Article | Published:

Multiple Coulomb phase in the fluoride pyrochlore CsNiCrF6

Nature Physicsvolume 15pages6066 (2019) | Download Citation

Abstract

The Coulomb phase is an idealized state of matter whose properties are determined by factors beyond conventional considerations of symmetry, including global topology, conservation laws and emergent order. Theoretically, Coulomb phases occur in ice-type systems such as water ice and spin ice; in dimer models; and in certain spin liquids. However, apart from ice-type systems, more general experimental examples are very scarce. Here we study the partly disordered material CsNiCrF6 and show that this material is a multiple Coulomb phase with signature correlations in three degrees of freedom: charge configurations, atom displacements and spin configurations. We use neutron and X-ray scattering to separate these correlations and to determine the magnetic excitation spectrum. Our results show how the structural and magnetic properties of apparently disordered materials may inherit, and be dictated by, a hidden symmetry—the local gauge symmetry of an underlying Coulomb phase.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Data availability

The experimental data and their supplementary information, analyses and computer codes that support the plots within this paper and the findings of this study are available from the corresponding author upon reasonable request.

Additional information

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

References

  1. 1.

    Landau, L. D. & Lifshitz, E. M. Statistical Physics (Pergamon, New York, 1980).

  2. 2.

    Pekker, D. & Varma, C. M. Amplitude/Higgs modes in condensed matter physics. Annu. Rev. Condens. Matter Phys. 6, 269–297 (2015).

  3. 3.

    Henley, C. L. The “Coulomb phase” in frustrated systems. Annu. Rev. Condens. Matter Phys. 1, 179–210 (2010).

  4. 4.

    Jaubert, L. D. C. et al. Topological-sector fluctuations and Curie-law crossover in spin ice. Phys. Rev. X 3, 011014 (2013).

  5. 5.

    Huse, D., Krauth, W., Moessner, R. & Sondhi, S. L. Coulomb and liquid dimer models in three dimensions. Phys. Rev. Lett. 91, 167004 (2003).

  6. 6.

    Hermele, M., Fisher, M. P. A. & Balents, L. Pyrochlore photons: the U(1) spin liquid in a S = 1/2 three-dimensional frustrated magnet. Phys. Rev. B 69, 064404 (2004).

  7. 7.

    Benton, O., Sikora, O. & Shannon, N. Seeing the light: experimental signatures of emergent electromagnetism in a quantum spin ice. Phys. Rev. B 86, 075154 (2012).

  8. 8.

    Gingras, M. J. P. & McClarty, P. A. Quantum spin ice: a search for gapless quantum spin liquids in pyrochlore magnets. Rep. Prog. Phys. 77, 056501 (2014).

  9. 9.

    Anderson, P. W. Ordering and antiferromagnetism in ferrites. Phys. Rev. 102, 1008–1013 (1956).

  10. 10.

    McClarty, P. A., O’Brien, A. & Pollmann, F. Coulombic charge ice. Phys. Rev. B 89, 195123 (2014).

  11. 11.

    Moessner, R. & Chalker, J. T. Properties of a classical spin liquid: the Heisenberg pyrochlore antiferromagnet. Phys. Rev. Lett. 80, 2929–2932 (1998).

  12. 12.

    Isakov, S. V., Gregor, K., Moessner, R. & Sondhi, S. L. Dipolar spin correlations in classical pyrochlore magnets. Phys. Rev. Lett. 93, 167204 (2004).

  13. 13.

    Moessner, R. & Chalker, J. T. Low-temperature properties of classical geometrically frustrated antiferromagnets. Phys. Rev. B 58, 12049–12062 (1998).

  14. 14.

    Conlon, P. H. & Chalker, J. T. Spin dynamics in pyrochlore Heisenberg antiferromagnets. Phys. Rev. Lett. 102, 237206 (2009).

  15. 15.

    Conlon, P. H. Aspects of Frustrated Magnetism. PhD thesis, Univ. Oxford (2010).

  16. 16.

    Henley, C. L. Power-law spin correlations in pyrochlore antiferromagnets. Phys. Rev. B 71, 014424 (2005).

  17. 17.

    Fennell, T. et al. Magnetic Coulomb phase in the spin ice Ho2Ti2O7. Science 326, 415–417 (2009).

  18. 18.

    Harris, M. J., Bramwell, S. T., McMorrow, D. F., Zeiske, T. & Godfrey, K. W. Geometrical frustration in the ferromagnetic pyrochlore Ho2Ti2O7. Phys. Rev. Lett. 79, 2554–2557 (1997).

  19. 19.

    Castelnovo, C., Moessner, R. & Sondhi, S. L. Magnetic monopoles in spin ice. Nature 451, 42–45 (2008).

  20. 20.

    Ryzhkin, I. A. Magnetic relaxation in rare-earth oxide pyrochlores. J. Exp. Theor. Phys. 101, 481–486 (2005).

