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Observation of magnetic fragmentation in spin ice

Nature Physics volume 12, pages 746–750 (2016)Cite this article

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Abstract

Fractionalized excitations that emerge from a many-body system have revealed rich physics and concepts, from composite fermions in two-dimensional electron systems, revealed through the fractional quantum Hall effect1, to spinons in antiferromagnetic chains2 and, more recently, fractionalization of Dirac electrons in graphene3 and magnetic monopoles in spin ice4. Even more surprising is the fragmentation of the degrees of freedom themselves, leading to coexisting and a priori independent ground states. This puzzling phenomenon was recently put forward in the context of spin ice, in which the magnetic moment field can fragment, resulting in a dual ground state consisting of a fluctuating spin liquid, a so-called Coulomb phase5, on top of a magnetic monopole crystal6. Here we show, by means of neutron scattering measurements, that such fragmentation occurs in the spin ice candidate Nd2Zr2O7. We observe the spectacular coexistence of an antiferromagnetic order induced by the monopole crystallization and a fluctuating state with ferromagnetic correlations. Experimentally, this fragmentation manifests itself through the superposition of magnetic Bragg peaks, characteristic of the ordered phase, and a pinch point pattern, characteristic of the Coulomb phase. These results highlight the relevance of the fragmentation concept to describe the physics of systems that are simultaneously ordered and fluctuating.

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Figure 1: Spin ice and magnetic fragmentation.
Figure 2: Pinch point pattern in Nd2Zr2O7.
Figure 3: Magnetic excitation spectrum.
Figure 4: Temperature and field dependence of the pinch point pattern.

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References

  1. Stormer, H. L. Nobel lecture: the fractional quantum Hall effect. Rev. Mod. Phys. 71, 875–889 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  2. Sachdev, S. Quantum Phase Transitions (Cambridge Univ. Press, 2011).

    Book  Google Scholar 

  3. Bolotin, K. I., Ghahar, F., Shulman, M. D., Stormer, H. L. & Kim, P. Observation of the fractional quantum Hall effect in graphene. Nature 462, 196–199 (2009).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. Brooks-Bartlett, M. E., Banks, S. T., Jaubert, L. D. C., Harman-Clarke, A. & Holdsworth, P. C. W. Magnetic-moment fragmentation and monopole crystallization. Phys. Rev. X 4, 011007 (2014).

    Google Scholar 

  7. den Hertog, B. C. & Gingras, M. J. P. Dipolar interactions and origin of spin ice in Ising pyrochlore magnets. Phys. Rev. Lett. 84, 3430–3433 (2000).

    Article  ADS  Google Scholar 

  8. 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).

    Article  ADS  Google Scholar 

  9. Ramirez, A. P., Hayashi, A., Cava, R. J., Siddharthan, R. & Shastry, B. S. Zero-point entropy in spin ice. Nature 399, 333–335 (1999).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  11. Bergman, D. L., Fiete, G. A. & Balents, L. Ordering in a frustrated pyrochlore antiferromagnet proximate to a spin liquid. Phys. Rev. B 73, 134402 (2006).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  15. Morris, D. J. P. et al. Dirac strings and magnetic monopoles in the spin ice Dy2Ti2O7 . Science 326, 411–414 (2009).

    Article  ADS  Google Scholar 

  16. Ciomaga Hatnean, M. et al. Structural and magnetic investigations of single-crystalline neodymium zirconate pyrochlore Nd2Zr2O7 . Phys. Rev. B 91, 174416 (2015).

    Article  ADS  Google Scholar 

  17. Lhotel, E. et al. Fluctuations and all-in–all-out ordering in dipole-octopole Nd2Zr2O7 . Phys. Rev. Lett. 115, 197202 (2015).

    Article  ADS  Google Scholar 

  18. Ferey, G., de Pape, R., Leblanc, M. & Pannetier, J. Ordered magnetic frustration: VIII. Crystal and magnetic structures of the pyrochlore form of FeF3 between 2.5 and 25 K from powder neutron diffraction. Comparison with the other varieties of FeF3 . Rev. Chim. Miner. 23, 474–484 (1986).

    Google Scholar 

  19. Abragam, A. & Bleaney, B. Electron Paramagnetic Resonance of Transition Ions (Oxford Classic Texts in the Physical Sciences, Oxford Univ. Press, 1970).

    Google Scholar 

  20. Watahiki, M. et al. Crystalline electric field study in the pyrochlore Nd2Ir2O7 with metal-insulator transition. J. Phys. Conf. Ser. 320, 012080 (2011).

