203 (2014).

12. 12

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

13. 13

Miyahara, S. & Ueda, K. Exact dimer ground state of the two dimensional Heisenberg spin system SrCu2(BO3)2 . Phys. Rev. Lett. 82, 3701–3704 (1999).

14. 14

Kageyama, H. et al. Direct evidence for the localized single-triplet excitations and the dispersive multitriplet excitations in SrCu2(BO3)2 . Phys. Rev. Lett. 84, 5876–5879 (2000).

15. 15

Gaulin, B. D. et al. High resolution study of spin excitations in the singlet ground state of SrCu2(BO3)2 . Phys. Rev. Lett. 93, 267202 (2004).

16. 16

Aso, N. et al. High energy-resolution inelastic neutron scattering experiments on triplet bound state excitations in SrCu2(BO3)2 . J. Phys. Soc. Jpn 74, 2189–2192 (2005).

17. 17

Cépas, O. et al. Dzyaloshinskii-Moriya interaction in the 2D spin gap system SrCu2(BO3)2 . Phys. Rev. Lett. 87, 167205 (2001).

18. 18

Romhanyi, J., Totsuka, K. & Penc, K. Effect of Dzyaloshinskii–Moriya interactions on the phase diagram and magnetic excitations of SrCu2(BO3)2 . Phys. Rev. B 83, 024413 (2011).

19. 19

Romhanyi, J., Penc, K. & Ganesh, R. Hall effect of triplons in a dimerized quantum magnet. Nat. Commun. 6, 6805 (2015).

20. 20

Totsuka, K., Miyahara, S. & Ueda, K. Low-lying magnetic excitation of the Shastry–Sutherland model. Phys. Rev. Lett. 86, 520–523 (2001).

21. 21

Smith, R. W. & Keszler, D. A. Synthesis, structure, and properties of the orthoborate SrCu2(BO3)2 . J. Solid State Chem. 93, 430–435 (1991).

22. 22

Bewley, R. I., Taylor, J. W. & Bennington, S. M. LET, a cold neutron multi-disk chopper spectrometer at ISIS. Nucl. Instrum. Methods Phys. Res. A 637, 128–134 (2011).

23. 23

Ewings, R. A. et al. HORACE: software for the analysis of data from single crystal spectroscopy experiments at time-of-flight neutron instruments. Nucl. Instrum. Methods Phys. Res. A 834, 132–142 (2016).

24. 24

Sachdev, S. & Bhatt, R. N. Bond-operator representation of quantum spins: mean-field theory of frustrated quantum antiferromagnets. Phys. Rev. B 41, 9323–9329 (1990).

25. 25

Cheng, Y. F., Cépas, O., Leung, P. W. & Ziman, T. Magnon dispersion and anisotropies in SrCu2(BO3)2 . Phys. Rev. B 75, 144422 (2007).

26. 26

Knetter, C., Bühler, A., Müller-Hartmann, E. & Uhrig, G. S. Dispersion and symmetry of bound states in the Shastry–Sutherland model. Phys. Rev. Lett. 85, 3958–3961 (2000).

27. 27

Thouless, D. J., Kohmoto, M., Nightingale, M. P. & den Nijs, M. Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405–408 (1982).

28. 28

Katsura, H., Nagaosa, N. & Lee, P. A. Theory of the thermal Hall effect in quantum magnets. Phys. Rev. Lett. 104, 066403 (2010).

29. 29

Matsumoto, R. & Murakami, S. Theoretical prediction of a rotating magnon wave packet in ferromagnets. Phys. Rev. Lett. 106, 197202 (2011).

30. 30

Lemmens, P. et al. Collective singlet excitations and evolution of Raman spectral weights in the 2D spin dimer compound SrCu2(BO3)2 . Phys. Rev. Lett. 85, 2605–2608 (2000).

31. 31

Gozar, A., Dennis, B. S., Kageyama, H. & Blumberg, G. Symmetry and light coupling to phononic and collective magnetic excitations in SrCu2(BO3)2 . Phys. Rev. B 72, 064405 (2005).

32. 32

Nojiri, H., Kageyama, H., Ueda, Y. & Motokawa, M. ESR study on the excited state energy spectrum of SrCu2(BO3)2 – a central role of multiple-triplet bound states. J. Phys. Soc. Jpn 72, 3243–3253 (2003).

33. 33

Honecker, A., Mila, F. & Normand, B. Multi-triplet bound states and finite-temperature dynamics in highly frustrated quantum spin ladders. Phys. Rev. B 94, 094402 (2016).

34. 34

Fukui, T., Hatsugai, Y. & Suzuki, H. Chern numbers in discretized Brillouin zone: efficient method of computing (spin) Hall conductances. J. Phys. Soc. Jpn 74, 1674–1677 (2005).

Acknowledgements

We thank R. Bewley, R. Ewings, J. Thompson and D. Voneshen for useful discussions. The STFC Rutherford Appleton Laboratory is thanked for access to neutron beam facilities. Computing resources were provided by the STFC e-Science facility. P.A.M. acknowledges financial support from a Keeley-Rutherford fellowship. Support is also acknowledged from EPSRC Grants EP/K028960/1 (D.P.) and EP/M020517/1 (D.P. and R.C.).

Author information

D.P. grew the crystal. T.G., P.A.M., S.F.P. and A.W.P. devised and carried out the experiment. P.A.M. and F.K. worked out the theoretical interpretation. F.K. and P.A.M. wrote the manuscript. All authors discussed the data and contributed to the analysis.

Correspondence to P. A. McClarty or F. Krüger.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 1698 kb)

Rights and permissions

Reprints and Permissions

McClarty, P., Krüger, F., Guidi, T. et al. Topological triplon modes and bound states in a Shastry–Sutherland magnet. Nature Phys 13, 736–741 (2017) doi:10.1038/nphys4117

• DOI

https://doi.org/10.1038/nphys4117

• A Field Guide to Spin Liquids

• J. Knolle
•  & R. Moessner

Annual Review of Condensed Matter Physics (2019)

• Multipolar edge states in the anisotropic kagome antiferromagnet

• Judit Romhányi

Physical Review B (2019)

• Thermodynamic properties of the Shastry-Sutherland model throughout the dimer-product phase

• Alexander Wietek
• , Philippe Corboz
• , Stefan Wessel
• , B. Normand
• , Frédéric Mila
•  & Andreas Honecker

Physical Review Research (2019)

• Topological magnon bands for magnonics

• M. Malki
•  & G. S. Uhrig

Physical Review B (2019)

• Triplon band splitting and topologically protected edge states in the dimerized antiferromagnet

• Kazuhiro Nawa
• , Kimihiko Tanaka
• , Nobuyuki Kurita
• , Taku J. Sato
• , Haruki Sugiyama
• , Hidehiro Uekusa
• , Seiko Ohira-Kawamura
• , Kenji Nakajima
•  & Hidekazu Tanaka

Nature Communications (2019)