  21. 21.

    Overy, A. R. et al. Design of crystal-like aperiodic solids with selective disorder–phonon coupling. Nat. Commun. 7, 10445 (2016).

  22. 22.

    Shen, L., Greaves, C., Riyat, R., Hansen, T. C. & Blackburn, E. Absence of magnetic long-range order in Y2CrSbO7: bond-disorder-induced magnetic frustration in a ferromagnetic pyrochlore. Phys. Rev. B 96, 094438 (2017).

  23. 23.

    Li, Y. et al. Crystalline electric-field randomness in the triangular lattice spin-liquid YbMgGaO4. Phys. Rev. Lett. 118, 107202 (2017).

  24. 24.

    Zhu, Z., Maksimov, P. A., White, S. R. & Chernyshev, A. L. Disorder-induced mimicry of a spin liquid in YbMgGaO4. Phys. Rev. Lett. 119, 157201 (2017).

  25. 25.

    Harris, M. J., Zinkin, M. P. & Zeiske, T. Magnetic excitations in a highly frustrated pyrochlore antiferromagnet. Phys. Rev. B 52, R707–R710 (1995).

  26. 26.

    Zinkin, M. P., Harris, M. J. & Zeiske, T. Short-range magnetic order in the frustrated pyrochlore antiferromagnet CsNiCrF6. Phys. Rev. B 56, 11786–11790 (1997).

  27. 27.

    Banks, S. T. & Bramwell, S. T. Magnetic frustration in the context of pseudo-dipolar ionic disorder. EPL 97, 27005 (2012).

  28. 28.

    Keen, D. A. & Goodwin, A. L. The crystallography of correlated disorder. Nature 521, 303–309 (2015).

  29. 29.

    Babel, D., Pausewang, G. & Viebahn, W. Die Struktur einiger Fluoride, Oxide und Oxidfluoride AMe2X6 der RbNiCrF6 -Typ. Zeitschrift für Naturforshung B 22, 1219–1220 (1967).

  30. 30.

    Shoemaker, D. P. et al. Atomic displacements in the charge ice pyrochlore Bi2Ti2O6O’ studied by neutron total scattering. Physical Review B 81, 144113 (2010).

  31. 31.

    Welberry, T. R. & Butler, B. D. Interpretation of diffuse X-ray scattering via models of disorder. J. Appl. Crystallogr. 27, 205–231 (1994).

  32. 32.

    Neder, R. B. & Proffen, T. “Diffuse Scattering and Defect Structure Simulations: A cook book using the program DISCUS”. (Oxford University Press, Oxford, 2008).

  33. 33.

    Paddison, J. A. M. & Goodwin, A. L. Empirical magnetic structure solution of frustrated spin systems. Phys. Rev. Lett. 108, 017204 (2012).

  34. 34.

    Billinge, S. J. L. & Levin, I. The problem with determining atomic structure at the nanoscale. Science 316, 561–565 (2007).

  35. 35.

    Brown, I. D. Recent developments in the methods and applications of the bond valence model. Chem. Rev. 109, 6858–6919 (2009).

  36. 36.

    Chernyshev, V. V., Zhukov, S. G., Yatsenko, A. V., Aslanov, L. A. & Schenk, H. The use of continuous atomic distributions in structural investigations. Acta Cryst. A50, 601–605 (1994).

  37. 37.

    Jaubert, L. D. C., Haque, M. & Moessner, R. Analysis of a fully packed loop model arising in a magnetic Coulomb phase. Phys. Rev. Lett. 107, 177202 (2011).

  38. 38.

    Blunt, M. O. et al. Random tiling and topological defects in a two-dimensional molecular network. Science 322, 1077–1081 (2008).

  39. 39.

    Jacobsen, J. L. & Alet, F. Semiflexible fully packed loop model and interacting rhombus tilings. Phys. Rev. Lett. 102, 145702 (2009).

  40. 40.

    Savary, L. & Balents, L. Quantum spin liquids: a review. Rep. Prog. Phys. 80, 016502 (2017).

  41. 41.

    Plumb, K. W. et al. Continuum of quantum fluctuations in a three-dimensional S = 1 Heisenberg magnet. Nat. Phys. https://doi.org/10.1038/s41567-018-0317-3 (2018).

  42. 42.

    Koza, M. M. et al. Breakdown of phonon glass paradigm in La- and Ce-filled Fe4Sb12 skutterudites. Nat. Mater. 7, 805–810 (2008).

  43. 43.

    Shimojima, T. et al. Interplay of superconductivity and rattling phenomena in β-pyrochlore KOs2O6 studied by photoemission spectroscopy. Phys. Rev. Lett. 99, 117003 (2007).

  44. 44.

    De Pape, R. & Ferey, G. A new form of FeF3 with the pyrochlore structure: Soft chemistry synthesis, crystal structure, thermal transitions and structural correlations with the other forms of FeF3. Mater. Res. Bull. 21, 971–978 (1986).