    Article  Google Scholar 

  21. Huang, Y.-P., Chen, G. & Hermele, M. Quantum spin ices and topological phases from dipolar-octupolar doublets on the pyrochlore lattice. Phys. Rev. Lett. 112, 167203 (2014).

    Article  ADS  Google Scholar 

  22. Jensen, J. & Mackintosh, A. R. Rare Earth Magnetism (International Series of Monographs on Physics, Clarendon, 1991).

    Google Scholar 

  23. Kao, Y. J., Enjalran, M., Del Maestro, A., Molavian, H. R. & Gingras, M. J. P. Understanding paramagnetic spin correlations in the spin-liquid pyrochlore Tb2Ti2O7 . Phys. Rev. B 68, 172407 (2003).

    Article  ADS  Google Scholar 

  24. Petit, S. et al. Order by disorder or energetic selection of the ground state in the XY pyrochlore antiferromagnet Er2Ti2O7. An inelastic neutron scattering study. Phys. Rev. B 90, 060410 (2014).

    Article  ADS  Google Scholar 

  25. Robert, J. et al. Spin dynamics in the presence of competing ferromagnetic and antiferromagnetic correlations in Yb2Ti2O7 . Phys. Rev. B 92, 064425 (2014).

    Article  ADS  Google Scholar 

  26. Matan, K. et al. Spin Waves in the Frustrated Kagomé Lattice Antiferromagnet KFe3(OH)6(SO4)2 . Phys. Rev. Lett. 96, 247201 (2006).

    Article  ADS  Google Scholar 

  27. Kimura, K. et al. Quantum fluctuations in spin-ice-like Pr2Zr2O7 . Nature Commun. 4, 1934 (2013).

    Article  ADS  Google Scholar 

  28. Bhatia, H., Norgard, G., Pascucci, V. & Bremer, P.-T. The Helmholtz–Hodge decomposition—a survey. IEEE Trans. Vis. Comput. Graphics 19, 1386–1404 (2013).

    Article  Google Scholar 

  29. Chang, L.-J. et al. Higgs transition from a magnetic Coulomb liquid to a ferromagnet in Yb2Ti2O7 . Nature Commun. 3, 992 (2012).

    Article  ADS  Google Scholar 

  30. Jaubert, L. D. C. et al. Are multiphase competition and order by disorder the keys to understanding Yb2Ti2O7? Phys. Rev. Lett. 115, 267208 (2015).

    Article  ADS  Google Scholar 

  31. Ciomaga Hatnean, M., Lees, M. R. & Balakrishnan, G. Growth of single-crystals of rare-earth zirconate pyrochlores, Ln2Zr2O7 (with Ln = La, Nd, Sm, and Gd) by the floating zone technique. J. Cryst. Growth 418, 1–6 (2015).

    Article  ADS  Google Scholar 

  32. Rodríguez-Carvajal, J. Recent advances in magnetic structure determination by neutron powder diffraction. Physica B 192, 55–69 (1993).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We acknowledge the ILL for the beam time. We also thank J. Robert, P. C. W. Holdsworth, V. Simonet and Y. Sidis for fruitful discussions. M.C.H., M.R.L. and G.B. acknowledge financial support from the EPSRC, UK, Grant No. EP/M028771/1.

Author information

Authors and Affiliations

  1. LLB, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France

    S. Petit

  2. Institut Néel, CNRS and Université Grenoble Alpes, F-38042 Grenoble, France

    E. Lhotel & B. Canals

  3. Department of Physics, University of Warwick, Coventry CV4 7AL, UK

    M. Ciomaga Hatnean, M. R. Lees & G. Balakrishnan

  4. Institut Laue Langevin, F-38042 Grenoble, France

    J. Ollivier, H. Mutka & A. R. Wildes

  5. INAC, CEA and Université Grenoble Alpes, CEA Grenoble, F-38054 Grenoble, France

    E. Ressouche

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  1. S. Petit
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Contributions

Crystal growth and characterization were performed by M.C.H., M.R.L. and G.B. Inelastic neutron scattering experiments were carried out by S.P., E.L., J.O. and H.M. Diffraction experiments were carried out by S.P., E.L., A.R.W. and E.R. The data were analysed by S.P. and E.L., with input from B.C., A.R.W., E.R. and J.O. RPA calculations were carried out by S.P. The paper was written by E.L. and S.P., with feedback from all authors.

Corresponding authors

Correspondence to S. Petit or E. Lhotel.

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The authors declare no competing financial interests.

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Petit, S., Lhotel, E., Canals, B. et al. Observation of magnetic fragmentation in spin ice. Nature Phys 12, 746–750 (2016). https://doi.org/10.1038/nphys3710

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