  45. 45.

    Kim, S. W. et al. RbFe2+Fe3+F6: Synthesis, structure, and characterization of a new charge-ordered magnetically frustrated pyrochlore-related mixed-metal fluoride. Chem. Sci. 3, 741–751 (2012).

  46. 46.

    Songvilay, M. et al. Anharmonic magnon excitations in noncollinear and charge-ordered RbFe2+Fe3+F6. Phys. Rev. Lett. 121, 087201 (2018).

  47. 47.

    Willmott, P. R. et al. The Materials Science beamline upgrade at the Swiss Light Source. J. Synchrotron. Radiat. 20, 667–682 (2013).

  48. 48.

    Rodriguez-Carvajal, J. Recent advances in magnetic structure determination. Physica B 192, 55–69 (1993).

  49. 49.

    Wilkinson, C., Cowan, J. A., Myles, D. A. A., Cipriani, F. & McIntyre, G. J. VIVALDI - a thermal-neutron Laue diffractometer for physics, chemistry and materials science. Neutron News 13, 37–41 (2002).

  50. 50.

    Campbell, J. W., Hao, Q., Harding, M. M., Nguti, N. D. & Wilkinson, C. LAUEGEN version 6.0 and INTLDM. J. Appl. Crystallogr. 31, 496–502 (1998).

  51. 51.

    Helliwell, J. R. et al. The recording and analysis of synchrotron X-radiation Laue diffraction photographs. J. Appl. Crystallogr. 22, 483–497 (1989).

  52. 52.

    Sheldrick, G. M. A short history of SHELX. Acta Cryst A64, 112–122 (2008).

  53. 53.

    Schefer, J. et al. Single-crystal diffraction instrument TriCS at SINQ. Physica B 276-278, 168–169 (2000).

  54. 54.

    Petricek, V., Dusek, M. & Palatinus, L. Crystallographic Computing System JANA2006: General features. Zeitschrift für Kristallographie 229, 345–352 (2014).

  55. 55.

    Stewart, J. R. et al. Disordered materials studied using neutron polarization analysis on the multi-detector spectrometer. D7. J. Appl. Crystallogr. 42, 69–84 (2009).

  56. 56.

    Lee, S.-H. et al. Emergent excitations in a geometrically frustrated magnet. Nature 418, 856–858 (2002).

  57. 57.

    Melko, R. G., den Hertog, B. C. & Gingras, M. J. P. Long-range order at low temperatures in dipolar spin ice. Phys. Rev. Lett. 87, 067203 (2001).

Download references

Acknowledgements

We thank R. Stewart, M. Green and B. Fåk for discussions, J. Chalker for reading and commenting on the manuscript, and X. Thonon for support of cryogenics at the ILL. M.R. was supported by the Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, grant no. 200021_140862. This work is based on experiments performed at the Institut Laue-Langevin, Grenoble, France; the Swiss spallation neutron source SINQ, Paul Scherrer Institut, Villigen, Switzerland; and the Swiss Light Source, Paul Scherrer Institut.

Author information

Affiliations

  1. Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut, Villigen PSI, Switzerland

    • T. Fennell
    • , M. Ruminy
    •  & O. Zaharko
  2. School of Divinity, University of Edinburgh, New College, Edinburgh, UK

    • M. J. Harris
  3. Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA

    • S. Calder
  4. Institut Laue-Langevin, Grenoble, France

    • M. Boehm
    • , P. Steffens
    •  & M.-H. Lemée-Cailleau
  5. Swiss Light Source, Paul Scherrer Institut, Villigen PSI, Switzerland

    • A. Cervellino
  6. London Centre for Nanotechnology and Department of Physics and Astronomy, University College London, London, UK

    • S. T. Bramwell

Authors

  1. Search for T. Fennell in:

  2. Search for M. J. Harris in:

  3. Search for S. Calder in:

  4. Search for M. Ruminy in:

  5. Search for M. Boehm in:

  6. Search for P. Steffens in:

  7. Search for M.-H. Lemée-Cailleau in:

  8. Search for O. Zaharko in:

  9. Search for A. Cervellino in:

  10. Search for S. T. Bramwell in:

Contributions

T.F., M.J.H., S.C., M.B., P.S. and S.T.B. carried out inelastic neutron scattering experiments. T.F., M.-H.L.-C. and O.Z. carried out neutron diffraction experiments. M.R. and A.C. carried out X-ray diffraction experiments. T.F. analysed all data and made calculations. T.F., M.J.H. and S.T.B. wrote the paper in collaboration with all other authors.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to T. Fennell.

Supplementary information

  1. Supplementary information

    Supplementary Text, Figures 1–3, Table 1

About this article

Publication history

Received

Accepted

Published

Issue Date

DOI

https://doi.org/10.1038/s41567-018-0309-3